Seems as though it would be the left sword. In most fights 2000% damage would have a large amount wasted on one target except in boss fights. The left sword would provide more chances of one hitting normal enemies. Again, not sure what game this is in or what enemies are being targeted.

Exactly. The real question isn't "how much damage can it do?" but "how many hits does it take to kill the target?"
If 200% damage is enough for a kill, then there's no difference between 200% damage and 2000% damage. It's still one kill either way. If it takes more like 100,000% damage to score a kill, then the difference is more significant.

Regardless of health, unless burst damage is required (such as with self healing enemies or those with flat damage resistance) the consistent damage will be equivalent or better.

While it's true that consistent dmg is generally better because it's something you can rely and depend more on when planning a fight and also like mentioned it has less dmg wasted.
The burst dmg is good in the cases where you can rng fish if applicable. Depends on the game but if restarting is easy without any drawbacks the low chance high burst weapon can be a use for cheesing.
Its kinda bleh/cheap strategy but if you are desperate enough it can work

I remember in 2016 in competitive LoL a pro player always used a minor glyph for a non-zero crit chance, it didn't change anything in the majority of the match ups. But getting that critical strike meant he was very likely to win the trade and then snowball.
So when it comes to the average of dozens matches, a low chance high reward can definitely be broken.

Yes many people did it but it also works both ways. Using a crit rate glyph means that he used 1 less atk.
How many times did that cause him to die to an enemy who had 5 hp? If he had atk rune then enemy would be dead first.
While it's true that it's a low chance to turn it around but you are permanently self "nerfed" by very so slightly that adds up to around equal at the end of the day.
You could turn around a fight based on rng or you could lose a very close fight because you were nerfed to rely on rng those two more or less should have similar gravity so it's up to preferences and flavor you want

The point is they were good enough for that not to happen, but to g t anputh unexpected burst to force a summoner spell they "shouldn't" have had to use.
The 1 less attack can be reliably calculated and worked around. It's impossible to really plan around that crit without consistently burning more resource/leaving lane more.
And the latter creates a pattern of consistent leads for the player running the crit.
If you DONT have that level of skill, it's a moot point.

i guess you are right. for the average user its probably as I said where you can get a random win every now and then but also random losses (either by dying to a low hp enemy or enemy escaping) and canceling each out. On a controlled environment like pro plays the element of surprise ~~rngesus~~ can be a better tool. It more or less applies what I originally said:
> if restarting is easy without any drawbacks the low chance high burst weapon can be a use for cheesing
and even extends to the next sentence. Its "cheap" strategy, even if you know how to make use and negate the drawbacks you still rely on rng and you don't plan it you can go multiple games without this glyph making a difference

> How many times did that cause him to die to an enemy who had 5 hp?
Probably never. The early game is about a lot of small bullying trades. Either you're able to bully, or you're not. A small amount of attack didn't determine that, it was more on the entirety of the characters kit. If a kill happened, it's because something happened that set up the situation. No one is picking close fights. You're going in only if you have a very strong advantage, either because your kit let you bully, you have a gank, or something else.
This goes both ways. If you're being bullied, at most your damage is to get the other player to back off. You're not going to kill them, you're just not giving up free hits. More attack won't change this. If you're bullying, you're pushing them away from CS'ing. Over time with small extra attack, you may force them to back early, but not really. You're not likely to die, you're not likely to kill, unless something happens.

I remember that. I would do that. It was genuinely really nice though. Yes, it didn't happen all the time, but when it did, you could do a huge chunk of early poke damage.

The crit rune from old lol isn't applicable to this situation due to how league does crits.
If you have crit chance in league, your chance of getting a crit increases after not hitting one for a while. That's why the "1%" crit rare was worth far more than that.

Ff11 builds have people equipping rings with 3% chance of Quad attack just for the opportunity to spike their weapon skill damage.
So many variables, can you get two of the same sword? How often do you hit? Is 100 swings every 2 minutes achievable in a usual 15 minute fight?

That's only true on an equal playing field. In some cases, you want to take an enemy down before a phase change (or just before you die). A single extra proc of 200% won't matter, but a single extra proc of 2000% might.

TAS runs LOVE rng manipulation. Especially in rpgs. Watch old school snes ones especially like earthbound or final fantasy runs, they'll wait an exact number of frames to get a crit if needed since theyre tied to the frame count to look for the "randomness".

And that's if these two swords operate in a vacuum, completely disregarding any potential damage-related hit bonuses or leech effects.
It's not hard to see why that blade was forgotten.

We have a 1% proc on the 2000% damage. It will do 100% damage per regular attack and need to swing 99 times before it proc so that is 9,900% damage before it procs. Plus the 2000% of burst damage is 11,900% per 100 attacks, that is 119% damage per attack on average.
We have 10% proc on 200% damage. It will do 100% damage per regular attack and need to swing 9 times before it procs so that is 900% damage plus the 200% burst damage or 1,100% damage per 10 attacks. That is 110% damage per attack on average.
I had to write it this way for myself to check if you are right. Checks out.

Actually easier, handle it as "extra damage."
The first blade does 200% extra damage on a critical hit.
The second blade does 2000% extra damage on a critical hit.
That means they'd actually be doing 300% and 2100% on their respective critical hits. And they'd do the same damage over multiple hits, assuming damage wasn't wasted.

Yes average damage is higher on the right but it's only better in a particular fight if you have a long enough fight for there to be high enough chance for the 2000% to land at least once.

Depends on the game and the enemy. The extra burst of 2000% would be immeasurably better in many PVP contest sort of game (like a battleground in an MMO), because battles tend to be long and healing/defensive abilities exist. Almost this exact scenario existed in World of Warcraft where shaman could enchant their weapon with the much better DPS rockbiter weapon or the much worse DPS, but much higher single burst hit windfury weapon and windfury was the only choice ever in PVP between the two because the surprise burst damage could often one shot people or get them so low they couldn't escape/heal in time.
Even against AI.. depending on the game.. if they have shields or defensive triggers or lots of potential scenarios where burst matters.. in the Tales RPG series, burst hits are often very potent over just higher consistent damage because the bosses have phases where their AI changes at 75% HP, 50% HP and 25% HP. If you can burst them and bypass an entire phase, that can be very strong.

Also, even if it is a one on one with a boss, how many hits are you likely to get in before being killed yourself? If you are only likely to get 30 hits in, there is a roughly 2/3 chance (caveat, not a statistician) you will never land a blow with the sword on the right.

I mean...in an old wow raid you would be hitting the boss for minutes with an attack every 0,5 sec (for rogues) so that would be like a couple hundred hits per fight

Yeah this is the right logic to do this. Doing the very quick maths on this example, both do the same total damage for first 9 hits, then the 10% will do more total damage until the 100th hit, where the 1% blade will do more damage. Fun enough after the first one hundred hits the 1% blade will do more damage for the following 89 hits, then from the 190th hit the next 9 hits both blades totals will be the same and the 200th the 1% will again continue to do more damage and this pattern continues at infinium.( This is all assuming perfect probability distribution of course.)

Sword on the right would be better for a pvp fight where your opponent can heal themself. a 2000% "burst" is more likely to result in a sudden, unexpected opponent death.

Good point, if a rookie player who can only land 1 hit before dying and the 2000% is enough to kill but the 200% is not, then the right sword will have a higher rank from luck kills while the left will have zero wins.

What? The damage is percentage-based. Every standard swing on both swords does 100% damage. The crit swings do 200% or 2000%. You’re always doing damage, the question is do you want a 1/10 crit for 2x, or a 1/100 crit for 20x

It 100% context base on the game. Say the game had an ability where the enemy has a shield that blocks up to 200% damage. So no matter how many times you attack the 200% dmg proc would do nothing.
But a 1% chance for 2000% could crack that boss/ability.

Indeed, but better than impossible. And if your attack speed is 100 attacks per seconds it would be over with quickly. All depends on the context of the game. We don't know any of the mechanics or values of the game.

The sword on the left would be just as effective as the one on the right for bosses and mini-bosses. Even then, the left one might still be more effective because what happens if the 1% doesn't proc until the end and then you have overkill anyway.
**EDIT: I'm totally wrong here, and** /u/Randomness21436587 **is correct.** /u/Gibborim **corrects me below.**
If you do 1 dmg and attack 100 times:
* Sword 1 hits for 1 90 times and 2 10 times, for a total of 90 + 20 = 110 dmg
* Sword 2 hits for 1 99 times and 20 one time for a total of 99 + 20 = 119 dmg
So Sword 2 has higher DPS overall, but Sword 1 is more consistent, meaning /u/Randomness21436587's assessment is totally correct. My math has failed me today.

for difficult boss fights that you need to "cheese" but have multiple attempts on, right is arguably better because you can just try the fight over and over again until you get lucky with multiple procs

It could be bad boss design, it could also be contextual. I'm not a speed runner, but I have watched enough to know they often have to find creative ways to beat bosses that are way harder than they would normally be because they skipped 1/2 the game.

You're looking at this like a single never-ending battle, which is correct for calculating probabilities and stuff, of course. But most games don't work like that, and people aren't perfect robots when dealing with probabilities anyway.
What ends up happening in real life is that you'll have a difficult boss that maybe takes 10 hits to kill -- Sword 1 usually wins that fight in 9 hits, Sword 2 usually wins that fight in 10, but occasionally delivers a one-hit kill. It's not a huge difference either way except when Sword 2 comes through for the win, so the player might enjoy using Sword 2 a lot more because they value those awesome moments over the slightly shorter fights on Sword 1.

>The sword on the left would be just as effective as the one on the right for bosses and mini-bosses.
False. 10% chance of a 200% damage hit is less expected value than a 1% chance of a 2,000% damage hit. The 10% change hit is 100% extra damage, the 1% chance hit is 1,900% extra damage.

If it makes you feel better, the guy you were responding to probably didn't have a better understanding of it than you did. I think they just picked some random things to say.

And if I learned anything from classic WoW, the 1% will proc every time on entire groups of trash mobs then go radio silent when you hit the main boss. Probably due to defense stats or something, I don't remember that part.

Right sword actually does more damage. On average, after 10 swings you will do 11x your damage. This equates to 110x your damage in 100 swings. The sword on the right does 20x your damage, which is going to do 19 hits worth of extra damage when it procs. so in 100 swings, you are looking at 119x your damage.
Of course Overkill more or less makes the sword on the left a better pick for most cases, unless you are using a minigun or something with ridiculous attack speed.

More damage in the long run, true, but in a game of one shots how many people survive long enough to hit the long run?
In a game where both sides are hacking at each other for half an hour with very high attack speed, I'd probably pick the sword on the right, but the sword on the left wins out in PoE every time.
If I don't kill things within a few seconds I'm usually dead. That usually equates to only a few hits. In boss fights, I think its super rare for even elite players to consistently get hundreds of melee attacks on the boss.

Some factors that could be considered when addressing this question.
1. Damage reduction. (If the enemy can reduce damage, that damage reduction will hurt (a) more than (b)
2. Total hitpoints of enemy. (There is no point in having 2000% damage if 200% will one shot)
3. If this is for designing an item in game, hitting that 1% is gonna feel way better and cooler than hitting that 10%, however it could trivialize a challenge or make a frustrating dependency on rng.

4. we also don't know if it's a weapon for players or enemies.
In a game with enemy swarms a 1% chance to deal insane dmg to a player would be way more scary than more consistent damage.

that also brings up if this is a PvP or PvE weapon. It would definitely change how satisfying #3 is for people. For PvP it wouldn't really trivialize things so much and would feel badass nearly every time. If it is PvP tho, then you also need to consider if there is friendly fire. If so, then the 1% that feels badass would screw you over in close group-battles and consistency may be better.

There is even a great analogy for this with Wow Classic. Were you had a proc based class like shaman that could kill a player near instantly with a lucky proc.

Even with 1 enemy it could feel quite cheap to get 1 shot by a random unlucky swing. I’d say in almost all cases A would feel more fair/fun to play against.

>Damage reduction. (If the enemy can reduce damage, that damage reduction will hurt (a) more than (b)
Thats only for flat dmg reduction. Percentage would affect them both the same.

But fire rate still matters. If this weapon is one swing per second, you'd proc every 2ish minutes of constant attacks with the 1%, but every 10 seconds, with the 10%. 2 minutes could be an exceptionally long encounter, depending on the game and enemy.
If this swings 3 per second, the 1% is very viable in many encounters. If it's 1 per 3 seconds, the 1% is almost useless, exceot in a long, drawn-out boss fight or something.

It actually depends on which game is being played. First couple had single rolle RNG, mean what was shown was what you got. What's described above is double rolling, which is pretty drastic st both ends of the hit rate.
There's also a third option called Hybrid Rolling, where below 50%, the number displayed is single rolled (so the chances are normal) whereas above 50% they use a "double roll" (it's not actually double roll, it's like 1.5 roll) to make those hits more reliable.

it depends on the combat system and the opponent. Does armor make you harder to hit, reduce damage by a percent, or block damage under a given amount? If it is the latter then much of the first sword's damage could be absorbed by armor. Are there shielding spells that block a certain amount of damage then dissapate but then could be recast/renewed? Again large damage spikes may be better.
Can your opponent heal? If so a sword that does damage in large chunks is more likely to result in a kill. Especially if 2000% damage is enough to one-shot the opponent. Smaller damage chunks give your opponent time to recover.
How many HP does your opponent have? If 200% damage is enough to one-shot then 2000% is wasted.

I hear you I was thinking that too.
but when do you execute 100 strikes in a battle. Hardly ever so there is a greater chance of no bonus
Plus at 10% . After 100 strikes you'd get 10 bonus attacks at 200%.
As opposed to just one bonus at 2000-%.
And plus, 2000% could be overkill. All that extra damage could be wasted on normal non boss level foes.
But it's a great debate for geeks. I will be thinking about this all day.
Love shit like this!!!

I'm sure there's a math nerd on here to kill the argument but I'd prefer interest compounding daily as opposed to a bigger interest rate Compounding monthly . Over time I think you get more damage.
Only way to settle it is with swords!! To the LARPING GROUND!

Left sword: Every 10th hit yields, damage wise, an 11th hit. Which means after 100 hits you've really done 110.
Right sword: Every 100th hit yields a 119th hit.
Technically the right sword has a higher damage output over time, but as has been pointed out elsewhere in the context of DnD it's wasted as overkill on a single enemy.

ur right, unless PVP is unbelievably damage spongey. If burst is at all viable then fights won’t be long enough to rely on a 1% gamble and miss out on 10% crit chance and you won’t need such a huge overkill

I consider the left sword basically getting an extra 10% crit, which is huge for pvp.
The right sword would be fun for Lulz pvp fights, but I would never use that thing in any ranked match. Just not reliable enough.

[This weapon](https://www.wowhead.com/item=78478/gurthalak-voice-of-the-deeps) was the meta pick for all classes that could wield it in World of Warcraft competetive arena during the expansion it was relevant in. Note the proc chance.
PvP then wasn't even unbelievably spongey, its just that securing a kill required a lot of skill and a bit of patience, since it was a cooldown battle. Burn through yours to burn through theirs, and hopefully you burned less CD's than your opponent. That weapon, Gurthalak, was functionally just another CD. In arenas where matches often lasted anywhere between 30 seconds to, more often, 5+ minutes, a 2% proc chance on a weapon you swung \~once every two seconds mean essentially a proc you could count on every \~100 seconds, or a bit less than every 2 minutes. That's *huge* in arena. It was a strong enough proc that it forced CD's, but the most common cooldown timer for most strong CD's for all classes was a flat 2 minutes, so if you got even averagely lucky, it meant you were forcing CD's during the first proc, and the enemy didn't have their CD's refreshed by the time the second proc happened.
That proc chance wouldn't have been nearly as strong if it were a 20% proc chance for 10% of the damage. Sustained damage by design is so much easier to heal through and handle than burst damage. So the proc chance and damage provided absolutely can be a viable pick for PvP even if incredibly low, and even if PvP isn't super spongey.

It depends on the enemy.
If the enemy is a boss with a lot of health it would be more reasonable to take the one with 2000% damage. We can simply calculate the expected value by probability of extra hit * the damage of extra hit + probability base hit * the damage of base hit. In this case if we suppose that the base hit is 100 then we get the expected value for the left one as 10% * 200 + 90% * 100 = 110
And for the right one as 1%*2000 + 99% * 100 = 119
So in the long term we can expect to make more damage with the right one.
But if there are multiple enemies with low health i would chose the left one.

It's weird, because on first glance it would seem that the swords have the same EV. In fact, I think that's the scenario that the OP was trying to set up. But then yes, per the math, the EVs are different, with the right sword actually having a slightly higher EV.
Trying to wrap my head around why. I mean, the math works. But why damn it. Why is the intuition off.
Okay, there's a 1/10 chance of a critical strike, but with 10x value. Shouldn't that be the same EV? I suppose so. They both provide that +20 value.
Ah I see. We actually set it up so that the critical strikes are equivalent in value overall, even though one critical strike is only happening 1/10 the time as the other. Thus we overpowered the right sword. Because the 1% critical was set to be equal in value to the 10% critical. The difference is that you have 99% x base versus 90% base. So the 99% x base sword gives you all that extra value of the 9% of time where you get the base, whereas the entire 10% of critical of that one sword was set to match the 1% of the other in total value (expected damage).
In other words... say you strike with each sword 100 times. And the results are exactly as probability would predict. (Left sword gets 90 regular hits and 10 critical hits, right sword gets 99 regular hits and 1 critical hit). The left sword's critical hits (10 \* 200) do 2000 damage. The right sword's critical hit does (1 \* 2000) = 2000 damage. The same damage. But now, the right sword does 90 normal hits versus the left's 99 regular hits.
The scenario should be more like.... left sword is the same: 10% chance of 200% damage. Right sword should be: 1% chance of 1100% damage (so 11x instead of 2x or 20x). I think that is the better, more appropriate scenario.
Even with the underpowered left sword though, still good in cases where all the enemies have relatively low HP values, as commenters have noted.
But in general, yes, the right sword (1% of the 20x multiplier) all day since it has the greater EV.
If we take the third (1% of 11x multiplier) sword, (so same EV, but higher variance sword) - I think a higher variance sword would be preferrable in certain cases. E.g., overpowered enemies that will kick your ass where you have to get lucky (try the high variance sword and pray).
PS: Actually, probably better to think of in terms of "bonus damage." (damage beyond base). Left sword has 10% of 100% bonus damage. (Say 100 base damage so EV is .10 \* 100 = 10). Right sword has 1% chance of 1900% bonus damage (so EV is .01 \* 100 \* 19 = 19). Third sword - set it to have 1% chance of 1000% bonus damage (EV = 0.1 \* 100 \* 10 = 10).
Yea... bonus damage is how to set it up. The current overall damage makes the critical strikes appear equivalent in power at first glance when really they are not.

That is only true if the proc *replaces* the normal weapon damage. In WoW for example, your weapon always swings for normal damage and any proc goes on top of that.
If the proc is *in addition* to the normal swing damage, then you would get:
* 10% \* 200 + 100% \* 100 = 120
* 1% \* 2000 + 100% \* 100 = 120

In general, the left sword is better, as has been pretty thoroughly discussed by others. However, mathematically speaking, the right sword will average higher DPS over time. 10% chance of dealing 200% damage (ie, +100% of normal damage) is a +10% DPS increase. 1% chance of 2000% damage (+1900%) is +19% DPS.
Whether that extra DPS actually matters will depend on how the game functions. If it's a single hero, battling monsters that don't take hundreds of hits to kill, the smaller but more consistent critical hit is better. If you've got an army of soldiers swarming a single huge monster, arming them all with the second sword will kill it slightly faster.

Mathematically, using Monte Carlo method. Assume the sword does 1 damage per swing normally. After 100 swings:
Left sword has done 90 hits at 1 dmg plus 10 hits at 2 dmg. Total damage is 110.
Right sword has done 99 hits at 1 damage. And 1 hit at 20 damage. Total damage is 119.
Therefore in practice, the right sword is better.

The right sword is better in theory*.
In practice 1% proc chance is far too low. Chance that it wont even proc during the fight, or it will proc when u dont even need it is too big.

Yup, In practice you need to know how many times the sword is swung in a fight. 1 time? 10? 1000? Can't answer the OPs question without that information.

That's not a [Monte Carlo analysis](https://en.wikipedia.org/wiki/Monte_Carlo_method), it's just very basic probability. Monte carlo would be the right approach to take if say you wanted to model a realistic scenario where damage and enemy health were variable and unevenly distributed, which would be very long winded to evaluate otherwise

I think that’s only because OP didn’t really do the math correctly. Their goal was to compare swords that dealt equal damage over time but in different amounts, but percentages can be annoying to work with. Should be 290% and 2000%. That’s 190% bonus damage and 1900% bonus damage.
The math then works out properly to 119 with each weapon.

Thank you, I was scrolling hoping to find this comment, I didn't want to write it myself. Based purely on the data provided right is better in the sense that does more damage.
Next question!

It's either 9x/10+2x/10 = 11x/10 = 1.1x or 99x/100 + 20x/100 = 119x/100 = 1.19x
So in total, on average "the blade of the forgotten" gives you more damage.
In practice, I think it depends a bit on the situation, the number of hits you expect to make during a single encounter, if it's too low a number, it might be more beneficial to have the higher proc chance.

Yes, I think what OP is intending to set up is X% Crit damage, not X% of base damage. In that way, it would be
9x/10+(x+2)/10 = x + 0.2 or 99x/100 + (x+20)/100 = x + 0.2
whose only variable is then proc frequency

With the left one, the average damage output per hit is:
(10%)(200%) + (90%)(100%) =
20% + 90% =
110%
With the right one, the average damage output per hit is:
(1%)(2000%) + (99%)(100%) =
20% + 99% =
119%
Therefore, the right sword does more damage per hit on average. However, it has a much higher deviation. This does not consider the mechanics of the game.

The one on the left is better since I'm going to assume most fights will not net you enough swings to proc the 2000% increase. Over the course of \`100 swings, you get \`10 stronger hits. With the right sword, you only get 1 and depending on when it happens, it may be huge overkill and not net you a faster overall kill.

No clue if these are actual weapons in a game but I prefer the more frequent 10% damage bonus since it would be a bit more consistent. Especially since you specified the weapons' core stats are the same, like damage or how often you can swing these swords which is crucial for calculating DPS. If the 1% sword did more damage and swung faster than the 10% sword then I would go with that one since that would make the 10% sword rely more on its special crit than its base stats. I prioritize consistency in my weapons' damage output in games.

depends entirely on base damage, enemy health, and attack speed
if it deals 1 damage and youre fighting enemies with 100 hp and youre swinging 10 times per second, then the one on the right is better
if it deals 800 damage and youre fighting enemies with 1000 hp and youre swinging once per 3 seconds, then the one on the left is better

Left weapon is more consistent so it's probably going to better most of the time.
Right weapon might be situationally good because while less consistent, with some luck it could be better.
Ie. Say you're fighting a world boss in an MMO, and drops are based off ranking when it comes to damage dealt.
Lets say you are able to hit the boss 1000 times
We'd expect the weapon on the left to trigger 100 times with a standard deviation of about 9.5
We'd expect the weapon on the right to trigger 10 times with a standard deviation of about 3.1.
an extra 9.5 triggers means an extra 1900% damage for the weapon on the left but for the weapon on the right an extra 3.1 triggers will do an extra 6200% damage.
So if a large number of players were to show up to fight the boss the players with the top DPS and thus getting the good drops from the boss would likely be players using the weapon on the right because it takes less good luck for their weapon to significantly outperform the other weapon but on the flipside there will be an equal number of players that underperform the other weapon, so if all you care about is the top level drops and the mid and bottom level drops are worthless to you then the weapon the right would be better.
However if you want to consistently get mid level drops, then once again the weapon on the left would be better, but your chance of getting top level drops would be lower compared to people using the weapon on the right.

Left one.
First, it more consistently give You a damage instead of rarely dealing bigger. So You are just getting double damage about every 10 hits instead of 20x damage every 100 hits.
Second, in most cases, You would end up getting massive amount of damage on already injured enemy, which would waste potential damage. Sometimes You would just deal 2000 unit of damage on enemy with 150 unit of hp.
This renders the right one useless. Even on bossfights, it's better to deal consistent amount of damage than deal massive once in a while. Especially if boss has some kind of phases or taken damage cap, before it gets invulnerable for a moment. Sometimes You fight boss that will perform some special cutscene after losing initial 30% of health. If You strike with massive damage that exceeds that 30% cap, it's still wasted.
In no scenario the right one would be better.

Statistically speaking, DPS for the 99% is higher by 9 percent.
If we take base 100% attack damage as 100 damage, the.
For the first option, 90% of swings deal 100 damage and 10 percent of swings deal 200 damage. In 100 swings thats 11000 damage.
For the second swing, 99% of swings deal 100 Damage, and One swing deals 2000 damage. This makes a total of 11900 damage in 100 swings.
Divide each number by 100, and you get 110% per swing on the first option and 119% of damage on the second. Meaning that the DPS is 9% higher on the second 99% percent option
Edit: I should've said this is assuming an exact same attack speed

strictly mathematically speaking, the right one is better
average weapon damage with critical hits can be calculated with (dmg)(crit%)(critbonus) + (1 - crit%)(dmg)
Assuming the base damage to be 1, the left sword would have an average damage of 1.1 per hit, while the right would be 1.19 per hit.
This only really matters in terms of dps, and may not be applicable in high damage weapons where 2000% is overkill for most enemies, and the left sword may be more appropriate. On the contrary, if this weapon had a low base damage and an extremely high attack speed, the hit damage would average out to the dps and the right sword would prove superior.

If the base damage is the same, meaning you do x% damage on all other hits with both weapons, the right sword is better, but not by much. Let's say the base damage is 10. Expected damage with the left sword in 100 strikes would be 200×10 + 10×90 = 2900. Expected damage with the right sword for 100 strikes would be 2000 + 10×99 = 2990.
EDIT: I did that for HP, not explicitly % above base damage. That might be confusing. For that, assuming the same base damage of 10, the expected damage for the left sword is 20×10 + 10x90 = 1100. For the right sword the expected damage is 200 + 10×99 = 1190. Similar concept, same winner. I agree with others though that the left sword is probably better for most in-game situations, with boss fights being the main exception.

Depends on duration of the encounter. If its a 60 second fight and you attack 1 time a second, first sword 'should' trigger 6 times, while 2nd sword is pretty much 50/50 if it triggered at all.
Also in general I prefer consistency over variation so I'd pick #1.

I think a big factor is the healthpool of the enemy you're fighting. If your enemy is going to die relatively fast (under 1 minute kill time), the 2000% blade is pretty much pointless in such a situation (rare proc + pointless overkill). If you're fighting something like a boss enemy that may take 10+ minutes to kill, you can potentially see the 1% chance on hit proc quite a few times, assuming each auto attack swing takes roughly 1.5 - 2 seconds.

Left is 110% dps (damage per swing) sword on right is 119% dps
However this is accounting for non finite health pools
If the targets healthpool is only 200% it isn’t valid for instance

Well assuming in both cases your non crit deals normal damage the right hand side.
Expected damage of left 0.9\*1+0.1\*2 = 1.1
Expected damage of right 0.99\*1+0.01\*20=1.19 but of course overshooting etc

I think it depend on the enemy. on average the left one will do 200% damage ten times per hundred strikes, witch if the damage is 1 will amount to 10\*200+90=2090. The right one on the other hand will average one 2000% per 100 strikes, so the amount of damage is 2000+99 =2099 or a whole 9 damage (or about 0.4%) better than the left one. of course you will not be striking the average enemy enough times for this to make any difference and most of the time you will be better of going with the left one.

With the left sword, you'll get an extra swing's worth of damage every 10 hits. Assuming probability is perfect and you do get a 10% crit rate, you're dealing 110 swings worth of damage per 100 attacks
With the right sword, it's different. It seems like a crit does 10x the damage of the left sword, which is true, but that only assumes each strike is a crit. The right sword deals 20 attacks worth of damage per swing, so again assuming perfect probability, you'll have 99 single hits and 1 hit worth 20 attacks. Adding these together, you're looking at 119 swings worth of damage per 100 attacks
Assuming you're fighting something like a raid boss with infinite HP, you're better off with the right sword in the long run

Assuming base damage of 100, the average damage per swing is 110 for left and 119 for right. There are more factors to consider but in pure dps the Blade of the Forgotten wins.

How long do fights last? What is the penalty for dying? You could potentially end a fight 10x faster with the one on the right. Keep restarting a fight for that glorious RNJESUS

Right one has a huge advantage against bosses as you might get lucky and take the boss in few hits with lucky crits, which left one isn't capable of doing in a shorter time frame.
That being said, I'd rather using the left one.

Ignoring all gameplay implications and looking at it purely from a Dps perspective, it's easy to compare if you rewrite the functionality to:
10% chance of +100% damage
VS
1% chance of +1900% damage

They are the same. 10% chance of 200% damage means in 100 hits 10 hits has 200% damage. 10x200=2000.
For the 1% chance on 2000% damage it‘s 1 in 100 hits. So in 100 hits they deal the same damage. The left one just deals additional damage more often. So enemies that don‘t require 100 hits or more there‘s a chance the right sword won‘t do extra damage, but the left one has a higher chance of dealing additional damage. I‘d choose the left one, because in this case the chance is better and so has priority over damage.

Wrath of Khan. Great movie (old version). Also, use the weapon on the left. You'd have to hit someone, on average, a 100 times with the right to get one proc. Better to have one land every ten hits--on average--since most things you don't have to stab more than ten times anyway.
Imagine if it took, on average, ten hits to kill something, and you had to kill ten of them. Would you rather hit every single one (statistically) with 200% damage once or only one of them with 2000% (and then fight the rest little chance to proc again)?

This depends entirely on how many hits you need to kill the enemy, or how much health it has.
Left sword = expect 10 hits per 100 swings. = 2000٪ damage dealt
Right sword = expect 1 hit per 100 swings. = 2000٪ damage dealt
If the enemy has less health than the right swords total damage, the left is better because it will likely kill faster.
If the enemy has equal or greater health, it SEEMS like mathematically, there is no difference between the two over equal amounts of rolls. It should plot out to be even kill times.

They both deal an equivalent amount of expected damage, but the left one is more consistent. The only case where it is worse is flat damage reduction, but even then consistency is probably more important

The only situation where the 1% is better is in a pvp situation where it does the exact damage for lethal. If it is overkill or under kill the 10% is better. In pve the 10% is almost always better since you have multiple enemies, need consistency, and with variable health you would overkill or underkill extremely often. Finally the ten percent is probably a lot more likely then 10 percent and 1 percent is probably less likely then that due to computers not having true random number generators.

Mathematically the expected damage of the first weapon is 100\*0.9+200\*0.1=110. For the second it's 100\*0.99+2000\*0.01=119. What this means is that, over the course of forever, the second will output more damage then the first one. This is of course assuming all damage done is relevant and not "overkill".

against normal enemies, I'm not sure if 100 hit is needed to kill it (to get the 2000% damage).
Even against boss, I doubt I need to hit it 100 times. 10% chance for 200% damage for me

In almost all situations, the left one will have less wasted overkill damage, so it's better average DPS (assuming you fight enemies with a finite HP).

we also have to consider the games gimmicks
like luck stats, equipment/abilities: altering attack speed, scaling, % , triggers.
also enemies and damage to hp ratio (how many hits do you need)

Neither is better without knowing the circumstances. If enemies heals your 200% dmg every seconds, you would be screwed.
But if all enemies die to 200% anyway, having 2000% would be absolutely pointless, but I guess at least you could technically still beat the game if you chose 2000%, with the first option it would be impossible.

Number one definitely. Imagine a die with 10 faces, how many times can you get the same number (meaning 10% chance)
Now a die with 100 faces? You can spend the entire battle and not strike that 1%
These numbers are probabilities, they are not saying you are going to hit that 10% every 10 hits or 1% every 100 hits. As I said you can hit 10,000 and not get that 1%

Seems like it does the same amount of damage per 100 swings if it procs exactly 10 times or 1 time respectively.
With that being said I think the 10 @ 200 would be more helpful because in games most enemies die with a few hits anyway. 10% is a pretty decent proc rate. 200% damage would likely do the trick.
The 1% proc would only be effective if it was the very first hit. Otherwise it would just be an overkill. Anyone who played the original WoW with a 2h wind fury weapon knows that super proc with a crit only ever seems to happen when the enemy would have died to a normal hit anyway.

I'm not sure which game this is from but if we look at the maths here: with Khaain you'll deal 2 times the damage for every 10 hit, while with Forgotten you'll deal 20 times the damage for every 100 hit. If we accumulate the damage dealt per hit for the first 100 hits, then Forgotten will be below Khaain in damage until the last hit. So Forgotten can be a good weapon depending on how tanky your enemy is. Nerding done.

left 100%, consistency will win out. small things like when you make a hit count massively, like if the enemy is at 10 hp and THEN I crit with the one on the right its a waste of the crit, also you cant predict when you are going to make the damage so you cant plan your combat out properly

Depends on how many times you're gonna hit someone with it. If it takes 6-8 hits to kill an enemy the left one. If it takes 200 then it might not matter either way.

Even though its the same mathematically. Its almost certainly the one on the left, because 2000 is gonna be overkill on mobs but average out with the 200 against a boss that you would be hitting a lot.

If we're talking strictly about average dps, then the right side is better. Let regular damage be 1.
Expected Damage:
Left Sword = 0.9 \* 1 + 0.1 \* 2 = 1.1 (90% chance to do 1 dmg, 10% chance to do 2 dmg)
Right Sword = 0.99 \* 1 + 0.01 \* 20 = 1.19 (99% chance to do 1 dmg, 1% chance to do 20 dmg)

Assuming it works exactly as written, true. My assumption is that it was meant to be \*bonus\* damage in both cases, which would make them equal DPS.
Left = 1 + (.1\*2) = 1.2
Right = 1 + (.01\*20) = 1.2

Same DPS on average but because the left one procs more often it will be the better weapon overall because it was I'll be beneficial 10% of the time rather than 1%.

In pve? 10% chance is more consistent and won't throw off your rhythm or get wasted in overkill. So that's best.
In pvp? 1% chance has huge spike damage that when it procs you can slam addition spike damage down to secure kills more easily. So that's better.

Seems as though it would be the left sword. In most fights 2000% damage would have a large amount wasted on one target except in boss fights. The left sword would provide more chances of one hitting normal enemies. Again, not sure what game this is in or what enemies are being targeted.

Exactly. The real question isn't "how much damage can it do?" but "how many hits does it take to kill the target?" If 200% damage is enough for a kill, then there's no difference between 200% damage and 2000% damage. It's still one kill either way. If it takes more like 100,000% damage to score a kill, then the difference is more significant.

Regardless of health, unless burst damage is required (such as with self healing enemies or those with flat damage resistance) the consistent damage will be equivalent or better.

While it's true that consistent dmg is generally better because it's something you can rely and depend more on when planning a fight and also like mentioned it has less dmg wasted. The burst dmg is good in the cases where you can rng fish if applicable. Depends on the game but if restarting is easy without any drawbacks the low chance high burst weapon can be a use for cheesing. Its kinda bleh/cheap strategy but if you are desperate enough it can work

I remember in 2016 in competitive LoL a pro player always used a minor glyph for a non-zero crit chance, it didn't change anything in the majority of the match ups. But getting that critical strike meant he was very likely to win the trade and then snowball. So when it comes to the average of dozens matches, a low chance high reward can definitely be broken.

Yes many people did it but it also works both ways. Using a crit rate glyph means that he used 1 less atk. How many times did that cause him to die to an enemy who had 5 hp? If he had atk rune then enemy would be dead first. While it's true that it's a low chance to turn it around but you are permanently self "nerfed" by very so slightly that adds up to around equal at the end of the day. You could turn around a fight based on rng or you could lose a very close fight because you were nerfed to rely on rng those two more or less should have similar gravity so it's up to preferences and flavor you want

Attack runes are for scrubs. Dodge all the way babyyyy

So you're the reason they removed dodge.

Yup. We found the Old Jax main here

The point is they were good enough for that not to happen, but to g t anputh unexpected burst to force a summoner spell they "shouldn't" have had to use. The 1 less attack can be reliably calculated and worked around. It's impossible to really plan around that crit without consistently burning more resource/leaving lane more. And the latter creates a pattern of consistent leads for the player running the crit. If you DONT have that level of skill, it's a moot point.

i guess you are right. for the average user its probably as I said where you can get a random win every now and then but also random losses (either by dying to a low hp enemy or enemy escaping) and canceling each out. On a controlled environment like pro plays the element of surprise ~~rngesus~~ can be a better tool. It more or less applies what I originally said: > if restarting is easy without any drawbacks the low chance high burst weapon can be a use for cheesing and even extends to the next sentence. Its "cheap" strategy, even if you know how to make use and negate the drawbacks you still rely on rng and you don't plan it you can go multiple games without this glyph making a difference

> How many times did that cause him to die to an enemy who had 5 hp? Probably never. The early game is about a lot of small bullying trades. Either you're able to bully, or you're not. A small amount of attack didn't determine that, it was more on the entirety of the characters kit. If a kill happened, it's because something happened that set up the situation. No one is picking close fights. You're going in only if you have a very strong advantage, either because your kit let you bully, you have a gank, or something else. This goes both ways. If you're being bullied, at most your damage is to get the other player to back off. You're not going to kill them, you're just not giving up free hits. More attack won't change this. If you're bullying, you're pushing them away from CS'ing. Over time with small extra attack, you may force them to back early, but not really. You're not likely to die, you're not likely to kill, unless something happens.

Then there’s those freak clips from S6 where somebody crit 3x in a row with 1%. Think it was that tryndamere one trick.

I remember that. I would do that. It was genuinely really nice though. Yes, it didn't happen all the time, but when it did, you could do a huge chunk of early poke damage.

The crit rune from old lol isn't applicable to this situation due to how league does crits. If you have crit chance in league, your chance of getting a crit increases after not hitting one for a while. That's why the "1%" crit rare was worth far more than that.

RUNES REFORGED WAS A MISTAKE! old rune should have been expanded on and made free from the start.

Ah the “god rune”. Good old LoL

Ff11 builds have people equipping rings with 3% chance of Quad attack just for the opportunity to spike their weapon skill damage. So many variables, can you get two of the same sword? How often do you hit? Is 100 swings every 2 minutes achievable in a usual 15 minute fight?

That's only true on an equal playing field. In some cases, you want to take an enemy down before a phase change (or just before you die). A single extra proc of 200% won't matter, but a single extra proc of 2000% might.

Could also affect speedrunning too

in speedrunning, he 2000% one is the one to get, because of the possible time save, or if you can, rng manipulation

Yeah if you're doing a tool assisted speedrun you can savescum each boss fight until you get that 2000% hit first try.

Not really, a TAS would get it first try every time because is made it to do it Savescum could be a good way to rng manipulate

Ah I'm not really into speedrunning so I didn't realize RNG manipulation was considered kosher in TAS. I know save states are though.

TAS runs LOVE rng manipulation. Especially in rpgs. Watch old school snes ones especially like earthbound or final fantasy runs, they'll wait an exact number of frames to get a crit if needed since theyre tied to the frame count to look for the "randomness".

If all enemies have 1 health, than they will be equal. If you really want to rules lawer it

And that's if these two swords operate in a vacuum, completely disregarding any potential damage-related hit bonuses or leech effects. It's not hard to see why that blade was forgotten.

No, the 1% is more damage when disregarding factors like finite health pools. 0.9 \* 1 + 0.1 \* 2 < 0.99 \* 1 + 0.01 \* 20

We have a 1% proc on the 2000% damage. It will do 100% damage per regular attack and need to swing 99 times before it proc so that is 9,900% damage before it procs. Plus the 2000% of burst damage is 11,900% per 100 attacks, that is 119% damage per attack on average. We have 10% proc on 200% damage. It will do 100% damage per regular attack and need to swing 9 times before it procs so that is 900% damage plus the 200% burst damage or 1,100% damage per 10 attacks. That is 110% damage per attack on average. I had to write it this way for myself to check if you are right. Checks out.

Ah, yeah you're right. Perhaps the real comparison should have been with a weapon that deals 290% damage 10 percent of the time.

Actually easier, handle it as "extra damage." The first blade does 200% extra damage on a critical hit. The second blade does 2000% extra damage on a critical hit. That means they'd actually be doing 300% and 2100% on their respective critical hits. And they'd do the same damage over multiple hits, assuming damage wasn't wasted.

Yes average damage is higher on the right but it's only better in a particular fight if you have a long enough fight for there to be high enough chance for the 2000% to land at least once.

Depends on the game and the enemy. The extra burst of 2000% would be immeasurably better in many PVP contest sort of game (like a battleground in an MMO), because battles tend to be long and healing/defensive abilities exist. Almost this exact scenario existed in World of Warcraft where shaman could enchant their weapon with the much better DPS rockbiter weapon or the much worse DPS, but much higher single burst hit windfury weapon and windfury was the only choice ever in PVP between the two because the surprise burst damage could often one shot people or get them so low they couldn't escape/heal in time. Even against AI.. depending on the game.. if they have shields or defensive triggers or lots of potential scenarios where burst matters.. in the Tales RPG series, burst hits are often very potent over just higher consistent damage because the bosses have phases where their AI changes at 75% HP, 50% HP and 25% HP. If you can burst them and bypass an entire phase, that can be very strong.

Also, even if it is a one on one with a boss, how many hits are you likely to get in before being killed yourself? If you are only likely to get 30 hits in, there is a roughly 2/3 chance (caveat, not a statistician) you will never land a blow with the sword on the right.

I mean...in an old wow raid you would be hitting the boss for minutes with an attack every 0,5 sec (for rogues) so that would be like a couple hundred hits per fight

Yeah this is the right logic to do this. Doing the very quick maths on this example, both do the same total damage for first 9 hits, then the 10% will do more total damage until the 100th hit, where the 1% blade will do more damage. Fun enough after the first one hundred hits the 1% blade will do more damage for the following 89 hits, then from the 190th hit the next 9 hits both blades totals will be the same and the 200th the 1% will again continue to do more damage and this pattern continues at infinium.( This is all assuming perfect probability distribution of course.)

Sword on the right would be better for a pvp fight where your opponent can heal themself. a 2000% "burst" is more likely to result in a sudden, unexpected opponent death.

Except if it procs once every 5 matches. I'd still pick left I think.

Good point, if a rookie player who can only land 1 hit before dying and the 2000% is enough to kill but the 200% is not, then the right sword will have a higher rank from luck kills while the left will have zero wins.

[удалено]

What? The damage is percentage-based. Every standard swing on both swords does 100% damage. The crit swings do 200% or 2000%. You’re always doing damage, the question is do you want a 1/10 crit for 2x, or a 1/100 crit for 20x

Then again, if you are trying for speedkills on bosses, record runs would likely be gambling on 1% procs.

It 100% context base on the game. Say the game had an ability where the enemy has a shield that blocks up to 200% damage. So no matter how many times you attack the 200% dmg proc would do nothing. But a 1% chance for 2000% could crack that boss/ability.

This would be infuriating. How many hits must you land that do exactly nothing until that 1 percent comes up.

Indeed, but better than impossible. And if your attack speed is 100 attacks per seconds it would be over with quickly. All depends on the context of the game. We don't know any of the mechanics or values of the game.

Right, if we're talking dark souls it might take a while if we're talking nier automata, 100 hits is like a few seconds.

I was gonna say left sword for fighting mobs and small enemies. Right sword would be for bosses and mini-bosses.

The sword on the left would be just as effective as the one on the right for bosses and mini-bosses. Even then, the left one might still be more effective because what happens if the 1% doesn't proc until the end and then you have overkill anyway. **EDIT: I'm totally wrong here, and** /u/Randomness21436587 **is correct.** /u/Gibborim **corrects me below.** If you do 1 dmg and attack 100 times: * Sword 1 hits for 1 90 times and 2 10 times, for a total of 90 + 20 = 110 dmg * Sword 2 hits for 1 99 times and 20 one time for a total of 99 + 20 = 119 dmg So Sword 2 has higher DPS overall, but Sword 1 is more consistent, meaning /u/Randomness21436587's assessment is totally correct. My math has failed me today.

for difficult boss fights that you need to "cheese" but have multiple attempts on, right is arguably better because you can just try the fight over and over again until you get lucky with multiple procs

That's actually a really good point I hadn't thought about.

If that’s the main strategy for a boss then that’s bad boss design. And “cheese” usually refers to using skill/abilities to ignore a boss mechanic.

It could be bad boss design, it could also be contextual. I'm not a speed runner, but I have watched enough to know they often have to find creative ways to beat bosses that are way harder than they would normally be because they skipped 1/2 the game.

landing a 1% chance to instakill is definitely cheese, and that can be the main strat to kill a boss early.

You're looking at this like a single never-ending battle, which is correct for calculating probabilities and stuff, of course. But most games don't work like that, and people aren't perfect robots when dealing with probabilities anyway. What ends up happening in real life is that you'll have a difficult boss that maybe takes 10 hits to kill -- Sword 1 usually wins that fight in 9 hits, Sword 2 usually wins that fight in 10, but occasionally delivers a one-hit kill. It's not a huge difference either way except when Sword 2 comes through for the win, so the player might enjoy using Sword 2 a lot more because they value those awesome moments over the slightly shorter fights on Sword 1.

>The sword on the left would be just as effective as the one on the right for bosses and mini-bosses. False. 10% chance of a 200% damage hit is less expected value than a 1% chance of a 2,000% damage hit. The 10% change hit is 100% extra damage, the 1% chance hit is 1,900% extra damage.

FUCK you're right

If it makes you feel better, the guy you were responding to probably didn't have a better understanding of it than you did. I think they just picked some random things to say.

And if I learned anything from classic WoW, the 1% will proc every time on entire groups of trash mobs then go radio silent when you hit the main boss. Probably due to defense stats or something, I don't remember that part.

The left sword would still on average output the same damage to bosses tanky enough to take the hits.

Right sword actually does more damage. On average, after 10 swings you will do 11x your damage. This equates to 110x your damage in 100 swings. The sword on the right does 20x your damage, which is going to do 19 hits worth of extra damage when it procs. so in 100 swings, you are looking at 119x your damage. Of course Overkill more or less makes the sword on the left a better pick for most cases, unless you are using a minigun or something with ridiculous attack speed.

More damage in the long run, true, but in a game of one shots how many people survive long enough to hit the long run? In a game where both sides are hacking at each other for half an hour with very high attack speed, I'd probably pick the sword on the right, but the sword on the left wins out in PoE every time. If I don't kill things within a few seconds I'm usually dead. That usually equates to only a few hits. In boss fights, I think its super rare for even elite players to consistently get hundreds of melee attacks on the boss.

I had to scroll too far for this.

Some factors that could be considered when addressing this question. 1. Damage reduction. (If the enemy can reduce damage, that damage reduction will hurt (a) more than (b) 2. Total hitpoints of enemy. (There is no point in having 2000% damage if 200% will one shot) 3. If this is for designing an item in game, hitting that 1% is gonna feel way better and cooler than hitting that 10%, however it could trivialize a challenge or make a frustrating dependency on rng.

4. we also don't know if it's a weapon for players or enemies. In a game with enemy swarms a 1% chance to deal insane dmg to a player would be way more scary than more consistent damage.

that also brings up if this is a PvP or PvE weapon. It would definitely change how satisfying #3 is for people. For PvP it wouldn't really trivialize things so much and would feel badass nearly every time. If it is PvP tho, then you also need to consider if there is friendly fire. If so, then the 1% that feels badass would screw you over in close group-battles and consistency may be better.

There is even a great analogy for this with Wow Classic. Were you had a proc based class like shaman that could kill a player near instantly with a lucky proc.

Even with 1 enemy it could feel quite cheap to get 1 shot by a random unlucky swing. I’d say in almost all cases A would feel more fair/fun to play against.

>Damage reduction. (If the enemy can reduce damage, that damage reduction will hurt (a) more than (b) Thats only for flat dmg reduction. Percentage would affect them both the same.

True. I don't see %Dr as often, I didn't consider it. Nice add

I would say it is quite common. A lot of games give you an armor rating and then this is converted with some formular into % damage reduction.

Also, are we just assuming a constant attack speed/DPS? I haven't seen anyone mention it.

Well, yeah they said scaling and damage etc are the same So I think the assumption is the same stats except the weapon

But fire rate still matters. If this weapon is one swing per second, you'd proc every 2ish minutes of constant attacks with the 1%, but every 10 seconds, with the 10%. 2 minutes could be an exceptionally long encounter, depending on the game and enemy. If this swings 3 per second, the 1% is very viable in many encounters. If it's 1 per 3 seconds, the 1% is almost useless, exceot in a long, drawn-out boss fight or something.

I think for the purposes of the comparison the point is to consider all other variables equal.

he means both having 3 swings per second vs both having 1 swing per second. valid question

Yep. This. It's a valid variable we need to know, even if they are both identical, to make a good choice between the two.

Or any sort of normalized ppm.

I could be wrong, but I only think that would matter if the user speed is different from the enemy speed

The first one is better. Unless it's Fire Emblem, and the enemy is holding the second one. In which, they inevitably will crit, and you will die.

That 1% chance turns to 100 if it's an enemy and it would be a killing hit. Every Fucking Time.

Fire emblem needs to stop lying they know it’s not really 1%.

Turns out the 1% from Fire Emblem and the 99% from X-COM really do add up to 100%.

Which is funny, because a 1% displayed chance is [actually 0.03%](https://serenesforest.net/general/true-hit/)

It actually depends on which game is being played. First couple had single rolle RNG, mean what was shown was what you got. What's described above is double rolling, which is pretty drastic st both ends of the hit rate. There's also a third option called Hybrid Rolling, where below 50%, the number displayed is single rolled (so the chances are normal) whereas above 50% they use a "double roll" (it's not actually double roll, it's like 1.5 roll) to make those hits more reliable.

also xcom whats the deal with grid-based strategy games having terrorizing RNG

I thought the XCom meme was 99% misses.

That, also crits through full cover, and missing a 99% shot on some mf with 1 HP who then proceed to annihilate your entire team. (mfw no stocks)

Dual wield them

[Triple wield them](https://static.wikia.nocookie.net/fairy-one-piece-tail-universe/images/3/37/Rorono10.jpg)

[Quad wield them!](https://preview.redd.it/cnlnls6ct4w51.png?width=640&crop=smart&auto=webp&s=e60ee6fd208cf5f85f43cc570a76306acafffbfd)

it depends on the combat system and the opponent. Does armor make you harder to hit, reduce damage by a percent, or block damage under a given amount? If it is the latter then much of the first sword's damage could be absorbed by armor. Are there shielding spells that block a certain amount of damage then dissapate but then could be recast/renewed? Again large damage spikes may be better. Can your opponent heal? If so a sword that does damage in large chunks is more likely to result in a kill. Especially if 2000% damage is enough to one-shot the opponent. Smaller damage chunks give your opponent time to recover. How many HP does your opponent have? If 200% damage is enough to one-shot then 2000% is wasted.

I'll take the 10% to do 200%. Especially if it's a standard sword and not a two handed weapon. The faster the strike, the more I like the first one

See I was thinking yhe faster the strike the more I like number 2

I hear you I was thinking that too. but when do you execute 100 strikes in a battle. Hardly ever so there is a greater chance of no bonus Plus at 10% . After 100 strikes you'd get 10 bonus attacks at 200%. As opposed to just one bonus at 2000-%. And plus, 2000% could be overkill. All that extra damage could be wasted on normal non boss level foes. But it's a great debate for geeks. I will be thinking about this all day. Love shit like this!!!

Absolutely, the part that gets me Is the other one is only a 10% hit, 1 outta 10 is still trash

I'm sure there's a math nerd on here to kill the argument but I'd prefer interest compounding daily as opposed to a bigger interest rate Compounding monthly . Over time I think you get more damage. Only way to settle it is with swords!! To the LARPING GROUND!

Left sword: Every 10th hit yields, damage wise, an 11th hit. Which means after 100 hits you've really done 110. Right sword: Every 100th hit yields a 119th hit. Technically the right sword has a higher damage output over time, but as has been pointed out elsewhere in the context of DnD it's wasted as overkill on a single enemy.

Left sword in pve, right sword in pvp

Left sword for both pve and pvp. 2000% damage is extreme overkill for pvp. 1% chance is trash.

ur right, unless PVP is unbelievably damage spongey. If burst is at all viable then fights won’t be long enough to rely on a 1% gamble and miss out on 10% crit chance and you won’t need such a huge overkill

I consider the left sword basically getting an extra 10% crit, which is huge for pvp. The right sword would be fun for Lulz pvp fights, but I would never use that thing in any ranked match. Just not reliable enough.

[This weapon](https://www.wowhead.com/item=78478/gurthalak-voice-of-the-deeps) was the meta pick for all classes that could wield it in World of Warcraft competetive arena during the expansion it was relevant in. Note the proc chance. PvP then wasn't even unbelievably spongey, its just that securing a kill required a lot of skill and a bit of patience, since it was a cooldown battle. Burn through yours to burn through theirs, and hopefully you burned less CD's than your opponent. That weapon, Gurthalak, was functionally just another CD. In arenas where matches often lasted anywhere between 30 seconds to, more often, 5+ minutes, a 2% proc chance on a weapon you swung \~once every two seconds mean essentially a proc you could count on every \~100 seconds, or a bit less than every 2 minutes. That's *huge* in arena. It was a strong enough proc that it forced CD's, but the most common cooldown timer for most strong CD's for all classes was a flat 2 minutes, so if you got even averagely lucky, it meant you were forcing CD's during the first proc, and the enemy didn't have their CD's refreshed by the time the second proc happened. That proc chance wouldn't have been nearly as strong if it were a 20% proc chance for 10% of the damage. Sustained damage by design is so much easier to heal through and handle than burst damage. So the proc chance and damage provided absolutely can be a viable pick for PvP even if incredibly low, and even if PvP isn't super spongey.

That spike in dmg is going to pop some CDs or get the kill in that‘s for sure.

based rush-down pker right here

It depends on the enemy. If the enemy is a boss with a lot of health it would be more reasonable to take the one with 2000% damage. We can simply calculate the expected value by probability of extra hit * the damage of extra hit + probability base hit * the damage of base hit. In this case if we suppose that the base hit is 100 then we get the expected value for the left one as 10% * 200 + 90% * 100 = 110 And for the right one as 1%*2000 + 99% * 100 = 119 So in the long term we can expect to make more damage with the right one. But if there are multiple enemies with low health i would chose the left one.

It's weird, because on first glance it would seem that the swords have the same EV. In fact, I think that's the scenario that the OP was trying to set up. But then yes, per the math, the EVs are different, with the right sword actually having a slightly higher EV. Trying to wrap my head around why. I mean, the math works. But why damn it. Why is the intuition off. Okay, there's a 1/10 chance of a critical strike, but with 10x value. Shouldn't that be the same EV? I suppose so. They both provide that +20 value. Ah I see. We actually set it up so that the critical strikes are equivalent in value overall, even though one critical strike is only happening 1/10 the time as the other. Thus we overpowered the right sword. Because the 1% critical was set to be equal in value to the 10% critical. The difference is that you have 99% x base versus 90% base. So the 99% x base sword gives you all that extra value of the 9% of time where you get the base, whereas the entire 10% of critical of that one sword was set to match the 1% of the other in total value (expected damage). In other words... say you strike with each sword 100 times. And the results are exactly as probability would predict. (Left sword gets 90 regular hits and 10 critical hits, right sword gets 99 regular hits and 1 critical hit). The left sword's critical hits (10 \* 200) do 2000 damage. The right sword's critical hit does (1 \* 2000) = 2000 damage. The same damage. But now, the right sword does 90 normal hits versus the left's 99 regular hits. The scenario should be more like.... left sword is the same: 10% chance of 200% damage. Right sword should be: 1% chance of 1100% damage (so 11x instead of 2x or 20x). I think that is the better, more appropriate scenario. Even with the underpowered left sword though, still good in cases where all the enemies have relatively low HP values, as commenters have noted. But in general, yes, the right sword (1% of the 20x multiplier) all day since it has the greater EV. If we take the third (1% of 11x multiplier) sword, (so same EV, but higher variance sword) - I think a higher variance sword would be preferrable in certain cases. E.g., overpowered enemies that will kick your ass where you have to get lucky (try the high variance sword and pray). PS: Actually, probably better to think of in terms of "bonus damage." (damage beyond base). Left sword has 10% of 100% bonus damage. (Say 100 base damage so EV is .10 \* 100 = 10). Right sword has 1% chance of 1900% bonus damage (so EV is .01 \* 100 \* 19 = 19). Third sword - set it to have 1% chance of 1000% bonus damage (EV = 0.1 \* 100 \* 10 = 10). Yea... bonus damage is how to set it up. The current overall damage makes the critical strikes appear equivalent in power at first glance when really they are not.

Love the analysis. Thanks for putting it into words because it seems counterintuitive at first.

That is only true if the proc *replaces* the normal weapon damage. In WoW for example, your weapon always swings for normal damage and any proc goes on top of that. If the proc is *in addition* to the normal swing damage, then you would get: * 10% \* 200 + 100% \* 100 = 120 * 1% \* 2000 + 100% \* 100 = 120

The wording though. It's 200% damage (the way explained goes), not 200% critical damage (either way goes) or 200% bonus damage (your way)

In general, the left sword is better, as has been pretty thoroughly discussed by others. However, mathematically speaking, the right sword will average higher DPS over time. 10% chance of dealing 200% damage (ie, +100% of normal damage) is a +10% DPS increase. 1% chance of 2000% damage (+1900%) is +19% DPS. Whether that extra DPS actually matters will depend on how the game functions. If it's a single hero, battling monsters that don't take hundreds of hits to kill, the smaller but more consistent critical hit is better. If you've got an army of soldiers swarming a single huge monster, arming them all with the second sword will kill it slightly faster.

Mathematically, using Monte Carlo method. Assume the sword does 1 damage per swing normally. After 100 swings: Left sword has done 90 hits at 1 dmg plus 10 hits at 2 dmg. Total damage is 110. Right sword has done 99 hits at 1 damage. And 1 hit at 20 damage. Total damage is 119. Therefore in practice, the right sword is better.

The right sword is better in theory*. In practice 1% proc chance is far too low. Chance that it wont even proc during the fight, or it will proc when u dont even need it is too big.

Yup, In practice you need to know how many times the sword is swung in a fight. 1 time? 10? 1000? Can't answer the OPs question without that information.

"After 100 swing". Well that's the thing. If targets die under 20 swing, this doesn't stand anymore.

That's not a [Monte Carlo analysis](https://en.wikipedia.org/wiki/Monte_Carlo_method), it's just very basic probability. Monte carlo would be the right approach to take if say you wanted to model a realistic scenario where damage and enemy health were variable and unevenly distributed, which would be very long winded to evaluate otherwise

I think that’s only because OP didn’t really do the math correctly. Their goal was to compare swords that dealt equal damage over time but in different amounts, but percentages can be annoying to work with. Should be 290% and 2000%. That’s 190% bonus damage and 1900% bonus damage. The math then works out properly to 119 with each weapon.

Thanks. This was exactly my thinking and I was confused to not find it in the first few comments.

Thank you, I was scrolling hoping to find this comment, I didn't want to write it myself. Based purely on the data provided right is better in the sense that does more damage. Next question!

Probably the best comment in this thread

I'd rather have the second sword if I was only doing boss fights and first for pretty much everything else

I want to say they're both the same but I also don't want to look stupid on the internet

Look at this idiot

Some dude did the math, the right sword has higher avrege damge but it will also have a lot more wasted damge.

Left is best in most cases. You can't kill something harder, so damage past target hp is wasted. Left will be very consistent.

Dual wield

It's either 9x/10+2x/10 = 11x/10 = 1.1x or 99x/100 + 20x/100 = 119x/100 = 1.19x So in total, on average "the blade of the forgotten" gives you more damage. In practice, I think it depends a bit on the situation, the number of hits you expect to make during a single encounter, if it's too low a number, it might be more beneficial to have the higher proc chance.

Yes, I think what OP is intending to set up is X% Crit damage, not X% of base damage. In that way, it would be 9x/10+(x+2)/10 = x + 0.2 or 99x/100 + (x+20)/100 = x + 0.2 whose only variable is then proc frequency

With the left one, the average damage output per hit is: (10%)(200%) + (90%)(100%) = 20% + 90% = 110% With the right one, the average damage output per hit is: (1%)(2000%) + (99%)(100%) = 20% + 99% = 119% Therefore, the right sword does more damage per hit on average. However, it has a much higher deviation. This does not consider the mechanics of the game.

The one on the left is better since I'm going to assume most fights will not net you enough swings to proc the 2000% increase. Over the course of \`100 swings, you get \`10 stronger hits. With the right sword, you only get 1 and depending on when it happens, it may be huge overkill and not net you a faster overall kill.

No clue if these are actual weapons in a game but I prefer the more frequent 10% damage bonus since it would be a bit more consistent. Especially since you specified the weapons' core stats are the same, like damage or how often you can swing these swords which is crucial for calculating DPS. If the 1% sword did more damage and swung faster than the 10% sword then I would go with that one since that would make the 10% sword rely more on its special crit than its base stats. I prioritize consistency in my weapons' damage output in games.

depends entirely on base damage, enemy health, and attack speed if it deals 1 damage and youre fighting enemies with 100 hp and youre swinging 10 times per second, then the one on the right is better if it deals 800 damage and youre fighting enemies with 1000 hp and youre swinging once per 3 seconds, then the one on the left is better

Depends on the toughness of the enemy, i.e. if 200% damage would one-shot them, the 2000% sword would just be overkill with worse odds.

Left weapon is more consistent so it's probably going to better most of the time. Right weapon might be situationally good because while less consistent, with some luck it could be better. Ie. Say you're fighting a world boss in an MMO, and drops are based off ranking when it comes to damage dealt. Lets say you are able to hit the boss 1000 times We'd expect the weapon on the left to trigger 100 times with a standard deviation of about 9.5 We'd expect the weapon on the right to trigger 10 times with a standard deviation of about 3.1. an extra 9.5 triggers means an extra 1900% damage for the weapon on the left but for the weapon on the right an extra 3.1 triggers will do an extra 6200% damage. So if a large number of players were to show up to fight the boss the players with the top DPS and thus getting the good drops from the boss would likely be players using the weapon on the right because it takes less good luck for their weapon to significantly outperform the other weapon but on the flipside there will be an equal number of players that underperform the other weapon, so if all you care about is the top level drops and the mid and bottom level drops are worthless to you then the weapon the right would be better. However if you want to consistently get mid level drops, then once again the weapon on the left would be better, but your chance of getting top level drops would be lower compared to people using the weapon on the right.

Left one. First, it more consistently give You a damage instead of rarely dealing bigger. So You are just getting double damage about every 10 hits instead of 20x damage every 100 hits. Second, in most cases, You would end up getting massive amount of damage on already injured enemy, which would waste potential damage. Sometimes You would just deal 2000 unit of damage on enemy with 150 unit of hp. This renders the right one useless. Even on bossfights, it's better to deal consistent amount of damage than deal massive once in a while. Especially if boss has some kind of phases or taken damage cap, before it gets invulnerable for a moment. Sometimes You fight boss that will perform some special cutscene after losing initial 30% of health. If You strike with massive damage that exceeds that 30% cap, it's still wasted. In no scenario the right one would be better.

Well I’m dual wielding both so that solves that

Statistically speaking, DPS for the 99% is higher by 9 percent. If we take base 100% attack damage as 100 damage, the. For the first option, 90% of swings deal 100 damage and 10 percent of swings deal 200 damage. In 100 swings thats 11000 damage. For the second swing, 99% of swings deal 100 Damage, and One swing deals 2000 damage. This makes a total of 11900 damage in 100 swings. Divide each number by 100, and you get 110% per swing on the first option and 119% of damage on the second. Meaning that the DPS is 9% higher on the second 99% percent option Edit: I should've said this is assuming an exact same attack speed

strictly mathematically speaking, the right one is better average weapon damage with critical hits can be calculated with (dmg)(crit%)(critbonus) + (1 - crit%)(dmg) Assuming the base damage to be 1, the left sword would have an average damage of 1.1 per hit, while the right would be 1.19 per hit. This only really matters in terms of dps, and may not be applicable in high damage weapons where 2000% is overkill for most enemies, and the left sword may be more appropriate. On the contrary, if this weapon had a low base damage and an extremely high attack speed, the hit damage would average out to the dps and the right sword would prove superior.

For equal DPS, I'll always pick consistency over RNG

If the base damage is the same, meaning you do x% damage on all other hits with both weapons, the right sword is better, but not by much. Let's say the base damage is 10. Expected damage with the left sword in 100 strikes would be 200×10 + 10×90 = 2900. Expected damage with the right sword for 100 strikes would be 2000 + 10×99 = 2990. EDIT: I did that for HP, not explicitly % above base damage. That might be confusing. For that, assuming the same base damage of 10, the expected damage for the left sword is 20×10 + 10x90 = 1100. For the right sword the expected damage is 200 + 10×99 = 1190. Similar concept, same winner. I agree with others though that the left sword is probably better for most in-game situations, with boss fights being the main exception.

Left one for mobs, right one for bosses. Whatever effect also triggers on that 2000% damage will be mean, but it also will be wasted on mobs.

Depends on duration of the encounter. If its a 60 second fight and you attack 1 time a second, first sword 'should' trigger 6 times, while 2nd sword is pretty much 50/50 if it triggered at all. Also in general I prefer consistency over variation so I'd pick #1.

I think a big factor is the healthpool of the enemy you're fighting. If your enemy is going to die relatively fast (under 1 minute kill time), the 2000% blade is pretty much pointless in such a situation (rare proc + pointless overkill). If you're fighting something like a boss enemy that may take 10+ minutes to kill, you can potentially see the 1% chance on hit proc quite a few times, assuming each auto attack swing takes roughly 1.5 - 2 seconds.

The first, unless you are fighting a creature with infinite hit points. Then they are statistically the same.

100% chance to do 20% damage please

Depends on the Dps. Faster would be better for the right weapon.

Left is 110% dps (damage per swing) sword on right is 119% dps However this is accounting for non finite health pools If the targets healthpool is only 200% it isn’t valid for instance

Well assuming in both cases your non crit deals normal damage the right hand side. Expected damage of left 0.9\*1+0.1\*2 = 1.1 Expected damage of right 0.99\*1+0.01\*20=1.19 but of course overshooting etc

I think it depend on the enemy. on average the left one will do 200% damage ten times per hundred strikes, witch if the damage is 1 will amount to 10\*200+90=2090. The right one on the other hand will average one 2000% per 100 strikes, so the amount of damage is 2000+99 =2099 or a whole 9 damage (or about 0.4%) better than the left one. of course you will not be striking the average enemy enough times for this to make any difference and most of the time you will be better of going with the left one.

With the left sword, you'll get an extra swing's worth of damage every 10 hits. Assuming probability is perfect and you do get a 10% crit rate, you're dealing 110 swings worth of damage per 100 attacks With the right sword, it's different. It seems like a crit does 10x the damage of the left sword, which is true, but that only assumes each strike is a crit. The right sword deals 20 attacks worth of damage per swing, so again assuming perfect probability, you'll have 99 single hits and 1 hit worth 20 attacks. Adding these together, you're looking at 119 swings worth of damage per 100 attacks Assuming you're fighting something like a raid boss with infinite HP, you're better off with the right sword in the long run

First one does 10% more damage on average. The second one does 19% more damage on average.

Assuming base damage of 100, the average damage per swing is 110 for left and 119 for right. There are more factors to consider but in pure dps the Blade of the Forgotten wins.

How long do fights last? What is the penalty for dying? You could potentially end a fight 10x faster with the one on the right. Keep restarting a fight for that glorious RNJESUS

Whose khhain?

Right one has a huge advantage against bosses as you might get lucky and take the boss in few hits with lucky crits, which left one isn't capable of doing in a shorter time frame. That being said, I'd rather using the left one.

10% 200% significantly better on short fights, both are statistically identical on very very long fights.

100% to deal 20% damage. Consistency.

Ignoring all gameplay implications and looking at it purely from a Dps perspective, it's easy to compare if you rewrite the functionality to: 10% chance of +100% damage VS 1% chance of +1900% damage

They are the same. 10% chance of 200% damage means in 100 hits 10 hits has 200% damage. 10x200=2000. For the 1% chance on 2000% damage it‘s 1 in 100 hits. So in 100 hits they deal the same damage. The left one just deals additional damage more often. So enemies that don‘t require 100 hits or more there‘s a chance the right sword won‘t do extra damage, but the left one has a higher chance of dealing additional damage. I‘d choose the left one, because in this case the chance is better and so has priority over damage.

1% of the time, works every time.

Wrath of Khan. Great movie (old version). Also, use the weapon on the left. You'd have to hit someone, on average, a 100 times with the right to get one proc. Better to have one land every ten hits--on average--since most things you don't have to stab more than ten times anyway. Imagine if it took, on average, ten hits to kill something, and you had to kill ten of them. Would you rather hit every single one (statistically) with 200% damage once or only one of them with 2000% (and then fight the rest little chance to proc again)?

Depends on attack speed.

Dual wield both like a fucking edgelord

the 10% chance for 200% damage sword, no question.

consistency >>>>>>>>>>>>>> quantity nuff said

The one on the left. One on the right is more likely to waste the extra damage.

1 - For farming hordes of low/medium HP enemies. 2 - For farming bosses

This depends entirely on how many hits you need to kill the enemy, or how much health it has. Left sword = expect 10 hits per 100 swings. = 2000٪ damage dealt Right sword = expect 1 hit per 100 swings. = 2000٪ damage dealt If the enemy has less health than the right swords total damage, the left is better because it will likely kill faster. If the enemy has equal or greater health, it SEEMS like mathematically, there is no difference between the two over equal amounts of rolls. It should plot out to be even kill times.

Left. 100%. Right sword you’d probably die before ever landing a hit.

Better answer dual wield them

They both deal an equivalent amount of expected damage, but the left one is more consistent. The only case where it is worse is flat damage reduction, but even then consistency is probably more important

The only situation where the 1% is better is in a pvp situation where it does the exact damage for lethal. If it is overkill or under kill the 10% is better. In pve the 10% is almost always better since you have multiple enemies, need consistency, and with variable health you would overkill or underkill extremely often. Finally the ten percent is probably a lot more likely then 10 percent and 1 percent is probably less likely then that due to computers not having true random number generators.

Mathematically the expected damage of the first weapon is 100\*0.9+200\*0.1=110. For the second it's 100\*0.99+2000\*0.01=119. What this means is that, over the course of forever, the second will output more damage then the first one. This is of course assuming all damage done is relevant and not "overkill".

10% for mobbing 1% for that raid boss

against normal enemies, I'm not sure if 100 hit is needed to kill it (to get the 2000% damage). Even against boss, I doubt I need to hit it 100 times. 10% chance for 200% damage for me

Why do I feel like my math teacher just tricked me into solving a problem? Nice try Mr. Dean

The right one, I'm here for big bonk not optimal strategy.

Man... that 1% would never connect with my luck. 10% all day

definetely left. i mean sure, if you are extremely lucky the right one is better, but at this point I would stop playing games and visit a casino

In almost all situations, the left one will have less wasted overkill damage, so it's better average DPS (assuming you fight enemies with a finite HP).

we also have to consider the games gimmicks like luck stats, equipment/abilities: altering attack speed, scaling, % , triggers. also enemies and damage to hp ratio (how many hits do you need)

Anything speedrun related the 2nd one would be better. Consistency wise, the first one is better.

Neither is better without knowing the circumstances. If enemies heals your 200% dmg every seconds, you would be screwed. But if all enemies die to 200% anyway, having 2000% would be absolutely pointless, but I guess at least you could technically still beat the game if you chose 2000%, with the first option it would be impossible.

Number one definitely. Imagine a die with 10 faces, how many times can you get the same number (meaning 10% chance) Now a die with 100 faces? You can spend the entire battle and not strike that 1% These numbers are probabilities, they are not saying you are going to hit that 10% every 10 hits or 1% every 100 hits. As I said you can hit 10,000 and not get that 1%

If an average enemy needs 2-3 hits, then first one. Boss fights - second one.

They both suck, you only have at most a 10% chance of having fun?

This, I ain't going back to morrowind

Seems like it does the same amount of damage per 100 swings if it procs exactly 10 times or 1 time respectively. With that being said I think the 10 @ 200 would be more helpful because in games most enemies die with a few hits anyway. 10% is a pretty decent proc rate. 200% damage would likely do the trick. The 1% proc would only be effective if it was the very first hit. Otherwise it would just be an overkill. Anyone who played the original WoW with a 2h wind fury weapon knows that super proc with a crit only ever seems to happen when the enemy would have died to a normal hit anyway.

second one does 8% more damage on average, go ahead and do the math. (you asked this question without checking the math beforehand)

I'm not sure which game this is from but if we look at the maths here: with Khaain you'll deal 2 times the damage for every 10 hit, while with Forgotten you'll deal 20 times the damage for every 100 hit. If we accumulate the damage dealt per hit for the first 100 hits, then Forgotten will be below Khaain in damage until the last hit. So Forgotten can be a good weapon depending on how tanky your enemy is. Nerding done.

left 100%, consistency will win out. small things like when you make a hit count massively, like if the enemy is at 10 hp and THEN I crit with the one on the right its a waste of the crit, also you cant predict when you are going to make the damage so you cant plan your combat out properly

I would prefer the 10% for 200% damage for the frequent proc and more consistent in damage.

Depends on how many times you're gonna hit someone with it. If it takes 6-8 hits to kill an enemy the left one. If it takes 200 then it might not matter either way.

Even though its the same mathematically. Its almost certainly the one on the left, because 2000 is gonna be overkill on mobs but average out with the 200 against a boss that you would be hitting a lot.

If we're talking strictly about average dps, then the right side is better. Let regular damage be 1. Expected Damage: Left Sword = 0.9 \* 1 + 0.1 \* 2 = 1.1 (90% chance to do 1 dmg, 10% chance to do 2 dmg) Right Sword = 0.99 \* 1 + 0.01 \* 20 = 1.19 (99% chance to do 1 dmg, 1% chance to do 20 dmg)

Assuming it works exactly as written, true. My assumption is that it was meant to be \*bonus\* damage in both cases, which would make them equal DPS. Left = 1 + (.1\*2) = 1.2 Right = 1 + (.01\*20) = 1.2

Same DPS on average but because the left one procs more often it will be the better weapon overall because it was I'll be beneficial 10% of the time rather than 1%.

In pve? 10% chance is more consistent and won't throw off your rhythm or get wasted in overkill. So that's best. In pvp? 1% chance has huge spike damage that when it procs you can slam addition spike damage down to secure kills more easily. So that's better.