Scourge Quantified

Scourge Quantified

Scourge will do damage based on how much HP the foe has left. This makes quantifying the benefit of scourge very difficult, but I was determined to quantify it, as I needed that quantification for future projects. This guide lists the methodology I followed to arrive at this quantification.

The Formula

The formula to calculate scourge is the following:
MINMAX[(Health% - 10) * 100 / (50 - 10), 0, 100] < rand() * 100

In simple terms: once the foe hits 50% hp, he starts to gain a 2.5% chance to scourge for every additional percentage of hp lost until it reaches 100% chance at 10% HP.

Expectations

I browsed the forums to be prepared with a bit of experienced player perception. One thing I gathered from many posts was that everyone agrees that a high HP foe will have more chances for scourge, while low HP ones, like minions, may rarely see a useful application of scourge due to how little time they spend on that HP rate.

So, whatever I do should reflect that minion combat benefits less from scourge and higher level combat also should benefit more, and finally, usage of high DS attacks should see less benefit from scourge.

Although this is an expectation it’s not a goal, I’m not attempting my process to achieve this, but if it does, it will be a good thing.

The Methodology

At first I figured I’d come up with some super smart formulae that would allow me to see how much, in average, Scourge would grant. There are so many variables though that even if I came up with the formula, I’d have little way of testing it. So instead of coming up with a formula I decided to start another way, I went through a procedural approach. This means I wrote code with logic that would simulate a player using one attack against a specified critter until it died, all the wile collecting overkill and scourge proc information.

This application takes various parameters and runs automatically for various level ranges. The parameters are:

• Rank: This modifies if I’m fighting a minion, boss, AV, or even a GM.
• Damage Scale: For simplicity I don’t simulate an attack chain, instead I just use one attack that has a fixed damage scale, and no recharge or cast time. The idea is just to quantify attacks, not time. This also means that regeneration is not accounted for, although if anything, I theorize it will just smooth things and reduce overkill rate.
• Enhancement: I can change this but by default I use 95% damage enhancement. The code automatically will convert this to DOs and TOs depending on the level range, and entirely ignore enhancements from level 1 to 9.

I wont go too deep into the code other than say the program will attempt to kill 100000 foes of the specified rank for each level and then accumulate the following stats:

• Total Damage: This is how much damage was tossed, includes what you attempted to do, overkill, scourge, anything that came out of you before the foe hit zero.
• Damage Applied: This is how much damage you activated, this basically ignores scourge.
• Overkill Damage: This is the total damage that went past zero. Scourge is accounted in it, as is overkill caused by regular attacks.
• Scourge Overkill: This is the total overkill caused by scourge. This one is tricky. If the foe has 2 HP, and the attack is for 3 points of damage, and you scourge, you do a total of 6 points of damage, but it won’t consider Scourge to have done overkill because the base damage overkilled first.
• Attacks used: This is the count of attacks that were used the whole fight.
• Scourges: This is the amount of scourges that took place during the fights.
• Scourges Wasted: These are scourges that did nothing; the base damage killed the foe.

With these numbers I then go to Google Docs and do some comparison to get some averages and try to guess, in average, how much scourge helps you after all wasted scourge is eliminated from the equation.


Run Results

As noted I pushed the data into Google Docs. The resulting document can be seen here.

I setup 5 tabs, the first one simply summarizes everything on a compact, easy to analyze, way.

On this tab you will see 4 blocks of data, each summarize one of the tabs on 5 rows. Each row represents a 10 level range: 1-10, 11-20, 21-30, 31-40 and 41-50 with columns for each foe type faced: Minion, Lt, Boss, EB, AV and Boss.

The other 4 tabs contain this information in more detail with every single level range being displayed plus additional stats like scourge rate, wasted scourge percentage and overkill due to scourge.

Looking at the data, all expectations seem to have been met. In many situations minions don’t even get to see any benefit out of scourge at all, while huge HP bags get to see, especially at high levels, around 20% damage boost.

Normal chains of tier 1 and Tier 2 attacks on minions may yield between 8% to 13% boosts, but using 12 second recharge powers with 2.12 or higher DS may result in absolutely no boosts.

With similar rules, the lt yields between +13% to +15% against lts with only +6% if using the 2.12 ds attacks.

Bosses are between +18% and +19% with +16% if you use 2.12 ds attacks near the end of the fight.

EBs seem to start to show resistance to attack selection keeping everyone between +19% and +20% despite attacks.

AVs and GM seem to always be at +20% and +21% respectively.


Conclusion

If forced to say a simple number, I’d be forced to still split it between ranks but say:

• Minions average +7% damage.
• Lts average +11% damage
• Bosses average +17.7% damage
• EB average +19.7% damage
• AV average +20.3% damage
• GM average +20.7% damage

Acknowledgements

I want to thank Arcanaville for helping me with the formula for corruptor scourge damage.

I also want to thank Supernumiphone for pointing me in the direction of an existing thread discussing player perception on the benefit's of Scourge.

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Incredible analysis. I had always used 25% as a "in the ballpark" rule of thumb, but I had always considered that about 1/5 of that would be wasted due to overkill. That you managed to quantify that, and in fact apply it to the relative strength between various player attacks and the HP of minions at the various levels gives far more detail than I could ever have expected.

It's nice to know that around 20% is a good value as a hard and fast rule for Bosses and higher, with the percentage against Minions and Lts varying depending on whether you choose to use your weakest attacks to take advantage of Scourge.

Now if only Fury were as easy to quantify.

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Awesome work.

I have one last thing you might try for interest: Ideal results.

You would make your program smart enough to figure out the best attack to deal the lowest overkill deathblow via scourge. Given the way Scourge chances increase as the target gets weaker, I'd say this should just kick in when the enemy can be single shotted by it - so against minions and Lts primarily (Though bosses should show a little change) have them be pinged down via random attacks until any of the standard blasts can one shot them if scourge triggers, then use the "best" (Least overkill but still fatal with scourge) attack rather than the random order in use until then.

This would simulate a player who has become very comfortable with their corrupter and is able to pick out attacks to try to trigger scourging for final blows without doing too much overkill. I try to do this, when I can clearly see a stronger blast is going to overkill I'll go for my tier 1.

Basically, it would be the corrupter "ideal" damage bonuses without going completely overboard and unrealistic on attack chains (Figuring out the exact attack order to use to get the best possible chances of scourge == unrealistic, imo).

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You would make your program smart enough to figure out the best attack to deal the lowest overkill deathblow via scourge.

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Well, I may be misanalyzing this, and Starsman can say if I'm making a mistake, but I think likely this would have no effect on just using the best possible table for that rank of foe. He's not really considering DPS or time to kill in these tables, merely what portion of the damage is overkill. If we assume that that portion is the same for every single table until the point where the foe dies, that is, there is no overkill prior to where the foe dies, then the only difference would be in the last shot. That difference would then be in the appropriate table.

So your best results would be for the 0.60 table, or if you want to say it is more likely you would use ONE of your weaker two powers (and they are not likely to both be available at all times) then an average between 0.60 and 1.0.

Best Results:

Minions (1-10) ~ +3.5% damage.
Minions (10-30) ~ +11% damage.
Minions (30-50) ~ +13% damage.
Lts ~ +15.5% damage
Bosses ~ 19% damage
EB ~ +20% damage
AV ~ +20.5% damage
GM ~ +21% damage

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[ QUOTE ]
You would make your program smart enough to figure out the best attack to deal the lowest overkill deathblow via scourge.

[/ QUOTE ]

Well, I may be misanalyzing this, and Starsman can say if I'm making a mistake, but I think likely this would have no effect on just using the best possible table for that rank of foe. He's not really considering DPS or time to kill in these tables, merely what portion of the damage is overkill. If we assume that that portion is the same for every single table until the point where the foe dies, that is, there is no overkill prior to where the foe dies, then the only difference would be in the last shot. That difference would then be in the appropriate table.

So your best results would be for the 0.68 table, or if you want to say it is more likely you would use ONE of your weaker two powers (and they are not likely to both be available at all times) then an average between 0.68 and 1.0.

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Doing it would accomplish two things, I think.

First, it would show more realistic numbers for a skilled scourge user - you're not going to be pinging the enemies down with a certain attack constantly, and there's going to be more variance in when their life reached deathblow range.

Second, if any of those attacks tend to come up at just the wrong point for overkill, even the .68 damage attack could be wasting a noticable fraction on a minion.

If nothing else, it would be interesting to see if choosing your attacks to deathblow just as scourge triggered was better for not overkilling than just spamming your weakest on enemies near death. I don't know if much would change, it just seemed like a last thing to set up and he has most of the tools in place already.

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Second, if any of those attacks tend to come up at just the wrong point for overkill, even the .68 damage attack could be wasting a noticable fraction on a minion.

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It's interesting to note that according to the table, even the weakest attacks are usually overkill against a Minion. You can't get more than about a 14% bonus in any condition. This is because for the most part, even a basic attack is a large portion of a minion's HP.

I've actually underestimated this effect myself. However, it applies to Scrapper/Stalker/Controller Criticals and Brute Fury, as well. So I'm not sure it compares Scourge unfavorably to those Inherents.

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[ QUOTE ]
Second, if any of those attacks tend to come up at just the wrong point for overkill, even the .68 damage attack could be wasting a noticable fraction on a minion.

[/ QUOTE ]

It's interesting to note that according to the table, even the weakest attacks are usually overkill against a Minion. You can't get more than about a 14% bonus in any condition. This is because for the most part, even a basic attack is a large portion of a minion's HP.

I've actually underestimated this effect myself. However, it applies to Scrapper/Stalker/Controller Criticals and Brute Fury, as well. So I'm not sure it compares Scourge unfavorably to those Inherents.

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You asked what it might show to do specific attacks for less overkill, I was answering that. It has no relation to being favorable or unfavorable to criticals or fury, simply to seeing if an "ideal real world" test achieved different results (It's informative however it turns out, imo) than simply hitting a minion to death with one attack.

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Jade is right, the most skilled ever scourger would indeed get the results from the .6 table, and then again that is if he is a rad or is willing to waste endurance from AoE, but that second option would be highly counterproductive. After all, using your lowest damage attacks tend to also mean your slowest ones, at that point you are not optimizing for damage but for endurance efficiency.

The 1.0 table is the most realistic one to look at because that’s the weakest attacks most blast sets have.

Again, do note that if you want to maximize scourge for kill speed, you may desire to spam that damage even if overkill (everyone does overkill after all, that is unavoidable so you won't be on a true disadvantage.)

Trying to maximize for scourge usage only results in better endurance/damage ratios, not faster damage.

As for adding a true attack chain calculator to the mix (right now i just test spamming one attack without recharge or cast time or regeneration) may help to compare how scourge may benefit some sets more than others but also would require a much more complex combat simulator code that would take a lot of time to develop.

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Jade is right, the most skilled ever scourger would indeed get the results from the .6 table, and then again that is if he is a rad or is willing to waste endurance from AoE, but that second option wold be highly counter productive. After all, using your lowest damage attacks tend to also mean your slowest ones, at that point you are not optimizing for damage but for endurance efficiency.

The 1.0 table is the most realistic one to look at because thats the weakest attacks most blast sets have.

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This is not automatically true. Let me present a scenario:

You're pinging an enemy down with the .6 attack. It gets to a point where the 1 attack with scourge would fully kill the enemy with only a tiny (If any) bit of damage overkill. But you use the .6 attack twice instead. It scourges both times, and the enemy is left with an almost full overkill scourge. That means that the scourge on the 1 scalar attack yielded close to 100% effective bonus damage, but the scourge on the .6 scalar attack only yielded 50% effective bonus damage (Total over the two hits).

Would the % chance of the 1 damage attack scourging be better for damage boost from scourge than the overkill damage from the .6? I think in some situations yes. That is what the test would identify. But it would require an intelligent selection of that final blow, not just pinging with the weakest attack -- because when you're just pinging every single case, of course the .6 is superior in the long run.

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You're pinging an enemy down with the .6 attack. It gets to a point where the 1 attack with scourge would fully kill the enemy with only a tiny (If any) bit of damage overkill. But you use the .6 attack twice instead. It scourges both times, and the enemy is left with an almost full overkill scourge. That means that the scourge on the 1 scalar attack yielded close to 100% effective bonus damage, but the scourge on the .6 scalar attack only yielded 50% effective bonus damage (Total over the two hits).

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This is assumes that the foe has an HP which is a multiple of the 1.0 factor. (after true damage is factored in) While this may be the case, it is probably only likely at particular levels. (For instance, foes might have 3, 3.2 and then 3.5 times the damage factor at each of three levels, just for an example)

It is just as likely that the 0.60 attack would do exactly the damage needed and the 1.0 attack would end up creating overkill. Or, even more likely, it is totally random. It will become even more random as you mix in various attacks with different damage scales.

I'm guessing that this is why there are often such severe jumps in the percentage tables, like when it jumps from 14% for 0.60 at levels 30-40, and then goes DOWN to 13% at 40-50. The HP levels from 40-50 may not be quite as evenly divisible by 0.60.

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[ QUOTE ]
You're pinging an enemy down with the .6 attack. It gets to a point where the 1 attack with scourge would fully kill the enemy with only a tiny (If any) bit of damage overkill. But you use the .6 attack twice instead. It scourges both times, and the enemy is left with an almost full overkill scourge. That means that the scourge on the 1 scalar attack yielded close to 100% effective bonus damage, but the scourge on the .6 scalar attack only yielded 50% effective bonus damage (Total over the two hits).

[/ QUOTE ]

This is assumes that the foe has an HP which is a multiple of the 1.0 factor. (after true damage is factored in) While this may be the case, it is probably only likely at particular levels. (For instance, foes might have 3, 3.2 and then 3.5 times the damage factor at each of three levels, just for an example)

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It simply assumes that after the previous damage the foe has that much health remaining. This means it could be ideal for any of the three (four for rad) blasts, which is why it would need to select the one that would have the least overkill.

Starsman: The exact same scenario applies to the 1 scalar attack with regards to the next strength up, just replace the .6 with 1 and 1 with 1.64.

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The charts are interesting, but I have a couple of questions since they weren't listed in the methodology:

1. What damage slotting were you using in the attacks? If you are using base damage only, then it seems clear that with the lower damage attacks producing a higher usefulness from Scourge, slotting will reduce the effectiveness equally as much because you're now no longer using a (for example) 0.6 DS Neutrino Bolt, with 95% slotting it would be 1.17.

2. In a similar vein, it should represent a higher percentage of increase against higher level mobs - how difficult would it be to set it up with +1 (90% effectiveness), +2 (80% effectiveness), and +3 (65% effectiveness) mobs to show the levels that a Corruptor will run into during normal game play with the various difficulty settings?

Both of those would affect things, especially when you're looking at increasing the lowest possible damage that you're doing through slotting, or reducing the highest by fighting higher level mobs.

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Woops i missed answering that last question!

I can’t remember clearly now, but I think I used variant enhancement for level ranges (can’t tell exactly the level range but sure before lvl 10 there were no enhancements and at 25+ everything was 95%)

And now I remember why I never replied to this, you made the second question hard! Got the numerics but got derailed.

I made this table that denotes at what point a foe matches the next rank.

For example, you will notice that level 1, fighting a foe that is +4 equates a level 1 lt (HP wise, he hits MUCH harder) while at level 50, a +3 Minion equates a level 33 Lt HP wise (as if you fought him at even level) so the purple patch may do something but won’t make scourge jump to the next rank easily. By the time you find something that will take you to the next rank, it will also likely kill you with eyes closed.

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