In my down time from the daily battles I decided to do some basic data collection to see how the new damages are distributed. It was clear right away that attacks often do damage on the high side or the low side and much less often towards the middle. I used Mathematica 7 to make histograms of the data. My ability to manipulate the ticks and bins proved less than impressive, but the histograms do a good enough job of showing the distributions.
I first decided to test Burn with an S/S Fiendish Imp and Missile with a P/P Warbot in the PvP queue. The range of Burn is 235 to 352, the range of Missile is 289 to 434. I gathered data for 122 Burns and 143 Missiles. When attacks were crits, weak or strong I scaled the data back to its initial damage before the modifier.
Burn PvP Histogram, 59 bins:
The mean of the damage was 298.1, the midpoint of the damage range is 293.5.
Missile PvP histogram, 37 bins:
The mean of the damage was 370.3, the midpoint of the damage range is 366.
The data gathering process was too slow in the PvP queue so I turned to PvE to speed up the process. I used an S/S Fiendish Imp and an H/H Emerald Shale Hatchling to test Burn. Both of their Burns hit in the 235 to 352 range. I battled Dragonbone Hatchlings in Dragonblight for quick data collection. I gathered data from 430 attacks.
Burn PvE, 59 bins:
The mean of the damage was 294.9, the midpoint of the damage range is 293.5. That peak is from 18 333 damage attacks and 10 334 damage attacks.
I changed the number of bins to see the data in some different ways.
Burn PvE, 12 bins:
Burn PvE, 4 bins:
There were a lot of rabbits as secondary pets so I was able to gather a lot of data on weak attacks. At one point I thought that weak attacks were leading to damage on the low side more often than they should. It turns out I was wrong, there were actually more high attacks with the weak data. It just goes to show how gathering data can easily disprove those things that “seem” to be true.
Burn PvE weak damage:
All of the crits except for one were on the high side (above the midpoint). There were 24 crits in 430 attacks, which is 5.58%. The average of the crits was 334.0.
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Actually it looks like there’s no “midrange” damage at all, which squares with how they’ve said they designed the system. The distributions for the high and low rolls don’t even have overlapping tails–it’s basically bimodal normal, so probably best to report the mean/SD for high attacks and mean/SD for low attacks because they’re two distinct populations, rather than talking about the overall mean.
I’m not sure I like this change. I wasn’t sure I liked it before it was implemented.
And while I know they were aiming to have the long-term average damage of an attack come out the same, why in the world did they decide a 50/50 high-low split was the way to do it, rather than preserving the old hit chances in the new model and bringing the top end of the range down? It makes the 25% hit chance buffs vastly less useful than 50% hit chance buffs, when previously a 25% hit chance was just as good if you wanted to prop up an 80% attack. (And Rain Dance was only better because it brought crit and forced the 50% attacks to 100%.)
I don’t think the designers at Blizzard can probability much better than the people on the forums.
Yeah, that makes more sense to find the upper and lower means and standard deviations.
The mean of the high hitting damage is 335.05, with a standard deviation of 11.24.
The mean of the low hitting damage is 249.50, with a standard deviation of 12.07.
These are very close to the actual means (337.7 and 249.3) and std (11.4) that I computed here:
Burn Damage Distribution
Oh, my low hitting crit from this data must have been an error in collecting data, since I’ve since found out that crits aren’t supposed to hit low. Either that or they really can hit low, but I would attribute the anomaly to my error before making claims that something isn’t working properly.
That’s intriguing. I’ll need to reread it in more detail but I like what you’ve done there.
I would say tentatively to watch out for another low-hitting crit. We’re told they’re not supposed to crit when they hit low, but that doesn’t mean the system works that way. 😛