World of Warcraft

Response to Kelani and Hazel videos regarding spell variance

wow8 - Response to Kelani and Hazel videos regarding spell variance
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In recent videos released by Kelani and Hazel they touched on spell variance and since their videos have so much reach I thought it would be a good idea to supply some numbers behind the effect of the new spell variance. If you are not interested in the math skip to the plots below.

The blue post stated spells would have "5% variance". This could mean a few things, but because we cannot know let's assume it means that the range a spell can hit for has a 5% window. To make the math easy, let's assume we have a spell which hits for 19-20 damage uniformly. The average is 19.5, and you can see that 20/19 – 1 ~ 5% gives us the 5% window.

Each spell hit can be written as X = 19 + U(0, 1), where U(0, 1) is a uniform random variable between 0 and 1. Let D = sum_{k}(X_{k}), where D is the sum of 'K' of these spell hits. X is our damage for a single spell, D is the sum across an entire fight of K spell casts.

D is distributed as Irwin-Hall, which can be approximated with the normal distribution when K is not small (here I have chosen K >= 20 for all analysis where the approximation error is negligent). The approximation is to match the mean and variance of D. Now we have D ~ N(19.5K, K/12).

Now for various values of K, we can ask the question "What is the probability I lose y% or more of my damage relative to no spell variance". No spell variance would just be the mean damage. First we define D = 19.5K + sqrt(K/12)*Z, where Z ~ N(0,1). Then we write the probability question as P(D <= 19.5K * (1 – y)) => P(19.5K + sqrt(K/12)*Z <= 19.5K * (1 – y)) => P(Z <= -y * 19.5K / sqrt(K/12)), which is just the CDF of a N(0,1) evaluated at that loss ratio y and over K casts.

I am not an expert at estimating the number of casts that occur in a raid, so I have included wide ranges in the plots below. I think a good starting point would be a 20 person raid with 14 dps, assume 40 casts per minute, and a 6 minute fight length. Over the entire raid this would give us 14 * 40 * 6 = 3360 casts. Adjust for your expectations.

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The charts in the link show these probabilities across various inputs. Each line is a different loss probability (variable y above), so the line for 0.0025 is the probability you would lose 0.25% or more damage. The x-axis is the number of spell casts K. The y-axis is the corresponding probability.

So for example, let's look at the 2nd chart, and the orange line for 0.002. Assume we have 240 casts in a fight. The y-axis at that point is roughly 2.5%. In English this means that after 240 casts, there is a 2.5% chance that you will lose 0.2% or more damage relative to if no spell variance was in the game. Because this distribution is symmetric, another way to think of this is there is a 100% – 2.5%*2 = 95% chance that your damage will fall in the range , where mu is your mean damage (damage if no spell variance was in the game).

There are two charts, the one with larger numbers is to show what an entire raid team might expect while the one with smaller numbers is for individuals.

https://imgur.com/a/uVCeTty

Conclusion: Across an entire raid fight the probability you lose 0.1% or more damage is basically 0. For individuals there are higher chances to see 0.1% and 0.2% losses (because this is symmetric the probability of seeing damage gains is the same). These damage differences in some instances do move players up or down one rank on warcraftlogs, but these differences are incredibly small relative to other procs (crits, abilities, boss mechanics, etc).

Note: This assumes all spell casts are the same damage, which is not true. It's easy to see that you can just scale X by some scalar to match any other spell and keep the "5% variance". However this complicates the analysis, depends on the class, and likely has a small effect if any.

Source: Original link


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