APM is not important

[lllIlIlIlIl-1983]

@Farbros-21406

But hey, everyone who does not believe a random guy on the forum, who makes paint pictures and present them as a proof is vaccine denier

By the way, I am not the only person to have published these findings. Some Blizzard employees did a slideshow presentation wherein they said the correlation between APM and win-rate was 0.63 (if memory serves). There are other papers (link below) which show the correlation between MMR and APM to be 0.65. I once calculated how much APM can vary on a per-individual basis for the corr(Winrate, APM) == 0.65 to be true. In 95% of cases, a player’s APM will vary from what’s predicted by their win-rate by no more than 26 APM. It’s simply a fact that APM is the majority of the skill in the game.

https://iccm-conference.neocities.org/2020/papers/Contribution_287_final.pdf

Side note: at the time I made that calculation, I didn’t have access to mass replays for data mining. I calculated that off of the figures from the slideshow, an average APM table for each league, and the assumption that APM was normally distributed. Well, this paper confirms my calculations (congats to past batz) and shows my assumptions were justified (congrats again to past batz). Source:

@lllIlIlIlIl-1983

APM=Skill – A Monte-Carlo Simulation (Definitive Edition)

Using data from SC2replaystats (n=2,892,019):

https://sc2replaystats.com/stats/analytics?group_by%5B%5D=player_division&matchup%5B%5D=PvT&matchup%5B%5D=PvZ&matchup%5B%5D=TvZ&format%5B%5D=1v1&game_type%5B%5D=AutoMM&metric_options%5B%5D=games&metric_options%5B%5D=avg_player_apm&metric_options%5B%5D=avg_player_mmr&date=January%201,%202020%20-%20December%2031,%202020

APM correlates with MMR with an R^2 value of 0.997 using a 2 term polynomial equation:

APM = 0.00000119 * MMR^2 + 0.05411901 * MMR^1 + -53.28971110

We can see that clearly in this chart:

https://i.imgur.com/u9CfWkd.png

Given this equation we can input an MMR value and get the average APM of a player (assuming no scattering). First we need an MMR distribution that matches the ladder. Experimentally this was determined as:

MMR ~ N(4500, 170)

This produces players >5000 mmr at a rate of ~0.2% which matches the parameters of GM league of the NA ladder. We can verify the sample size for the simulation (n=7,000) is large enough to achieve normalization using a histogram chart:

https://i.imgur.com/eSb5rrh.png

Using data from a Blizzard analysis available here:

https://conf.splunk.com/files/2019/slides/FN1698.pdf

We know the correlation between APM and win-rate is ~0.64. Using this figure, we can estimate the variance in APM on a per-player basis such that corr(APM, MMR)=0.64. We do this by taking an MMR value, plugging it into the polynomial equation above that calculates average APM assuming no scattering, then adding scattering, which is assumed to be normally distributed. Experimentally this was determined to be:

Scattering ~ N(0, 13)

Which has achieved the desired correlation of corr(Fapm(MMR)+scattering, MMR)=0.649, And can be seen on this chart:

https://i.imgur.com/YXbOVZb.png

The spreadsheet output of the simulation is available for download (CSV format):

https://controlc.com/1775c004

I’ll add a quick sub-note to this. This is calculated for players in masters league under the assumption that corr(MMR, APM+scattering)=0.65. When calculated for the ladder as a whole, the result is Scattering ~ N(0, 65). To contrast my simulation against the data in the paper I referred to previously:

https://i.imgur.com/QfIlmxx.png

As you can see, it’s spot on.

I’ll add another sub-note. Because MMR is a very dynamic system and players’ mmr values are always fluctuating up and down, it’s likely the vast majority of the variability in this correlation is due to the instability of MMR and not APM. I don’t have any figures on the variability of MMR so I don’t know exactly how much to attribute to it but we do know the correlation between average MMR and average APM is certainly > 0.65. It’s probably something like 0.8.