APM=Skill -- A Monte-Carlo Simulation

General Discussion
1

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

Thus it is proven: APM correlates with MMR at such an insanely high rate that other factors only scatter the result at most +/- 13 APM in 68% of cases, +/- 21 in 95% of cases, +/- 36 in 99.7% of cases. So if you think you are some kind of “Strategy” or “Game Knowledge” GOD, then congrats, you netted yourself what a whopping +13 APM could have netted you instead.

APM==Skill=true.

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I have been stuck in Diamond for a long time.
So I just need to spam more APM to get to Master.
Good to know.

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Meh i watch King cobra he was GM and have like 120 apm now what

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Protoss is ridiculosly OP against Terran

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5

Not another “statistical analysis” that’s probably full of errors and leads to absolutely nothing…

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careful now, he’s a genius 0.01% top intelligence. He acquired untold wisdom in many disciplines by watching printers go BRRRRR. BEHOLD !!

10 Likes
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Thats not answer it complain

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It’s crystal clear that APM=skill since corr(APM, MMR)=0.65. This simply puts into perspective how much APM can vary from MMR on a per individual basis. In 68% of cases, it’s <=13 apm. But if you were to ask any random person, 99.99999999999999% of them will tell you APM doesn’t matter / how you use it matters. So yes this is yet another indication of just how much I outflank people in terms of IQ. They can’t even understand obvious, basic facts about the format of an RTS game, let alone mine data from a database, design a model and perform a statistical analysis on the data to estimate some parameters. They are egotistical and believe in the “tooth fairy of sc2” aka they believe game knowledge, strategy, etc are what make them good. Rather, it is APM.

SC2 is a game of grinding hours of ladder to get your reaction speed as low as possible and your APM as high as possible. Maru’s builds in the hands of Bronze league players will net Bronze league MMR and nonsense builds in the hands of Maru will win GSL’s. It’s all about the APM.

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Ever hear of an “anecdote?”

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I mean, haven’t you already demonstrated that literally no amount of data that doesn’t support your conclusion that Protoss is just fine will ever be valid in your eyes? I’m not saying he’s right, but I can throw a million other stats at you and it will bounce off you like science bullets on the superman of stupid.

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I’ve never doubted the raw numbers like big picture tournament win rates. Find someone else to project your delusions onto.

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apm is skill becuse i have 400 apm so it proof im very skill

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You mean like… the aligulac numbers that show Protoss being favored in PVT for the last 4 years? Glad you’re in agreement.

15

Why do you guys reply to this guy’s threads ??? That is exactly what he wants you to do. He is trolling now. He wants to instigate conflicts and arguing.

Ignore him. The less response he gets the less frequently he will come here.

16

its really fun for me to watch him. He is really good at trolling.

Stuff like:

Are little gems that would trigger a lot of people. Its like watching picasso painting, an artist going at it.

He ABSOLUTELY is trolling. There’s not a shadow of a doubt in my mind.

17

:clown_face: HONK HONK :clown_face:

I just beat a GM protoss using a 3 hatch before pool build into a drone pull allin out of which I macroed and beat mass carrier using queen ravager:

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

You can clearly see the three bases, drone pull and that the replay goes to 18 minutes:

https://i.imgur.com/ZOV4dlc.png

This is a complete nonsense build beating a GM. When tier 1 zerg units are hard-countering tier 3/4 ultimate protoss comp supported by mass shield batteries, while fighting off creep, we can definitively say: Strategy does not matter.

APM is all that matters. If you think basic facts about the game are “trolling” then I am sorry to tell you you have an extremely poor understanding of SC2.

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bronze builds include floating 600 minerals at the 2 minute mark and going 2 robo pumping immortals on one base while being supply blocked for half the game time on one base. Please beat a gm with that build and send me the replay.

I understand what you are saying and there is of course a very clear correlation between APM and skill. But you are clearly exaggerating it to get a raise out of people. I have no doubt a gm player could destroy me with half my APM just by better positionning and having superior macro.

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APM problem.

Has won top level games.

APM problem.

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you said bronze builds. A build order is having the same build as them at the same timings. Careful with the words you use, mister genius. But yes of course, just spending money well enough (mostly through APM) is enough to beat almost anybody. I believe that the cases where strategy won games are almost only true at the top 0.1% level. Everything below is just having more stuff.

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It’s true. He and his followers have long gone crazy. It’s not worth it after 1-2 responses, so I’ll be taking my leave on this thread. Stay safe every other sane person here