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0 pointslmm5y ago0 comments

Show your working?

If you're matchmaking players against equal-ranked players, then each match is just +/- 50 points, you'll get a binomial distribution which tends to normal as n gets large (assuming a large player pool so each player's results are independent). If players play players with different ratings then that will tend to push their rating back towards neutral. You certainly don't get a geometric distribution because the rating algorithm is completely symmetric.

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dvt5y ago· 4 in thread

> each match is just +/- 50 points

This only happens in the rare cases where you're matching players against (exactly) equally-ranked players. You can mitigate this by always trying to match as "close as possible," but it's only a mitigation. Try simulating random matchmaking with Elo, and you'll get something like this: https://i.imgur.com/1Y08jUB.png (1000 players, 100,000 games). In my simulation, I set k (the Elo constant) = 50.

I think it's going to tend to a geometric distribution for reasons discussed here (which is another interesting and non-intuitive result): http://www.decisionsciencenews.com/2017/06/19/counterintuiti...

lmmOP5y ago

> Try simulating random matchmaking with Elo

I will. I was hoping you'd post the actual simulation details rather than more unlabelled graphs.

dvt5y ago

https://gist.github.com/dvx/e3311a984e14dca7c5eeb9214e0be3d5

Using: https://github.com/HankSheehan/EloPy (with a custom k-value of 50).

lmmOP5y ago

> with a custom k-value of 50

So you've patched this library somehow? Because when I run your code I get a result that's just full of 0 ratings.

But in any case I'm not at all convinced that your charts don't just show the normal distribution that we'd expect, just in some weird way. (Did you test your plotting methodology against some simpler rating system before using it to draw conclusions about Elo?). Plot a normal histogram, or a density plot if you're feeling fancy: https://towardsdatascience.com/histograms-and-density-plots-... . I'm betting the result is just the bell curve that we'd want and expect.

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LudwigNagasena5y ago

Elo can be negative, so this doesn’t apply.

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