4 ms·

> 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

by dvt 6y ago

> 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 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/counterintuitive-problem-everyone-room-keeps-giving-dollars-random-others-youll-never-guess-happens-next/ http://www.decisionsciencenews.com/2017/06/19/counterintuiti...

LudwigNagasena 6y ago
Elo can be negative, so this doesn’t apply.
lmm 6y ago
> Try simulating random matchmaking with Elo I will. I was hoping you'd post the actual simulation details rather than more unlabelled graphs.
- dvt 6y ago
  https://gist.github.com/dvx/e3311a984e14dca7c5eeb9214e0be3d5 https://gist.github.com/dvx/e3311a984e14dca7c5eeb9214e0be3d5 Using: https://github.com/HankSheehan/EloPy https://github.com/HankSheehan/EloPy (with a custom k-value of 50).
  - lmm 6y 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-in-python-f6bda88f5ac0 https://towardsdatascience.com/histograms-and-density-plots-... . I'm betting the result is just the bell curve that we'd want and expect.
    - dvt 6y ago
      > So you've patched this library somehow? Yes, as mentioned, I set the k-value to 50 on this line: https://github.com/HankSheehan/EloPy/blob/master/elopy.py#L80 https://github.com/HankSheehan/EloPy/blob/master/elopy.py#L8... Author decided to do something fancy which will only work when number of players is less than 1/2 * starting Elo rating. > 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. As mentioned, you end up with a geometric distribution. I covered a similar phenomenon in a blog post I wrote last year[1]. See Theorem 3.3 in this paper: https://kconrad.math.uconn.edu/blurbs/analysis/entropypost.pdf https://kconrad.math.uconn.edu/blurbs/analysis/entropypost.p... But in short, the geometric distribution has maximal entropy over (0,∞) given a known mean (in our case, the mean will always be 1000). [1] https://dvt.name/2017/07/10/confusing-math-with-morality/ https://dvt.name/2017/07/10/confusing-math-with-morality/
      - lmm 6y ago
        > As mentioned, you end up with a geometric distribution. I covered a similar phenomenon in a blog post I wrote last year[1]. See Theorem 3.3 in this paper: https://kconrad.math.uconn.edu/blurbs/analysis/entropypost.p.. https://kconrad.math.uconn.edu/blurbs/analysis/entropypost.p.... But in short, the geometric distribution has maximal entropy over (0,∞) given a known mean (in our case, the mean will always be 1000). Another reply already told you that's irrelevant to Elo, because Elo can go negative (and if it couldn't then the mean wouldn't always be 1000). It's probably going to be normal, and drawing an actual histogram of a simulation like yours comes out looking pretty much like a bell curve: https://imgur.com/YBDp4uI https://imgur.com/YBDp4uI . As far as I can see none of your claims about Elo stand up. Why do you think you've shown the things that you're claiming?

by dvt 6y ago

LudwigNagasena 6y ago

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

lmm 6y ago

> Try simulating random matchmaking with Elo I will. I was hoping you'd post the actual simulation details rather than more unlabelled graphs.

dvt 6y ago
https://gist.github.com/dvx/e3311a984e14dca7c5eeb9214e0be3d5 https://gist.github.com/dvx/e3311a984e14dca7c5eeb9214e0be3d5 Using: https://github.com/HankSheehan/EloPy https://github.com/HankSheehan/EloPy (with a custom k-value of 50).
- lmm 6y 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-in-python-f6bda88f5ac0 https://towardsdatascience.com/histograms-and-density-plots-... . I'm betting the result is just the bell curve that we'd want and expect.
  - dvt 6y ago
    > So you've patched this library somehow? Yes, as mentioned, I set the k-value to 50 on this line: https://github.com/HankSheehan/EloPy/blob/master/elopy.py#L80 https://github.com/HankSheehan/EloPy/blob/master/elopy.py#L8... Author decided to do something fancy which will only work when number of players is less than 1/2 * starting Elo rating. > 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. As mentioned, you end up with a geometric distribution. I covered a similar phenomenon in a blog post I wrote last year[1]. See Theorem 3.3 in this paper: https://kconrad.math.uconn.edu/blurbs/analysis/entropypost.pdf https://kconrad.math.uconn.edu/blurbs/analysis/entropypost.p... But in short, the geometric distribution has maximal entropy over (0,∞) given a known mean (in our case, the mean will always be 1000). [1] https://dvt.name/2017/07/10/confusing-math-with-morality/ https://dvt.name/2017/07/10/confusing-math-with-morality/
    - lmm 6y ago
      > As mentioned, you end up with a geometric distribution. I covered a similar phenomenon in a blog post I wrote last year[1]. See Theorem 3.3 in this paper: https://kconrad.math.uconn.edu/blurbs/analysis/entropypost.p.. https://kconrad.math.uconn.edu/blurbs/analysis/entropypost.p.... But in short, the geometric distribution has maximal entropy over (0,∞) given a known mean (in our case, the mean will always be 1000). Another reply already told you that's irrelevant to Elo, because Elo can go negative (and if it couldn't then the mean wouldn't always be 1000). It's probably going to be normal, and drawing an actual histogram of a simulation like yours comes out looking pretty much like a bell curve: https://imgur.com/YBDp4uI https://imgur.com/YBDp4uI . As far as I can see none of your claims about Elo stand up. Why do you think you've shown the things that you're claiming?