Alright, so I'm looking to build a small program (C# and XAML) that, essentially, does this:
Generate array of players. Each player has a current rating and a true rating. I set current rating to 1200 as a starting point right now; I've also tried setting it to true rating and the average of the two. True rating is what their skill level actually is. Their true rating is calculated based on percentages from the current League of Legends rating system; generating an array of 970 thousand generates results very similar to the data from here: (removed due to URL limit - but trust me, the results are very similar). This array is of length specified by the user. If need be, sort the array from smallest to largest.
Play X number of games, again specified by the user. This is done by taking the array of players (which is sorted by Current Rating after being created) and running through it in groups of 10. The first five are on team one, the second five are on team two. It then takes the True Rating of these players and calculates an expected chance to win using the Elo system. It generates a random double and compares it to the expected chance to win; if the number is lower, team one wins - otherwise team two wins. I then update the rating of the players via, again, the Elo system - giving the winning team a score of 1 and the losing team a score of 0. I use a K value of 36 (but have tried 12, 24, and even higher ones) and an F value of 400. After going through the entire loop of players (which I have conveniently forced to be a multiple of ten), it sorts the array - again via current rating.
This, if my understanding of the Elo system is correct, runs properly. However, it doesn't seem to work. I have a running test telling me how many players of the full array are within 100 current rating of their true rating. I would expect some portion of the population to be outside this range (as probability is not always going to go in their favor), but a full 40-45% of the population is outside of this range. I also have it outputting the maximum difference between true and current rating - and I have never seen this drop below 500! It hovers between 550-600, occasionally going over or under.
I'm at a loss as to what to change - I've fiddled with the K and F values, where I start all the players, etc. but nothing changes the fact that eventually a good 40% of the population is outside the range. And it isn't that I have it playing too few games - it's now run through over 60 thousand games and the problem never disappears or really fluctuates.
The full C# code, including everything except the XAML file and the Player class (pastebin is being very slow and I can only post two links, so I can't link to the XAML file):
http://pastebin.com/rFcZRL84
The Player class:
http://pastebin.com/4cJTdTRu
I guess my question is did I do anything wrong? Is there a problem with the way I implemented the system, or is it just that Riot uses a significantly modified Elo system? I don't think it's the latter, as that still wouldn't explain the massive true and current rating differences to me, however.
