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Win Rate as a function of PR difference - XG Feature

Posted By: Maik Stiebler
Date: Saturday, 22 August 2015, at 7:07 a.m.

In Response To: Win Rate as a function of PR difference - XG Feature (AdamStocks)

Many thanks for taking the time for answering me. Unfortunately, I'm still not happy.

With a ramp, max and min are pushed further apart in the same timeframe, giving a wider rating range even though the PR range of the player pool can be assumed to be fixed.

I'm still not sure how this works. Is this an effect of the ramp per se or, as is my best guess, just of players on the ramp introducing more noise into the pool than the other ones? In other words, if you had two hypothetical servers with the same population, both without a ramp in the usual sense, but one of them (I will call it the 'permaramp' server) exchanging double the normal amount of rating points per match, as if all players were on a certain point on the ramp all the time, would you expect that you would observe a wider rating range on the permaramp server than on the 'normal' one? If I may answer myself, I think that the rating range would indeed be wider on the permaramp server due to increased fluctuations, even if each individual player's rating were on average over infinite time equal on both servers. But a linear regression should deal with the noise, so in that case you would not expect to find a steeper Elo(PR) function on the permaramp server with your methodology, would you?

Then again, another insight from afore-mentioned article is that at any point in time, players with high ratings tend to be overrated (i.e. they tend to be on a lucky streak), while those with low ratings tend to be underrated. I can believe that players' habit of inviting those close in Elo rating to themselves may stabilize the noise, so to say, so that you would see a wider range on the permaramp server even regarding time-averaged ratings. Is that idea somewhere close to the one behind what you were writing about here?

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