It occurred to me on the drive home that I was being an idiot. (a) If you want more games, raise the qualifying floor. (b) Riot may well be more interested in baiting players into ranked than in getting more play out of those already deep into ranked play.
If I had to guess, that's the direction I would bet. Why, what's your guess?
The basis of my guess is that the uncertainty falls with games played (I'm pretty sure that a 1600 with a 941-919 record is in the right spot; I'm less certain of a player with a 33-16 record). I also guess that the distribution of true skill mirrors the distribution of mirrored skill, which would tell us that there are more players with a true skill below 1600 than above it.
So it's a little bit more likely that a player with a 1600 ranking is slightly weaker than that but lucky than it is he is slightly stronger than that but unlucky.
Put another way; if you were to take the 10 1600s with 1000 games played, and add up their rating change over their next 10 games, I'd expect that number to be pretty close to zero. Try the same experiment with 50 games played, and I would expect their aggregate rating to drop, slightly.
Now, this is a model that has some clear problems on the low end; a player who goes 11-0 may have a 1600 rating, but I don't think we have a clue about his true rating from that data alone. You could probably get a better estimate by looking at historical data (what's the average rating of players who start 11-0?) or by putting together a decent model that correctly factors in the changing probabilities as a player gets closer to their true rating.
Cull Wrote:So a player who floats in 1600-1700 with 500+ games is better then a player with <50 games who got to 1600-1700?
If I had to guess, that's the direction I would bet. Why, what's your guess?
The basis of my guess is that the uncertainty falls with games played (I'm pretty sure that a 1600 with a 941-919 record is in the right spot; I'm less certain of a player with a 33-16 record). I also guess that the distribution of true skill mirrors the distribution of mirrored skill, which would tell us that there are more players with a true skill below 1600 than above it.
So it's a little bit more likely that a player with a 1600 ranking is slightly weaker than that but lucky than it is he is slightly stronger than that but unlucky.
Put another way; if you were to take the 10 1600s with 1000 games played, and add up their rating change over their next 10 games, I'd expect that number to be pretty close to zero. Try the same experiment with 50 games played, and I would expect their aggregate rating to drop, slightly.
Now, this is a model that has some clear problems on the low end; a player who goes 11-0 may have a 1600 rating, but I don't think we have a clue about his true rating from that data alone. You could probably get a better estimate by looking at historical data (what's the average rating of players who start 11-0?) or by putting together a decent model that correctly factors in the changing probabilities as a player gets closer to their true rating.
