I'm not a mathematican. I don't claim this simplistic approach has any real predictive value. I just did it for fun.
Problem: Predict a player's win rate on moving to a different game level.
Given: average pfr% and vp$ip numbers for limits from $.5/1 to $10/20.
Source of some of this is here:
stats at different levels, posted by joseki
Assumptions:
1) The parameter S=pfr%/vp$ip is a measure of skill.
2) Expected WR is proportional to skill level difference:
WR= WRh*(Sh-Sg)/Sp, where
WRh= hero's winrate at current game
Sh= hero's skill level
Sp= Skill level of average player at current game
Sg= Skill level of average player at a given game
Results:
The expected WR for a player who currently plays $2/4 with a WR of 2 BB/100, pfr%=7% and vp$ip=20% is shown in the Excel chart below (yellow line). I haven't checked this against any actual player results.
