WR and Moving Up-- a Simple Model

[uuDevil]

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.

[spamuell]

This is interesting, but I don't really think that [ QUOTE ]

1) The parameter S=pfr%/vp$ip is a measure of skill.

[/ QUOTE ]

is very close to being true, although there will be a relation to skill level. A LAG with a vpip of 50% and pfr of 30% would have a higher skill rating than a TAG with a vpip of 16 and pfr of 9.

Also, my S value is about 0.6, which would have me winning astronomical amounts at any level.

[uuDevil]

[ QUOTE ]
Also, my S value is about 0.6, which would have me winning astronomical amounts at any level.

[/ QUOTE ]
This would only be true if you are winning astronomical amounts at your current level. But you're right that this measure is flawed, especially at the extremes.