Thursday, September 20, 2007

How to Calculate Probability of Winning Based on In-Game Stats

A reader e-mailed me asking how to calculate the P(win | in-game performance) I've been posting each week and thought I would share with the rest of the class. It's a simple logistic regression model that calculates ln(p / 1-p), so any of you can try it at home.

Below is the set of weights, B, a Nx1 matrix. Take your matrix of inputs X, where X is an MxN matrix of M games with N inputs.

P(win) = e(B*X) / ( e(B*X) + 1 )

Bias coeffiecient 0.25522 (Bias input is an input always equal to 1)
Home rush off YPC 0.36376
Away rush off YPC -0.28054
Home pass off YPA (includes sacks as pass atts) 0.60824
Away pass off YPA - 0.64551
Home sack rate allowed -0.0091494
Away sack rate allowed 0.0098494
Home third down off. conversion rate 0.037002
Away third down off. conversion rate -0.042268
Home penalty yards -0.016932
Away penalty yards 0.016868
Home int. rate thrown -0.25664
Away int. rate thrown 0.27914
Home fum. rate given (includes all fumbles not just lost fumbles, rate is by completions and rush attempts) - 0.26644
Away fum. rate given 0.28195


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