theoretical statistics

[jybrown]

Data Frame -- batter name -- batter attributes (age, L/R, weight, switch hitter) -- batter stats (up to that point in season) -- batter stat (life long) -- batter team stats (up to that point in season) e.g. winning percentage -- batter team stats (previous season) e.g. winning percentage-- starting pitcher -- starting pitcher stats (up to that point in season) -- starting pitcher stats (life long) -- starting pitcher team stats (up to that point in season) e.g. winning percentage -- starting pitcher team stats (previous season) e.g. winning percentage -- game informatioon (night/day, home/away, stadium) -- hit/no hit OR all walks -- number game during season

[herlands]

Model Types Generic batter models

• Use all statistics of batter-pitcher-teamA-teamB to build a model. This can be use to predict for any batter whether they will get a hit.

Individual batter models

• For each individual batters (with some basic sufficient amount of data) we can create individual models. We take all the data for that batter versus all pitcher-teamA-teamB. This can be use to predict for a particular batter whether they will get a hit. At this point we decided that we don't want to create specific batter-pitcher models because that would be very sparse.

Classification prediction

• Use all classifiers in sklearn to train whether a batter will get a hit. y=hit \in {0,1}
• Pick the point of the ROC curve with low FP rate and a statistically significant TP rate. We don't care really how high the TP rate is since we only need 1 or 2 players. Thus initially I would hope we can choose a FP < 0.05. This shows how to generate ROC for complex classifiers. We must extend this by then choosing the predictive rate appropriately to get our desired FP rate.
• Statistical significance can be crudely computed via ROC curves in each CV layer. See here for mean ROC via CV. We can extend that code trivially to compute the variation in ROC. This allows us to compute a (statistically questionable) confidence interval

Choice of player Each day we will choose 1 or 2 players with the following procedure: (1) Compute the mean( max (lower CI) ) over all batters (2) If >=2 players are above this value, choose the 2 players = max_{p1,p2} (lower CI) (3) Otherwise choose 1 player = max_{p} (lower CI)