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Now, I'm not taking sides on the PB Value issue here, but Ken what you describe isn't in detail enough to make sense to me.
How did you try to predict PB value in the first place? If you ran a regression using PB value as what you were predicting and other data (PAs, OPS, defense, etc) as the predictors, and then compared the sum of the predicted values with the actual values, you would, by definition, end up with an overall mean difference of 0.
What's actually important is not the sum of the differences between actual and predicted PB Value (the residual), but the standard deviation of the differences - this gives you a better sense of how confident you are with the assigned PB value for any single player. Of course even then, it doesn't really answer the question as to whether PB values mean anything, just how well you modeled it and how consistent it is...
Of course, you may have done something else...
Fred Cline