In Tuesday’s post, I outlined a method of regressing a team’s record to the mean to estimate its “true winning percentage talent” (the trick is to add eleven games of .500 ball to their record, at any point in the season). In the comments, FP reader Dave wondered if we could incorporate last year’s true WPct talent into our talent assessment for this season, so I thought I’d run a quick regression to look at that.
My dataset was simply every game from 2003-2012 (including Monday night’s game). For each game, I recorded:
- Whether the game was a win, loss, or tie for the team in question. Wins got you a “1”, ties a “0.5”, losses a “0”.
- The team’s WPct talent estimate going into the game. So in the first game of the season, that’s (0+5.5)/(0+11)=0.500 for everybody; meanwhile, for an 11-4 team going into the final game of the season, it’s (11+5.5)/(15+11)=0.635.
- The team’s WPct talent estimate from the previous season.
I then set up a logistic regression to predict whether the game was a win or a loss based on the two WPct talent variables, this year and last year:
Deviance Residuals: Min 1Q Median 3Q Max -1.7686 -1.1489 0.1616 1.1429 1.7072 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -2.6936 0.1982 -13.589 < 2e-16 *** currenttalent 4.0297 0.3509 11.485 < 2e-16 *** prevtalent 1.3571 0.2666 5.091 3.57e-07 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 6712.4 on 4843 degrees of freedom Residual deviance: 6508.0 on 4841 degrees of freedom AIC: 6516.1 Number of Fisher Scoring iterations: 4
That means to predict your likelihood of winning any given game, you plug your WPct talent numbers from this season and last season into this formula:
WPct ~ 1 / (1 + EXP(2.693606 - 4.029688*(Current_Talent) - 1.357123*(Prev_Talent)))
It's important to note the size of the coefficients here -- the current WPct talent coefficient is three times as big as that of last season's WPct talent, so it has much more bearing on the prediction.
At any rate, here are the probabilities of winning any given game that this formula implies for this year's teams: