Kobe is the G.O.A.T II, but his 3 botched possessions in the final 2 minutes of game 2 round 2 against the Thunder gave me some ass pain.
Specifically, the two back-to-back turnovers by Bean turned a game that was essentially `jiggling the jello,’ into a notch in the L column.
Let’s fire up [R]
For Kobe in 2012, We’ll look at turnovers as a response with some standard statistics as covariates.
I’m using the `XML’ package to pull the data straight from the NBA’s website.
Some Visuals of the raw data and covariates we’re going to work with.
Fitting a poisson regression model:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.86954 0.57768 3.236 0.00121 **
MIN -0.02198 0.01549 -1.419 0.15581
AST 0.05072 0.02937 1.727 0.08423 .
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 66.398 on 66 degrees of freedom
Residual deviance: 62.364 on 64 degrees of freedom
Besides the intercept term, we see that the number of assists is the most significant covariate. Intuitively this makes sense. When a ball handler is trying to make plays, the potential for a turnover is associated with the attempted pass. (Nothing groundbreaking)
However, I’m surprised at the negative coefficient in the number of minutes. I would have thought the more minutes played during a game would contribute to physical and mental fatigue which would associate with the propensity for carelessness. But, the coefficient isn’t statistically significant.
Before we dive further, we look at standard diagnostic plots which utilize deviance residuals.
We’re good to go.
Conducting a Likelihood-Ratio (Deviance) Test we compare the difference of residuals between $H_0$ and $H_s$ to a Chi-Squared distribution.
We simply use the residual deviance (this is quantity of interest) and it’s respective degree of freedom from the summary output above.
We see that with a large p-value, the Deviance Test says that our model is appropriate in modeling the expected value of Kobe’s butter fingers. Note, the alternative model is the saturated model. That is, a model that fits the data exactly.
Finally, we’ll look at how the observed data meshes with the fitted data.
A more detailed model would incorporate a time index. We would thus be able to look at Kobe’s propensity for butterfingers during clutch time. What’s Kobe’s expected turnovers as a function of covariates when the game’s on the line.
Lastly, for those in the know, we really should have treated “ASSISTS” as some sort of ‘offset.’ That is, we don’t want to estimate the effect of assists associated with turnovers. We saw the ‘obvious’ result in the above discussion when assists had a positive association with turnovers. We should consider a ratio of .