I have been looking at a new stat created by Jeremias Engelmann at his Stats for the NBA page that is intended to look at the effect each player has on his teammate's shooting. Engelmann's stat was created using a ridge regression methodology on teammate's point per shot similar to the methodology behind RAPM.

At the top of the list of player's who have a positive influence on their teammate's shooting is Manu Ginobili followed by Channing Frye. But aside from getting players with a sunroof and a killer Euro step or a heart condition, I wanted to see if I could find any systematic patterns of player types that helped their teammates score.

The modeling process still has a ways to go, like looking at Engelmann's long term study and exploring some additional data. But the initial runs of the data created a moderately successful and stable model, with an R^{2} of .31, that gives us some clues as to what attributes have positive synergies for teammates on offense.

**We Might Kind of Understand Basketball**

A big plus, to me anyway, is that all of the factors that entered the model were things that we already think help an offense function efficiently, though there appear to be some interesting relationships. The principal component analysis (PCA) I ran showed a great deal of interaction between the variables, many of which are tied to positionality, so I tried to make trade offs to create the most stable and explanatory model.

**Assists and Ball Handling:**Easily the most consistent stat giving a positive influence to teammates on the court were those relating to assists. For assist percentage there was a visible diminishing return in influence as assist percentage increased. For that reason it was modelled as the square root of assist percentage. Assist to turn over ratio is highly correlated to assist percentage, but still demonstrated independent explanatory power, which I interpret as measure of ball handling ability.

**Usage:**In the PCA percent of shots from mid-range was highly correlated to usage. That appears to be picking up the contrast to Bigs with little range and catch and shoot specialists. Percent of shots taken from the mid-range came in as a positive influence on teammates, but was swamped by usage. Usage also appears to have a non-linear relationship to shooter influence, but showing positive returns. In other words, low usage players did not appear to hurt teammates efficiency, but high usage players (Over 20% did have an increasing positive influence).

**Spacing:**Everyone loves spacing, and in fact shooting threes appears to open up opportunities for teammates. Percent of shots as three pointers was consistently as positive as expected, though when corner threes and above the break threes were tested as separate measures, above the break threes were much more consistently positive. Lastly, I included offensive rebounds and three point shot rate as an interactive variable. The idea essentially is to use it as an indication of front court players who shoot the three, similar to the interactive between height and three point rate used by talking practice in their IPV model. When usage was not included in the model percent of shots taken at the rim was a negative influence, but as players with limited range tend to get fewer opportunities there is a significant inverse relationship between the two and it had no effect if Usage was included.

**Shooting Efficiency:**Last, though not least, effective shooting percentage, eFG, came into the model as a positive factor, suggesting the pressure a highly efficient player puts on the defense may create some additional opportunities for his teammates.

There was a great deal of variation not explained by the model, some of that may in the nature of the Shooting Influence statistic, in a two year regression only some of the 'noise' has been pulled out of the model in terms of assigning credit to the 'Shot Influencer.' The effect of the primary subsitutes for any player can alter the Influence value, and the fact that what we are looking for here is by definition the complimentary effects player attributes have on their team's offense means it is lkely that there are either diminishing returns or additional line-up synergies not visible in individual player stats.

In terms of overall effect, here are the coefficients from the version weighted by possessions using players with more than 400 possessions played:

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -2.51397 0.46894 -5.361 1.43e-07 ***

eFG 2.39807 0.81644 2.937 0.00351 **

AST.TO 0.25405 0.10119 2.511 0.01246 *

SQASST 2.13354 0.71380 2.989 0.00298 **

HighUse 7.19591 1.70729 4.215 3.12e-05 ***

Offthree 0.13244 0.05689 2.328 0.02044 *

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 54.19 on 386 degrees of freedom

Multiple R-squared: 0.31, Adjusted R-squared: 0.301

F-statistic: 34.68 on 5 and 386 DF, p-value: < 2.2e-16

I should also note that in terms of R2 I got a much higher results adding offensive rating (ORTG) into the model, but individual ORTG is a complex formula and the interaction effects became somewhat unstable, though ball handling and stretch measures still appeared to have positive relationships to 'Influence.'

All stats used in analysis from NBA.com, except the Influence measure from Stats for the NBA.

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