I wanted to see how different one number player metrics lined up with how NBA coaches actually coach. So, I ran a series of simple linear regressions comparing the score on various player metrics to minutes player per game last year. Since each metric takes a slightly difference approach, it could tell us a bit about what NBA coaches value. The idea is similar to a Ari Caroline piece over at Wages of Wins last year comparing how their metric, Wins Produced, stacked up with minutes. Here I have added PER, ASPM, xRAPM and Win Shares.

The results are very preliminary but too interesting not to share. Among the caveats are that currently the WP number is a a three year average while the others are for current the year. Though I ran the 2012-2013 Win Produced numbers on a slightly different data set and got very similar results. Also, the two year ASPM actually did better than the single year, suggesting, sensibly, I think, coaches have prior beliefs coming into the season and adjust somewhat slowly to unexpectedly good or poor performances.

In any case, in the table below I have R squared numbers, or, goodness of fit, from each simple regression I ran.

R2 Player Metric and MPG | ||||||

WP48 | WS | PER | ASPM | xRAPM | 2 Yr ASPM | |

PG | 0.335 | 0.262 | 0.441 | 0.494 | 0.359 | 0.535 |

SG | 0.093 | 0.148 | 0.345 | 0.388 | 0.266 | 0.459 |

SF | 0.095 | 0.068 | 0.215 | 0.348 | 0.311 | 0.391 |

PF | 0.004 | 0.057 | 0.325 | 0.247 | 0.214 | 0.213 |

C | 0.145 | 0.144 | 0.394 | 0.335 | 0.348 | 0.339 |

ALL | 0.088 | 0.101 | 0.298 | 0.333 | 0.24 | 0.34 |

The yellow highlighted background cells are the highest correlation for that metric. Astute observers may notice a pattern; all of the stats agreed most with the minutes allocations given out at the Point Guard position. This supports the idea that the Point is the best defined and understood position in the game right now. Since I made the claim that's how I am going to interpret it.

The red highlighted lines are the position each stat agreed least with the minute allocation. In this case, the Power Forwards are the opposite of the Point Guards where each metric save PER had their lowest fit on that position. For PER the worst fit was at small forward.

Looking for the best fitting metric by each position, Daniel Myers' ASPM in both the single year and two year weighted average correlated the best to minutes assigned for Point Guards, Shooting Guards, and Small Forwards. While John Hollinger's PER fit the best for both Power Forwards and Centers.

By the way, my unofficial outlier awards goes to Ben Gordon, whose game all of the metrics hate and yet still managed to see 21 minutes a game. And the hyper efficient Jeremy Evans, loved by all except xRAPM and Ty Corbin getting just under six minutes a game.

So what does that say about the advanced metrics and about coaches?

Not all of the metrics are created equally in terms of preditive ability (or retrodictive ability). A blog called the Sports Skeptic did a retrodictive test a while ago, using the advanced stat scores from the year before applied to the playing minutes the next year. The author found that of the ones I am looking at PER had the lower predictive abilities. But confusingly ASPM had one of the highest predictive abilities.

So, coaches can judge guard's abilities, other than Ben Gordon, but not bigs? Probably too early to say that.

Also, I am currently working on some multiple regressions, which will include more years. So far, the plus/minus stat xRAPM has come in as a positive combination with each of the other box score based metrics, the next step will be to break up plus minus into its offensive and defensive components to see if my hunch that it is the defensive side of xRAPM that is adding value is correct. Also, games played, which I included as an indication of injuries, has come in has a positive contributor improving each metric's score.

As for the metrics, it looks like analytics movement still has a ways to go in gaining actual influence, Wins Produced and Win Shares in particular.

## Comments

You can follow this conversation by subscribing to the comment feed for this post.