My last article on the Low Usage Myth, which explains that usage itself has no effect on wins produced, has at the time of this writing garnered 119 comments. Which is unusual because it's not even close to the most provocative thing I have ever wrote (I talked about amnestying Kobe almost 2 years before Mark Cuban brought it up!). Most of the discussion revolves around the way the value of an assist is incorporated in the WP model, and reading the comments, it has become clear to me (or, us, since much of this content is paraphrased from Dr. David Berri, creator of the model) that most of the commenters do not understood how this works. This article is an attempt to clear some of that up.
Does it matter if all the assists went to Karl?
Firs, I get the sense that people think this is just a mindless team adjustment, where some value for an assist is just allocated across all players. That is not really the process.
Dr. Berri began by looking at how a player's shooting efficiency is impacted by his teammates' assists. The theory was that as assists went up, an individual would shoot better. To test this, he regressed a player's shooting efficiency in a given year on his shooting efficiency the previous year (this is an attempt to control for talent), his teammate's assists, and a variety of other factors that might influence performance. What he found was that as a player's teammates had more assists, the player shot better. This impact was then incorporated into the model so that for each player, he was credited for the impact of his assists and debited for the impact of his teammates' assists. So this is not just some team adjustment.
Let's revisit one statement: "as a player's teammates had more assists, the player shot better." Notice that this doesn't say "as a player is assisted more"; the statement describes a correlation observed over time, not a determination of cause and effect.
Nowadays we have new data on how many shots a player had that were assisted upon. This is fine. But the method people are suggesting to incorporate this effect reveals they did not understand how this was all done in the first place. First, one would have to establish with this new data the value of an assist. Dr. Berri used over 30 years of data to determine the value. How many years of data do we have with assists being directly allocated to beneficiaries? Are we sure that the value of an assist would be the same using this data? Would it be greater or lesser if you evaluated them using this new method? That coefficient detailed in step 2 of the adjustment process? It does not just come out of our sleeves. Would it be the same number?
Once you have a model at the player level, you would then need to repeat the steps above. You need to credit a player for his assists and debit the impact of teammate assists. Again, all of this requires a bit more work (than just leaving comments in a blog post with some simple algebra).
Furthermore, this part of the adjustment bears reqeating:
Note: In the above formulation, a teammate’s adjusted field goal percentage does have a small and positive impact on a player’s shooting efficiency. One should note that the effect is small, and the statistical significance of the effect does depend upon the specific formulation of the model. In other words, this result is not as robust as the result we see for defensive rebounds and assists. So it is ignored in the calculation of Wins Produced.
Note that this does not mean that Kobe Bryant (who isn't assisted much) is "penalized" in comparison to Tyson Chandler (who is assisted a lot). Rather it means that players who produce assists at an above average level get their WP48 adjusted higher, and players who do not assist much will get their WP48 adjusted lower. To understand this, re-read steps 5, 6 and 7:
Multiply step (4) by the impact points have on wins 0.032586. This allows us to see how much of a player’s production of wins should be credited to his teammates.
Sum step v across all players on a team.
Allocate the outcome of step #6 across all players on a team by the percentage of assists on the team that are credited to each player.
In other words, the process is to figure out how much of wins produced for a whole team is from assisting, and then distribute those "wins" on a weighted basis to all players, based on the assist percentage. The higher your assist rate, the more credit you get. This is important. This is not about how much credit a player gets for the points he scores. This is about how much credit each player gets for the points that all of his teammates scored. Most of my commenters are understanding this backwards.
In other words, take a hypothetical team, where all of the assisted buckets are scored by Tyson Chandler, no one else on the team ever benefits from an assist. We could then calculate that X% of Chandler's points are from assists. Those X assisted points are worth N wins. Then we divide up N wins according to who had the most assists.
In contrast, take a hypothetical Knicks team where all of the assists are spread out perfectly evenly, i.e. each player benefitted exactly equally from all the assists. We could then calculate how many total points all the players had that resulted from assists. Those X points would, again, be worth N wins, and we would divide up the N wins according to who had the most assists (in fact, this is the assumption that WP currently makes).
In both scenarios, nowhere does any player get extra credit for high FG% or less credit for low FG% (at least, for the purpose of this adjustment; those things certainly impact one's production), it is strictly about who gets the credit for the assists and how much credit that is. The adjustments many people are suggesting might change the total "point" value of all assists (for instance, it might lead to data that suggest that passing to Chandler is worth .6 points, but passing to Kobe is worth .7, or something like that). It's possible that therefore, the sum of N wins that the team then divides up would be different.
So, to take Kobe for an example, messing with this adjustment will determine how much his WP is impacted by his assists. However, it would have no effect whatsoever on how Kobe's points scored would impact his WP.
Now, you might want to argue about this very impact. You might argue that passing to Tyson is worth more (or less) than passing to some other player. You might want to argue that Tyson Chandler's points scored should be worth less because they are all assisted on. And if so, why don't you do the work to "improve" the model? In other words, if you think the current model is incorrect, do the work to generate a new model. And show that each change you are suggesting is supported by some empirical evidence (in other words, a simple retrodiction test is not going to be enough to justify your work).
But those aren't the arguments I see being brought forth in that thread of commenting doom.