# Prediction is hard, starring the Gay trade

After the Rudy Gay trade happened, we heard from several commenters who were eager to use the trade as a simple way of testing our Wins Produced based predictions. For example, there’s this one by commenter Andrew:

...this will be a v-e-r-y interesting test of the veracity of what on the surface seems to be irrefutable evidence that Toronto was killed in this deal. Calderon, except when his hamstrings were particularly bad a few years ago, has always been an advanced stats darling. But has he been a winner?….

And this one, by commenter Shrinidhi:

…I definitely like this trade as it sets up a (very uncontrolled) test of WP’s ability to measure the value of certain types of players. While Calderon is clearly terrific offensively, conventional wisdom and some more quantitative analysis (http://ascreamingcomesacrossthecourt.blogspot.com/2012/10/jose-calderon-example-of-how-wins.html) claim that Calderon is terrible on defense and that WP overrates him by setting his team defensive adjustment be equal to that of his teammates. If indeed Calderon plays significant minutes and Detroit does not improve significantly, would you consider re-evaluating the defensive measurements involved in wins produced?

Both pose the question: if what you thought would happen doesn’t happen, does that mean Wins Produced is flawed?

The answer is no, it probably just means that I predicted the minutes incorrectly. This is because our win predictions are largely based on minute projections for each player. Wins can be broken down simply into the following formula: Wins = Efficiency (WP48) x (Minutes Played / 48). If you increase either efficiency or minutes played, you increase your wins. For the season so far, efficiency varies between -1.068 and 0.452. Minutes, on the other hand, has varied between 1886 and 3 this season. This is a much larger range (even when we take into account that minutes get divided by 48). And minutes are much harder to predict. WP48 is very consistent from season to season, but minutes can vary wildly depending on rotations, injuries, suspensions, and trades. For example, for the three teams involved in that trade, we have already seen the following:

• In the Raptors’ last four games (one of which happened before the trade, when Amir Johnson was injured), Aaron Gray has played an average of 28.5 minutes per game, as compared to an average of 5.0 minutes per game over his previous 44 games.
• In the Grizzlies’ last two games, Ed Davis has played an average of 7.4 minutes per game, as compared to an average of 24.2 minutes per game over his previous 45 games.
• In their first game with Jose Calderon playing, the Pistons often played with three point guards on the court at the same time. Additionally, four players who have spent the bulk of their career playing PG played a total of 106.5 out of the teams’ 240 minutes played.

It’s worth pointing out that the circumstances mentioned above are likely to change — Gray probably isn’t going to average over 20 minutes for the rest of the season, Ed Davis is probably going to average more than 10 minutes for the rest of the season, and the Pistons will probably reduce the percentage of minutes played by their point guards — and the sample size is terribly small. But already we can see how that has affected the wins of each team involved in the short term:

• Aaron Gray is getting a lot of minutes at centre, which has allowed Amir Johnson to slide over to power forward. This has temporarily mitigated the loss of Ed Davis, at least until Andrea Bargnani returns.
• Ed Davis is coming off the bench as expected, but is stuck playing behind Darrell Arthur, who has played almost three times as much as Davis since the trade and has produced negative wins this season. This negates a large portion of the wins the Grizzlies stood to gain in the trade.
• Playing so many point guards so many minutes — particularly the ones who don’t produce efficiently (Rodney Stuckey, Brandon Knight, and Will Bynum) — negates the addition of Jose Calderon.

When we can’t predict minutes very accurately — and it’s a very hard thing to do — our win predictions can end up way off-base. This is true whether we are using Wins Produced, or Win Shares, or PER — or anything else. If we knew how many minutes each player will end up playing beforehand, then we could give you a much more accurate answer. But we can’t. As the season goes on (and barring any further trades or injuries) we’ll get a better idea of the rotations and we’ll do a better job a predicting minutes for the rest of the season. But until that time, everything is just an educated guess.

Predictions are hard.

- Devin