Sunday, March 4, 2012

Credit for scorers in Win Shares

Last post was all about the 3 pointer. For this one, lets travel back in time to 1978 and look at only 2 pointers. In addition, free throws are excluded from this discussion. The base credit for scoring in win shares is (points - missed shots). This tells us that a player will earn positive points so long as he shoots better than 33%. Some would tell us that this is terribly wrong and will overrate high volume, low percentage scorers.

This confuses absolute production with marginal production. My comparison is to the Wins produced metric from the Wages of Wins blog, although I don't mean to pick on them, there may be others who do it that way. The metric is (points - shot attempts), so a player will only add positive value if he shoots more than 50%.

Let's build a model:

Our player can shoot 60% if he only takes about 6 shots a game, 500 on the season. He mostly takes layups and dunks in transition, or short jumpers when a double team leaves him wide open. He can opt to take more shots, but if he does the opportunities are not as easy. For the next 100 shots, he only makes 57%. If he chooses to further expand his range, and take shots despite more defensive contest, he only makes 54% of the next 100. And so on. By the time he's up to 2400 shots, he's only able to make 3% of the last, most difficult 100 shots taken.

To maximize his win shares rating, he would take 1300 shots total. He only made 36 of the most difficult 100, and to take another 100 he'd only make 33, and drop his rating slightly. But at 1300 shots, his cumulative shooting percentage is a quite healthy .517. What if we observe this player shooting 1800 shots for a .448 percentage? Win shares will still show a positive total for him, but not as good as if he had stopped at 1300 shots and a .517 percentage.

Wages of Wins will give this player maximum credit up to the point where his last, marginal shots are made at 50%. This happens when he takes only 800 shots, at a cumulative rate of .578. Win shares will say that the 800 shot, .578 player has as much value as a 1900 shot, .434 player. Both are inferior to the 1300 shot, .517 player.

(Let's put some faces to the stats: This is saying Larry Bird > Dominique Wilkins, and Larry Bird > Robert Parish)

The average team last year took 6660 shots, which is 1332 per position. Shots MUST be taken, because there is a 24 second clock in the NBA. If you take a below average number of shots at a high efficiency, then one or more teammates have to make up for this by taking more shots.

I would fully endorse the Wages of Wins model if a team had the option of sitting for 5 minutes in the halfcourt, passing the ball around waiting for the perfect shot. Take away the shot clock and we might see a 19-18 final score again. Since we have the shot clock, taking a shot does not have the opportunity cost that Wins Produced assumes. They give credit for the absolute number of steals, rebounds, assists, etc. It is inconsistent to do this and then only give credit for points when they are scored at an above average rate.

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