In The Wages of Wins: Taking Measure of the Many Myths in Modern Sport, authors David Berri, Martin Schmidt and Stacey Brook construct a metric for determining the productivity of each player in the National Basketball Association, known as Win Score. The Win Score formula is as follows:
Win Score = Points + Possession gained (rebounds, steals) – Possession lost (turnovers, field goal shots, ½ free throws) + ½ Offensive help (assists) + ½ Defensive help (blocks) – ½ Help opponent (fouls)
They find that this metric does a pretty good job at predicting the number of games that a team will win over the course of the season. A strong point of this method is that it recognizes that the players that score the most points are not always the most productive. For example, a player who scores 30 points but makes only 25 per cent of their field goals is not a very efficient scorer, and may well have harmed their team’s chance of winning. However, the formula has come in for criticism for allegedly favouring rebounders over scorers. Under the formula, a top scorer like Allen Iverson is considered to be only an average player, while rebounding king Dennis Rodman is considered to be a superstar on par with Michael Jordan. Now I don’t subscribe to the theory that scoring should be seen as an inherently harder skill to master. As far as I am concerned, a player can be productive through being either a dead-eye shooter, a monster on the boards or a pin-point passer. My main concern is that the Win Score doesn’t weigh up these attributes equally. To see why, imagine a simplified version of basketball in which two players, A and B, take turns shooting from a designated spot on the court. After each shot, two other players, C and D, go up for the rebound. If C rebounds the ball, A takes the next shot, and if D rebounds the ball, B takes the next shot. If A makes a shot, B takes the next shot, and vice versa. Let’s say the statistics at the end of the game are as below:
Player A: 0 for 6, 0 points
Player B: 2 for 3, 4 points
Player C: 4 rebounds
Player D: 3 rebounds
Team E (Players A and C): 0 points
Team F (Players B and D): 4 points
Team F wins.
Now under Win Score, Player C would be the most productive player (4 points), followed by Player D (3 points), Player B (1 point) and Player A (-6 points). However, I would argue that Player B is clearly the most productive player. The reason that Team F has won is because Player B was much more effective at shooting than Player A. If A and B had shot with the same accuracy:
Player A: 2 for 6, 4 points
Player B: 1 for 3: 2 points
Player C: 4 rebounds
Player D: 2 rebounds
Team E: 4 points
Team F: 2 points
Team E wins
In this case, Player C is the most productive player, and Player D is the least productive. This is because, with A and B being equally effective at scoring, C’s extra rebounds are responsible for getting Team E over the line. (Under Win Score Player C would still be the most productive, but Player D would be more productive than Players A and B.)
Or to put it another way, if each team performs each skill equally well, nobody should win or lose. The difference between winning and losing is determined by differences in skill levels.
Now of course in a real game of basketball all players are able to both score and rebound, but the key point still remains that a player’s ability to perform a skill should be measured relative to everybody else’s ability to perform that skill. But with Win Score a player’s ability to rebound is overvalued relative to a player’s ability to score. Berri and company do calculate a Position-Adjusted Win Score, which could arguably take account of this fact, but that limits a player in a particular position to a particular role when in reality they may have another role in which they help their team (e.g. a point guard may be an efficient shooter rather than an efficient passer). Another argument is that Win Score does account for a player’s ability to score relative to other players’ abilities simply because it includes both points scored and field goals missed. However, that assumes each player takes their shots from a designated spot and with the same amount of defensive pressure. Allen Iverson might have made 40 per cent of his shots and Dennis Rodman might have made 55 per cent of his shots, but Iverson may still be a more efficient scorer because if Rodman had the same role as Iverson and was facing the same defensive pressure he might have only made 20 per cent of his shots. Or to put it another way, if Rodman had been a shooter of average skill he might have made 70 per cent of the shots that he had, and he hurt his team by only shooting at 55 per cent. Win Score does not account for this possibility.
Another problem is that Win Score gives full credit to the rebounder for gaining a possession and attributes full blame to the shooter for losing a possession. The latter is probably not so much of a problem because if a shooter should not always receive full blame for losing a possession (for instance, if the rest of his team is standing around twiddling their thumbs and he’s playing one-on-five) he probably should not always receive full credit for scoring the basket either (for instance, if the power forward sets a bone-shattering screen on the defender). But again this is going to overvalue players who happen to be very good at rebounding at the expense of the players who are very good at other skills.
It is difficult to see how any metric could address either of these problems. The first is hard to solve because we do not know the counterfactual while the second is hard to solve because it relies on intangibles. The Win Score metric is on the right track to working out the key factors between winning and losing. The tricky part is deciding who is truly responsible.
 This method for writing out the formula was actually used in a power point presentation by Joe Price and Justin Wolfers.
 By my reckoning, the final point margin is determined entirely by a team’s ability relative to the other team to create scoring opportunities and the team’s ability relative to the other team to capitalize on scoring opportunities. The first term would incorporate rebounds, steals and turnovers, while the second term would incorporate shooting percentages and assists. To work out a player’s productivity you would have to work out that player’s contribution to each of those two terms. Er, good luck.