We are less than two weeks into the NBA season. So far the early returns have been surprising. The Atlanta Hawks are currently 4-1. The Dallas Mavericks and Phoenix Suns have combined for only two wins, and one of these came from a game between these two teams. Of course it is early so Dallas and Phoenix fans should not despair. And Atlanta fans… well, its early. Our sample size is still very small so it is not clear that the Hawks are really enjoying a resurgence.
Still some games have been played. And we can look at the standings and see which teams have won and lost. What about the players? Ideally we would look at each player’s Wins Produced, but that is something I only calculate when the season is over. During the season I will use the simple metric, Win Score.
To compare players across the NBA we need to make a few simple adjustments to this measure. We need to consider differences in playing time, so Win Score per-minute is preferred. Position played must also be noted, so we should compare each player’s per-minute performance relative to the historical position averages. We could stop there, but I want to take one more step we briefly note in The Wages of Wins.
We note that there is a “short supply of tall people.” What this means is the NBA employs athletes who are quite tall and in the general population quite scarce. When your underlying population is small, the athletes a league employs will exhibit greater variations in performance. The reason we observe greater variations is because the supply of great athletes will be low and hence teams will have to fill out their rosters with less talented players.
As a consequence of this effect we observe competitive balance in baseball was much worse when baseball only employed white males from the Eastern United States. And as the theory predicts, the NBA has persistent low levels of competitive balance.
In terms of player evaluations, this means the standard deviation we observe in performance for big men – who are relatively scarce — will be larger than what we observe for guards. And this means that if all you do is compare a player relative to his position average, big men will tend to be a bit over-represented at the top of your rankings. To combat this problem one can calculate how many standard deviations above average a player has performed.
To illustrate, let’s look at each player in the current NBA season who has averaged at least 24 minutes per contest. First these players were evaluated in terms of Win Score and Win Score per minute. Then utilizing the position designations of Doug Steele (from Doug’s NBA & MLB Statistics Home Page), each player’s per-minute performance was evaluated in terms of the position average. And then, to account for the “short supply of tall people” problem, how many standard deviations each player was above or below the mean was calculated.
After these steps, we can create a list of the Top 30 NBA players. So far the top player in the NBA is Paul Pierce. His performance is 2.3 standard deviations above the average small forward. Chris Bosh, with a higher Win Score, Win Score per minute, and Win Score per minute adjusted for position, is still only 1.93 standard deviations above the average power forward. So he ranks second. Rounding out the top five are Carlos Boozer, Corey Maggette, and Kevin Garnett. Maggette is only averaging 25 minutes per game, so perhaps he should be getting more playing time as the season progresses.
Maggette is not the only one who could argue for more playing time. If we look at players with less than 24 minutes we find players like David Lee, Carlos Arroyo, Chuck Hayes, and Andrew Bynum. Each of these players are performing at least 1.5 standard deviations above the mean yet playing less than half the minutes available in each game.
Of course, teams have only played a handful of games. Some of these players will likely keep playing well, some will not. The best bets to stay towards the top are the players who have played well in the past. The best bets to drop are those who have not. Of course if you are placing bets on this information then you do not understand the lesson of sample size.
Our research on the NBA was summarized HERE.
Wins Produced and Win Score are Discussed in the Following Posts