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Bad math smugly explained
I really looked forward to this book after reading the review in The New Yorker. The reviewer's critical skills, evidently, do not extend to evaluating the merits of a logical argument.
There are so many logical problems with the analysis in this book, it is difficult to know where to begin.
I will limit myself to just a handful, among countless possibilities.
1) The authors find a correlation between the stability of a basketball team's roster and its winning percentage, and conclude that roster stability is a factor in producing wins! Classic problem of mistaking effect for cause. Clearly, winning teams are disinclined to make major roster changes, and losing teams are eager to. I was so amazed at this I reread it to see if I missed where they pointed this out. They didn't.
2) The authors show a correlation between more assists and winning percentage and conclude that assists help produce wins. Again, very silly. A team with a higher shooting percentage and fewer turnovers will of course get more wins and produce more assists. But the assists are not producing the wins - the shooting percentage is. Were these factors discounted? Not according to the text.
3) Most problematic, the authors define a way of measuring the value of players to a team, and then "prove" their method by summing these values, per player, across each team, and show that they do indeed predict the number of wins each team will get. What they fail to realize is that their method of apportioning value to a player necessarily sums back to team totals such as points per possession that we know correlate to wins per team. But this in no way proves that the apportioning is wrong. We could just as easily base each player's value "team's points while players is on the floor - opposing team's points while player is in the floor". Sum for all players on team, and you will find the team's points-per-game and the opposition's points per game, and you have just "proven" that your method of measuring a player's value is accurate.
4. In looking at rebounds, there is not even the slightest caveat that a player's rebounds per game are affected by who he shares rebounding responsibilities with. If you are in the front court with Shaq, you will get fewer rebounds, not because the other team gets them, but because your teammate does, so comparing rebounding stats between players across teams is highly questionable.
5. Ridiculously, they conclude that adding great players to your roster makes the other players worse not better (this is written as a great revelation, demythifying the common presumption that great players make teammates better). Adding great players indeed will make other players statistically less productive. They will take fewer shots, get fewer rebounds, fewer assists if a new ball-handler is added, etc. And so, according their evaluation method, the other players become worse. This should clearly tell them there is something wrong with their system, based so heavily on specific metrics of productivity. Instead, they simply accept the merit of their method as fact, and conclude that adding great players really makes other players worse!!!
The most frustrating thing about this book, however, for an analytically minded reader, is its smugness. They understand statistics. They have the answers. They are bringing them down from the mountains and explaining them to us idiot peons. All while their reasoning is so problematic.
I in no way am a supporter of the intuitive and nonsensical drivel one hears from so many sports coaches, players and commentators. I would have enjoyed a good, statistical, analytical study of the game of basketball. Unfortunately, this is not it.
July 2006 · Books