The great Bill James writes:
In sports, mathematical analysis is old news as applied to baseball, basketball, and football. . . . But it has not yet been applied to leagues. . . . Rather than beginning with the question “How does a team win?” – the query that has been the basis of all sports research to this point – what if we begin by asking “How does a league succeed?”
Take the problem of what we could call NBA “sluggishness.” In the regular season, players simply don’t seem to be playing hard all the time. . . . The NBA’s problem is that the underlying mathematics of the league are screwed up. . . . In the NBA, the element of predetermination is simply too high. Simply stated, the best team wins too often. If the best team always wins, then the sequence of events leading to victory is meaningless. Who fights for the rebound, who sacrifices his body to keep the ball from rolling out of bounds doesn’t matter. The greater team is going to come out on top anyway. . . . Everybody knows who’s going to win. Why do the players seem to stand around on offense? Why is showboating tolerated? Because it doesn’t matter. . . .
So how should the NBA correct this? Lengthen the shot clock. Shorten the games. Move in the 3-point line. Shorten the playoffs.
If you reduce the number of possessions in a game by giving teams more time to hold the ball, you make it more likely that the underdog can win – for the same reason that Bubba Watson is a lot more likely to beat Tiger Woods at golf over three days than he is over four. It’s simple math. The longer the contest lasts, the more certain the better team is to win. If the NBA went back to shorter playoff series – for example from best-of-seven games to best-of-three – an upset in that series would become a much more realistic possibility. A three-game series would make the homecourt advantage much more important, which, in turn, would make the regular season games much more important. The importance of each game is inversely related to the frequency with which the best team wins. . . .
I see James’s point (and I continue to enjoy his writing style, so memorably and affectionately parodied by Veronica Geng a couple of decades ago), but I disagree with the remedy of adding more randomness. I don’t think I really want to see the best team lose a lot. One appeal of a top-level sporting contest is seeing top players perform at their peak. I mean the number of people that use online casinos because they are confident that they’re about to see the top players give an amazing performance is huge! Despite the popular models of the “binomial, p=.55” type, which team is “best” is not generally defined. In baseball, it depends so much on who is pitching; in football, some new plays can make the difference. Not to mention practice, discipline, teamwork, and getting some sleep the night before the game. Ideally (to me), the outcome of a game is unpredictable not because the worse team has a good chance of winning, but because it takes a special effort for a team to be the best. (Even in a deterministic game such as chess, the “best” (according to rankings) player does not always win.)
These issues lead into a larger question about scoring systems in games, a paradox of sorts that continues to confuse me: on one hand, you don’t want the outcome to be random, on the other hand, you want the team that is behind to have a reasonable chance of catching up. I remember when I was a kid, my dad said that the tennis scoring system (games, set, match) was better than the ping-pong system (first player who gets 21 wins) because in tennis, you can always catch up. On the other hand, in a competitive game ping-pong, you should never be down 20-0 in the first place. There must be some principles here that can be stated mathematically, but I’m not quite how to state them. Perhaps someone has already looked into this.
P.S. I feel awkward disagreeing with Bill James, whose writings were one of the reasons I went into statistics. But I’m disagreeing with him about basketball, not baseball, so maybe it’s ok.