Log5 Questions

Phil Birnbaum explores the log5 method invented by Bill James and wonders if there are cases when it doesn’t work. He discusses a game where the winner is determined simply by the height of the players, so there is no randomness in a game.

Now: when a .600 team plays a .400 team, what happens? The log5 formula says it should win 69.2 percent of those games. But, of course, that’s not right — it will win 100 percent of those games, because it’s always taller.

For height, the log5 method fails utterly.

——

What’s the difference between real baseball and “height baseball” that makes log5 work in one case but not the other?

I’m not 100% sure of this, but I think it’s due to a hidden, unspoken assumption in the log5 method.

When we say, “Team A is a .600 talent,” what does that mean? It could mean either of two things:

— A1. Team A is expected to beat 60 percent of the opponents it plays.

— A2. If Team A plays an average team, it is expected to win 60 percent of the time.

Those are not the same! And, for the log5 method to work, assumption A1 is irrelevent [sic]. It’s assumption A2 that, crucially, must be true.

So far, so good. In fact, if you run simulations of biased coins, determining a winner where one coin is heads and one coin is tails, log5 does a great job of predicting the winning percentage of the coins.

Birnbaum goes on the postulate that the less luck involved in a game, the more log5 underestimates the winning percentage of the better team. In other words, the further one gets away from a random process the less log5 matters. So in basketball, where talent swamps luck more than in baseball, log5 does not tell us as much.

I wonder, however, if we just need to do a better job of estimating the true talent level of teams in basketball. I suspect in baseball the true talent level of most teams lies between .400 and .600. It’s quite possible in basketball that the true talent level lies between .300 and .700. For example the Golden State Warriors are currently outscoring their opponents 114 to 102. It strikes me that in the NBA, the first 80 points for a team don’t matter. Everyone is going to get to 80 points in a game. So in effect, Golden State is beating opponents 34 to 22. If you plug those numbers in the Pythagorean formula, GS is a .705 team. The 76s are a .213 team. Log5 says the Warriors should beat the Sixers nine out of ten times. Birnbaum feels that underestimates the Warriors against the Sixers. I don’t think so. The two losses by the Warriors were to Dallas, whose point averages make them a slightly better than .500 team, and Milwaukee, a team that allows six more points than they score, a .363 by my seat of the pants Basketball Pythagorean formula. I could see Philadelphia winning one out of ten over a long-term tournament against the Warriors.

from baseballmusings.com http://ift.tt/1n9UDhN