Who’s “best” and how do you know it?

So suppose you have your basic Major League Baseball (MLB) structure, consisting of two leagues having three divisions of five teams each, each of which plays a 162 game, strongly unbalanced*, schedule. There are, of course, inherent quality differences in those teams; some are better than others, when assessed over some very large number of games, i.e. “asymptotically” **. The question thus arises in your mind as you ponder why the batter feels the need to step out of the batter’s box after each pitch ***: “how often will the truly best team(s) win their league championships and thus play each other in the World Series”. The current playoff structure involves having the two wild card teams play each other in a one game elimination, which gives four remaining playoff teams in each league. Two pairings are made and whoever wins three games advances to the league championship series, which in turn requires winning four games.

I simulated 1000 seasons of 162 games with leagues having this structure. Inherent team quality was set by a normal distribution with a mean of 81 wins and a standard deviation of ~7, such that the very best teams would occasionally win about 2/3 (108) of their games, and the worst would lose about that same fraction. Win percentages like those are pretty realistic, and the best record in each league frequently falls between 95 and 100 wins.

1) The truly best team in each league makes the playoffs about 80 percent of the time under the current system, less when only four teams make it.
2) That team wins its league championship roughly 20 to 30 percent of the time, getting knocked out in the playoffs over half the time. It wins the whole shebang about 10 to 15 percent of the time.
3) Whenever MLB expands to 32 teams, in which the playoff structure will very likely consist of the four division winners in each league and no wild card teams, the truly best (and second and third best) teams in each league will both make the playoffs, and advance to the World Series, less frequently than they do now.

This type of analysis is generalizable to other types of competitions under structured systems, at least for those in which the losers of individual contests live to fight another day, or if they don’t, are replaced by others of the same basic quality. The inherent spread in team quality makes a very big difference in the results obtained however. It’ll apply very well to baseball and hockey, but not so well to the NBA, for example.

So the next time an MLB team wins it’s league, or the World Series, and you’re tempted to think this means they must be the best team in the league (or MLB overall), think about that again. Same for the NHL.

* Currently, each team plays around 3 times as many games against each intra-division opponent as inter-division opponents, not even including the 20 inter-league games (which I’ve ignored in these analyses, assuming all games are within-league).
** These records are conceived of as being amassed against some hypothetical, perfectly average team. This team is from Lake Wobegon Minnesota.
*** It is perfectly OK to think other things of course, and we need not worry about the particulars of the language embodied therein.


6 thoughts on “Who’s “best” and how do you know it?

  1. That’s fascinating! I’ve often wondered the same thing, but never tried a Monte Carlo for a full season. It’s easy enough to work out the odds for a 5- or 7-game playoff series, and it tells you that, just as the race is not always to the swift, the winner of the series is not always the “better” (in theory) team. Especially when, as is often the case, the teams are fairly evenly matched — a series will increase the chances for the better team to come out on top, but it’s not a huge enhancement. E.g., a 60% chance to win one game translates to a 71% chance for winning a seven-game series.

    By the way, how did you choose the odds for a game, given the “team quality”? Was it as simple as taking the ratio of the number of expected wins?

    And here’s another question — back in the pre-playoff days, second-best in the regular season didn’t cut it. But then you didn’t have to survive two playoff rounds. I’m guessing that this method gives a much better chance for the “best” team to go to the World Series. Can you run that scenario — that is, figure the chances for the “best” team in a league to have the best regular-season record?

    • Yes, it goes exactly along the lines you describe Harold, just over a much larger number of games.

      The odds for winning any particular game are yes, just the ratios of the two teams’ quality levels, so e.g. if team A = 0.6 and B = 0.5, then team A’s chance of winning is 0.6/(0.6 + 0.5).

      Great question and in fact I was going to write a longer post in which I address that and some other things, but had to keep it shorter today. If I do what you’re describing, that will give a reference point for the effect of placing teams in divisions and having them play an unbalanced schedule (or balanced for that matter, although there’s never been divisions and a balanced schedule in MLB). I think there’s no doubt that the best team will come out on top a higher % of the time without divisions and with a balanced schedule–and I’ll run the numbers as soon as I can.

  2. This is fun! Did you set the team quality and leave it the same for the entire year? I’m thinking of the 2012 Giants and the 2003 Marlins. Those teams were dominant at the end, but middle-of-the-pack when the season started. Is there a way to account for the “Marco Scutaro Effect?” I suppose it could just as easily be the “David Freese Effect.”

    • Yes, team quality is constant over a year. I could make it vary, but I always go with the simpler situation first. Next up is varying the league and playoff structure, and computing a reference situation with no divisions and a balanced schedule, like the pre-1969 conditions.

      After that I’m going to give Bud Selig a brain and see what effect that might have had. 🙂

  3. The team from Lake Wobegon… would they be the Meanies?? I can just imagine Garrison Keillor doing both the play by play and the color commentary.

    Sorry to see your Mud Hens miss the AAA playoffs. Maybe next year.

    • Garrison and the other guy who does the “Lives of the Cowboys” skit with him would be a great announcing team methinks.

      Of course, as we well know, all the children are above average in Lake Wobegon, so the baseball team is a bit of a letdown in that respect.

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