Friday, 25 September 2009

Luck Be a Lady

One of the most common aphorisms you hear in a given week is that this or that is "a toss of a coin." Usually, the implication is one of the randomness or vagaries of life. Coin tossing permeates the culture in song, book, and film. Two recent very popular movies ("The Dark Knight" and "No Country for Old Men") feature villains who make life and death choices using a coin - of course, Harvey "Two Face" uses a coin which has two heads, removing any actual chance, but the point is made.

My own academic training is in maths and applied statistics, and it's actually very helpful to reduce almost all questions around probability to variations of the coin toss.

But "randomness" does not imply "luck," and I personally don't believe in luck. A coin will land heads or tails based on a number of physical properties, some subtle (how much air resistance) and some not (when you grab it out of the air), but the process itself is deterministic once the coin is thrown into the air. Similarly, for cards, the shuffle, cut, and deal set in motion a series of events that is not at all based on luck. We think of luck perhaps as whether the gambler chooses heads or tails, takes a hit to 15, etc., and in these perhaps there is an element of luck.

I got to thinking about luck last night as I listened to the Toronto Blue Jays lose yet another late-inning, one-run game. The team has lost more than its share of such games this year (this, plus the lack of budget and hence talent has contributed to yet another dismal finish far out of contention), and I was curious to see just how badly it has done.

The results are remarkable.

In one-run games - games that more often than not are decided by tiny, tiny differences (a ball inches fair or foul here, a single swing of the bat that misses the sweet spot by fractions of an inch there) have an exaggerated effect on the outcome - Toronto is 18-27, the poorest record in the American League. (The California Angels, 27-18, have the best). In extra-inning games, the Blue Jays are 5-12, easily the worst in the Major Leagues.

The question is, is this luck, or something else?

In baseball, Bill James some years ago created what he called the Pythagorean Theorem, which, like the famous eponymous theorem of geometry, estimates a team's winning percentage as the ratio of the square of its runs scored to the sum of its runs scored and runs allowed squared. Put simply, if you score exactly the same number of runs as you allow, over the course of a season, you will win approximately half of the games you play.

What's useful as an exercise here is that teams that win a lot of close games, but lose a majority of the games that are blow outs will post a winning percentage much better than the one estimated by the Pythagorean Theorem. A team that loses a lot of close games, but wins the majority of the blow outs will do relatively poorly.

To convince yourself, consider Team A, which in a series of 10 games, wins 8 games 2-1, and in the other 2 games loses 4-0 in each. This team scores 16 runs, and allows 16. The theorem predicts it should win 5 and lose 5. Given that it won 8, it has won an excess of 3 games.

The idea here is that games that are close tend to be more influenced by random events (the one ball inches foul) than games that are not close. Good teams will win more blow-out games as a percentage than bad teams will. Of course, the good teams will also win a majority of the close games as well, but they tend to win a much higher percentage of the lop-sided ones. If the Yankees were to play the Baltimore Orioles, it's far more likely that the Yankees will win 10-0 than Baltimore. Not in a given game, mind you, but over a long series, the better team will almost always predominate.

This in mind, I looked at how Toronto (and the rest of the AL) had done for the past 5 years, plus this one.

This year, the Jays have scored more runs than they have allowed (a slight difference, but there you have it). They currently are 15 games UNDER .500. The Pythagorean Theorem predicts that they ought to have won 9 more games than they have. That is a serious under-performance.

But is it "luck?"

For the years 2004-2008, Toronto has won fewer games than the theorem predicts IN EVERY SINGLE SEASON. Put another way, they have tossed a coin and gotten five consecutive tails. This year almost certainly will be number six in a row. The "odds" of six straight heads are 1/64, or less than two per cent.

Cumulatively, the team was won 31 fewer games than the runs scored/allowed formula predicts.

Both of these figures are the worst in the American League (the Cleveland Indians are next, having been shorted 26 wins). Oddly enough, the California Angels (this year's best performer in one-run contests) have exceeded predictions in all five years, and this year will certainly make six, unless they lose a couple of games 20-0.

This is not "luck," for a team to be worse, every single year, than it ought to be. The players are different; the opposing rosters are different. Only the GM and management are the same.

I think the evidence is clear, and the prosecution rests. It's time for the management in Toronto to go, from top to bottom.

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