And there's winners and there's losers, but they ain't no big deal. - John Mellancamp
Like millions of others, I have been watching the 2011 NBA Finals between the Dallas Mavericks and the Miami Heat. At the time of this writing (June 8), the best of seven series is tied at 2-2, and the games have been close. I have enjoyed watching the games, but the post-game shows featuring basketball experts have left me a bit confused. Whatever the outcome of the game that just finished, these experts make incredible sense of what happened, calling on the numerous story lines that this series affords.
These experts convince me - almost - that the winner of the last game will of course be the winner of the next game. I keep waiting for someone - anyone - to say: "These teams are evenly matched, and the ball bounced one way for the winner, and another way for the loser. I wonder what will happen in the next game?"
Of course, if they said that, why would they have jobs as expert commentators? Anyone can say that kind of thing.
Like me for instance, although I have some evidence to back it up.
Suppose two basketball teams really are evenly matched, so much so that each has a 50-50 coin-flip chance of winning each game in a series. What would we expect to see? A handful of 4-0 sweeps, a few more 4-1 series, even more 4-2 series, and most frequently 4-3 series.
I've done a little homework. First, I figured out the numbers of 4-0, 4-1, 4-2, and 4-3 final series in the 64-year history of the NBA, from 1947 through 2010. Then, I calculated how many such series would be expected over the years if each game were a 50-50 toss-up between two evenly-matched teams.
Here are the results. I admit my arithmetic is a bit rusty, and if someone can correct my probability estimates, I would welcome the feedback, even to the point of taking down this entry. But assuming I crunched the numbers correctly, consider what I found:
These columns of figures look like they might be different, but an inferential statistics test - the venerable chi-square test, if you recall your STATS 101 course - is available that tells us that the actual results are not at all different from the expected results based on the assumption that the two teams have equal chances of winning each and every game in a series.
This conclusion is of course sports heresy. Said most bluntly: The best team does not win the series because there is no best team, at least not in the NBA finals where two outstanding basketball teams are invariably matched.
I expect readers of this entry who care about sports to beat me up about this conclusion, observing (correctly) that my simple analyses ignored home court advantage, the format of the series (i.e., 2-2-1-1-1 versus 2-3-2), or the possibility that in some series players might have been injured or suspended in earlier games, thereby influencing the outcome of later games. I did not have the energy to analyze margin of victory, which might yield a different conclusion.
But why not take these data at face value? I bet no one would have predicted my results, even with the simplifying assumptions. I have long believed in the transcendent will-to-win of Michael Jordan, who led the Chicago Bulls to five 4-2 final series wins and one 4-1 series win versus no series losses. But maybe it wasn't the shoes. Maybe it was just the bounce of the ball.
So what's the point for you readers who do not care about the NBA or sports? In some (not all) domains of life, there are winners and losers. That's just how these domains are constituted. Someone gets the job. Someone wins the election or the award. Someone earns the hand of the fair maiden or the handsome prince.
And if you are like me, you're usually not the winner. But that does not mean that you are a loser, just that the metaphorical ball may have bounced the wrong way for you. Much as we want to believe in a stable hierarchy of talent and merit, in sports and elsewhere, maybe there is no such thing.
Keep your head in the game, and trust the probabilities. Someday your time will come.