(If you have no interest in sports you probably won't find this that interesting either. It has more to do with probability and expectations (and uses sports as a context), but I betting there are more people interested in sports than probability and expectation. So for the one or two of you out there interested in both, here you go.)
I changed topic, you see, because Phil Jackson (head coach of the Lakers) is 47-0 in playoff series when his team wins the first game. Which caused a lot of discussion on basketball websites yesterday, as this stat was taken to mean that if the Lakers won the first game, they would win the series. I take issue with this, despite the seemingly compelling statistic. Lets take a closer look.
Phil Jackson has been a very successful head coach (maybe because he is good at it, or maybe he is lucky, to be discussed a different day). By the metric of championships, he is the most successful in NBA history (10 NBA titles as head coach). He has coached in 62 postseason series (53-9 record), which means that if he is 47-0 when his team wins the first game, he must be 6-9 when his team loses the first game. Clearly this is a person who wins more than he loses in general. So right off the bat, he is more likely to win a playoff series than lose it, based on his record.
Second, I would argue (and have to argue, because I don't have the stats handy) that any team that wins the first game of a series is more likely to win the series. Mathematically this just makes sense - that team now needs to win only 3 of the remaining 6 games, while the opposing team must win 4 of 6. It is also arguable that, on average, the better team (with 'better' to be defined in a post on another day) will win the first game (and the series) more often.
Furthermore, the team that performs better in the regular season has home-court advantage, which has been shown in research studies to actually give an advantage to the home team (mostly having to do with the love/hate from the crowd affecting testosterone). So what we have so far is:
- The team that has the better regular season record (thereby more probable to win) has home-court advantage in the first game.
- Home-court advantage increases this probability of winning this first game.
- This 'better' team also has an increased probability of winning the entire series.
- Winning the first game further increases these odds.
We have four factors all favoring the team that wins the first game (except in situations where the visiting team wins, then there are two factors) in terms of winning the series.
But what does this have to do with our friend Phil? I mean, an probabilistic advantage is one thing, but a perfect record is another. Clearly, the Lakers must be destined to win it all!
Not necessarily, say I. Do the Lakers have a greater chance of winning the series? Sure, but they probably did before last night's game was even played, because they had a better regular-season record and have home-court advantage. But if I were a betting man, I would probably bet against them today, because it would be easy to find someone to give me ridiculous odds based on Phil's record.
I'm a little late getting to this one, but since I am one of the 1 or 2 people interested in both sports and probability, I thought I had to comment...so here goes:
ReplyDeleteHell, yes.
As someone with a reasonably good understanding of probability, few things are more frustrating than listening to sports announcers. My favourite example (somewhat similar to yours above) is the idea of the "hot streak" and "cold streak" in basketball (although this also applies to other sports). When players take hundreds of shots with a (roughly) 50% chance of hitting each, there is a high probability that they will eventually hit a bunch in a row -- which does NOT necessarily suggest that they are any more likely to hit the next one!
Even better, some analysts will use both a hot streak and a cold streak as evidence that the next shot is more likely to go in (one because the player is clearly "feeling it" and the other because he is "overdue")...