Why Most "Streak" Statistics are Meaningless

The guys over at Sounder at Heart have done a good job of pointing out why most of the talk of the Sounders being up a creek in the second leg is bunk. Here's one gem regarding the "only 2 teams have won the two leg playoff after dropping the first leg at home" statistic:

Letting that number stand alone is just plain dumb, though. For one, it ignores the total sample size: Only six teams (not including the Sounders) have ever even lost the first leg at home. Looking just at those numbers, we're talking about a whopping one-third of teams coming from behind to win, hardly an insurmountable task.

Looking a little deeper, we see three of those home-leg losers lost by more than one goal. Of the three that lost by one goal, two of them have come back to win. So two-thirds of teams that lost by one goal at home, managed to advance anyway.

Luckily, statistics can tell us just how many games must be played to tell us whether such a win percentage is statistically meaningful. There are numerous resources for performing "power and sample" size calculations. I have used this one.

In analyzing the long term average of a playoff series, we can assume that each team has a 50% chance of winning (ignoring their seed as indication of prior performance). This would be the "known value". Let's assume a specific outcome of the first match - a loss at home - and then a specific outcome of the second match - overall loss in the two leg series for that team that lost at home in the first match. If we observed that the long term trend was that teams who lost that first match only won the two-leg series one-third of the time (like they have to date), how many series would that need to occur over to determine such a team has less than a 50% change of winning?

Using the power-and-sample size method, it turns out it's a lot - 54 two-leg series. The numbers don't get much better if the Sounders lose on aggregate goals. Such an occurrence would mean that only 2 of the 7 teams who fell behind after the first leg at home would have gone on to win the series. Given this percentage, it would still require 32 series where the host team in the first match lost, and no more than 9 of those 32 series could see that team go on to win the series. Ten or more series wins for the team that lost the first leg, and such a percentage is statistically no different than the team having an even shot at advancing.

And that's what the Sounders are facing in LA - an even shot at winning the series. Game on, boys!