Measuring the Dolphins' improvement
The Miami Dolphins were 11-5 this year, improving by 10 games over their abysmal 1-15 record in 2007. Carl Bialik wonders just how historic an improvement this was. On the one hand, he says, the improvement of 62.5 percentage points (.625) is huge. But on the other hand, there are only 16 games in the NFL season, so we're really only talking about 10 games.
Because of the shorter season, changes in winning percentages in the NFL tend to be larger than in other leagues, at least those changes that arise due to luck. For a .500 team, the standard deviation of wins in the NFL is 2 (the square root of .500 times .500 times 16). Expressed in winning percentage, that works out to .125. By comparison, it's only .039 in baseball, and .055 in basketball or hockey (ignoring the NHL's extra standings point for an overtime loss).
To get the SD of the difference between two consecutive seasons, you multiply the single-season SD by the square root of 2 (about 1.414). So a typical between-seasons luck difference would be 2.8 games. And 5% of the NFL – that's 1 or 2 teams – should have a swing of more than 5.6 games.
But it's not likely that *all* of the Dolphins' improvement is random luck. A substantial amount is probably due to better talent.
One way to check is to look, not just at the win-loss record, but at the component stats. In 2007, the Dolphins' opponents outscored them by 170 points. In 2008, the Dolphins actually scored more than the opposition, by 28 points.
According to "The Hidden Game of Football," by Bob Carroll, Pete Palmer, and John Thorn, it takes about 36 points to turn a loss into a win. That means the Dolphins "should have" been about 3-13 last year, and 9-7 this year. By that standard, they were 2 games unlucky last year, and 2 games lucky this year. (That four game swing is only about 1.4 standard deviations, which is nothing special.) This means that their talent improved by six games: 1-15 last year, plus 2 games luck last year, plus 2 games luck this year, plus 6 games skill difference, adds up to 11-5.
You can drill down even deeper – instead of points, you can look at yards gained and allowed, penalties, and turnovers. Brian Burke did that for 2007 and 2008. He found that Miami was the unluckiest team in the NFL last year, by a long shot, winning 4.4 games fewer than expected. In 2008, the Dolphins were 0.9 games lucky. That's a swing of 5.3 games due to luck, which leaves the remaining improvement of 4.7 games attributable to talent.
It makes sense that Brian found more luck with his method than just by looking at points. The total random effect can be broken up into three components:
-- players having "lucky" years by playing over their head and accumulating gaudier stats than normal;
-- teams scoring more points than you'd expect based on their stats;
-- teams winning more games than you'd expect based on their points scored.
In general, teams with extreme records, or extreme changes, are likely to rank high in each of these three categories. The "points" method counts only the third; Brian's method counts only the last two. It's likely that if you had a method of looking at the individual players, both years, you'd find even more luck. I have no way of knowing for sure, but if I had to give a best estimate, I'd say the Dolphins' 11-game renaissance looks like about 6 games luck, and 5 games skill.