Run Differentials, Luck, And Correcting Statistical Improbabilities

Yesterday, Jay detailed some of the reasons why he wasn't too keen on the possibility of facing the Red Sox in the ALCS. I had reasons of my own for not wanting that match up. Aside from the way that the local and national media would beat the story into the ground, and the usual onslaught of rarely entertaining and often unintelligent anonymous comments we'd see here, I had a more rational concern about facing Boston.

Back in June, as the Yankees entered their third series of the season against the Sox at 0-5, we wrote a series of previews about how the Yankees were due for a win. The Yankees came up empty in that set as well, falling to 0-8 against Boston in 2009. While some of the aforementioned anonymous commenters took that as an opportunity to have some fun at our expense, I still took some solace in the fact that if the Yankees and Red Sox were truly evenly matched teams - as I thought they were - then the odds were in favor of them having a nice turnaround over the remainder of the season series.

Sure enough, over the next two months the Yankees finally put to rest the issues that intermittently beset them during the early portions of the season. When they met the Sox again in early August, we knew the Yanks were still due, and it started a 8-1 head-to-head run to finish the season series at 9-9, with 101 runs scored and 99 runs allowed. In short, the two teams were about as dead even as possible, meaning were they to meet again, probability would favor neither. It would be starting from square one, only this time it would be decided over a relatively short best of seven series rather than eighteen games. There wouldn't be enough opportunity this time for short term statistical improbabilities to correct themselves over the long term.

Yet probability doesn't always win out. In stark contrast to the universe evening out in the season series between the Yankees and Red Sox, is the absurdly good fortune that smiled upon the Yankees in their ten meetings with the Twins this year.

The Yankees and Twins began their season series in mid-May with a four game wraparound series. The Yankees had already amassed two of their fifteen regular season walkoff wins, but it was during this series that the walkoff win started to become a hallmark of the 2009 season. In the series opener, Brett Gardner delivered an inside-the-park home run, and Melky delivered his second walkoff hit of the season, giving the Yanks a one run win. On Saturday, in just his eighth game of the season and his second at the new Yankee Stadium, Alex Rodriguez delivered his second big home run of the season. This time it was an extra inning walkoff, giving the Yankees a two run victory and making A-Rod the first Yankee to get pied on the season. On Sunday, Johnny Damon delivered an extra inning walkoff HR of his own, the third straight Yankee walkoff in the series, for another one run victory. On Monday, I made my debut at Fack Youk in the morning, shot down to the Stadium for the game, and watched the Yankees squeak out another one run win, this time without the drama of a walkoff. Despite a run differential of just five, the Yankees had a four game sweep for themselves.

The two teams met again in the Metrodome following Fourth of July Weekend. The first game would be the most lopsided affair in the season series. Behind CC Sabathia, the Yankees won by eight runs, representing 50% of the final run differential for the season series. The second game was another one run victory, and then Yankees swept the season series with a two run victory in the season finale.

All told, the Yankees went 7-0 against the Twins, with 41 runs scored and 25 runs allowed. Using the more accurate 1.83 exponent, those numbers predict a pythagorean record of 5-2. Instead they went 7-0. The Yankees swept seven from the Twins in 2003 as well, but outscored them 49 to 13 that year, predicting a pythagorean record of approximately 6.4-0.6. That is, in the same amount of games the Yankees had about 1.4 more wins of luck this year compared to that year.

That luck against the Twins continued into the ALDS of course. Not just with Phil Cuzzi's blown call, or with the baserunning gaffes from Carlos Gomez and Nick Punto, but in the numbers as well. The Yankees swept the series with a nine run differential. With only a three game sample size the numbers aren't at all reliable, but they still indicate that the Yankees got about a half win worth of luck in the series.

On a more specific level, the Yankees entered the bottom of the ninth Friday with just a 10.5% win expectancy. They were facing the best closer in the league that doesn't answer to "Mo". And the ever-unclutch A-Rod managed to tie it up. In the top of the eleventh, they faced a bases loaded, no one out jam, giving the Twins a run expectancy of about 2.28 runs. Instead, despite a screaming line drive off the bat of Delmon Young, they came away with none, and the Yankees walked off one more time.

Ten games. Ten wins. Five of them by a single run, two more by just two runs. An average margin of victory of just 2.5 runs; 1.9 runs removing the eight run victory in July. Four walkoff wins, three of them consecutively, the final three in extra innings. The Twins led in seven of the games, scoring first each time. Yet they didn't amass a single, solitary victory.

As I pointed out yesterday, the Twins were a relatively weak playoff team. Luck or no luck, the 2009 Yankees should take a five game series from the 2009 Twins nine times out of ten. But the Twins are still a good team, and it's highly improbable that any team, even one as good as the Yankees, should take ten straight games from them by such slim margins. That said, I'm relieved that if and when the Twins luck against the Yanks levels out, it'll be happening in the 2010 regular season rather than the 2009 post-season.