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March 3, 2005

Crooked Numbers

The Morning After

by James Click

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If you're heading down to Florida or Arizona in the next month, you'll surely be taking in a few spring training games here or there. One thing you won't see is extra innings. Much like the occasional All-Star game, spring training games sometimes end while tied. This is typically fine with everyone because teams aren't there to win the games, they're there to determine their roster, work on the fundamentals, and get a nice base tan. No one wants to get hurt and no one wants to get too tired, so after nine innings are up, everyone goes back to the batting cages or the golf course and has a great time.

During the regular season, things are obviously different and it's clear that extra-inning games can be a drag on a team. Playing nine innings every day is hard enough, but throw in the occasional 13- or 14-inning affair and players can show signs of fatigue, particularly in the bullpen or behind the plate. Managers find themselves with fewer options than normal the next day because players are still tired from the previous day. Doubleheaders have similar effects on clubs. Free baseball is great for the fans, but it can be rough on their team.

Just how much the extra innings affect a team is difficult to gauge. Looking at winning percentage in the following game doesn't reveal much because often the same two teams who battled through the long yesterday are playing again. Teams that played extra innings or a doubleheader and then play the next day are going to have a collective winning percentage of .500 no matter how tired they are or how many extra greenies are in the coffee. Instead, we must look at situations in which one team played extra innings the night before and the other did not.

In 2004, there were 218 extra-inning games. That may seem like a nice sample size, but 105 of those games were only 10 innings. Let's push ahead anyway and see what we find. Looking at all teams in 2004, we can find 89 games in which one team played extra innings the day before and their opponent did not. In those 89 games, the tired team--for lack of a better term--won 38 games for a winning percentage of .427. While that may seem to validate the idea that tired teams don't do well the next day, it may simply be a case where those tired teams happened to be very bad in general.

To correct for this, I've weighted the overall winning percentage of our tired teams by how many games they played and how good they were in general. For example, the Diamondbacks played in four such games, so their winning percentage--which looks a lot like a batting average--is counted four times. Add up all the teams like this and the teams in these 89 games had a weighted winning percentage of .505, nearly 80 points higher than their actual winning percentage in those day-after-extra-innings-games. Looks like we could be onto something.

Before we get too excited, let's see how things shaped up over the past 10 years:


YEAR   G    W    L   WIN %  eWIN %  DIFF
1995   99   50   49  .498   .505    .007
1996   78   32   46  .498   .410   -.088
1997  110   55   55  .502   .500   -.002
1998   99   46   53  .513   .465   -.048
1999   80   35   45  .516   .438   -.078
2000   85   41   44  .485   .482   -.003
2001   66   42   24  .508   .636    .128
2002   70   34   36  .497   .486   -.011
2003   97   53   44  .503   .546    .043
2004   89   38   51  .505   .427   -.078
In seven of the last 10 years, the tired teams have had a worse winning percentage than the fresh teams. However, throwing out years where the difference was almost zero--1995 (.007), 1997 (-.002), 2000 (-.003), and 2002 (-.011)--leaves four seasons in which the tired teams performed poorly and two in which they played very well. Overall, tired teams have a 426-447 record (.488) with a weighted winning percentage of just over .500. Tired teams perform just slightly worse than fresh teams.

Using all extra-inning games may not be the best way to determine if teams are in fact tired. As mentioned, in 2004 nearly half of all extra inning games were merely 10 innings. Removing those games from the numbers yields a much smaller sample, but much more dramatic results:


YEAR   G    W    L   WIN %  eWIN %  DIFF
1995   34   12   22  .516   .353   -.163
1996   43   17   26  .501   .395   -.106
1997   50   23   27  .497   .460   -.037
1998   57   28   29  .510   .491   -.019
1999   40   17   23  .531   .425   -.106
2000   48   22   26  .492   .458   -.034
2001   41   26   15  .505   .634    .129
2002   38   17   21  .476   .447   -.029
2003   49   24   25  .496   .490   -.006
2004   45   17   28  .511   .378   -.133
These teams underperformed their weighted winning percentage of right around .500 to the tune of nearly 50 points, going 203-242 since 1995. Only once in the last 10 years did tired teams outperform their weighted winning percentage.

As mentioned above, the other big exhaustion factor is doubleheaders. Though they are rare these days, they still happen from time to time and are certainly tiring, even for those of us in the stands. Running the same numbers, here's what we get:


YEAR   G     W    L   WIN %  eWIN %  DIFF
1995   10    8    2   .500   .800    .300
1996   13    6    7   .493   .462   -.031
1997   19   10    9   .530   .526   -.004
1998   12    9    3   .511   .750    .239
1999   15    6    9   .501   .400   -.101
2000   12    7    5   .508   .583    .075
2001    4    3    1   .529   .750    .221
2002    3    2    1   .431   .667    .236
2003    8    4    4   .458   .500    .042
2004   25    6   19   .464   .240   -.224
I was rather startled by the amazing jump in doubleheaders in 2004, but the reason isn't just because there were more doubleheaders (there were 38 as opposed an average of 25 for 2001-03), it was because there were more doubleheaders where one of the teams played someone else the next day. Looking at the list as a whole, it's certainly easy to point to 2004's nice large sample size and say that that validates the idea that tired teams don't do well. But the problem is that in most years, the sample size is just too small. Adding everything up, the tired teams went 61-60 while their weighted winning percentage is just below .500.

Though teams playing the day after a doubleheader don't appear to suffer adversely from the fatigue, those teams that played significant extra innings did. There are several possible reasons for this, mostly due to the ability to prepare for a doubleheader. Extra-inning games can run late into the night, taxing a bullpen that has little idea when the game will end. Doubleheaders usually last no later than regularly scheduled games and teams are able to prepare for them by sparing the bullpen in the days before and using another starting pitcher in the second game of the double dip.

The difference in performance in games after longer extra-inning games would turn a .500 team into a .450 team over a long period of time, costing a team about eight wins on the season. On average, teams only find themselves in such a disadvantageous situation about one or two times a season, so it's unlikely that it's a significant problem for any team. But the teams in spring training have at least one more small excuse to hit the bars a little earlier. And so do those of us in the stands.

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