## Sunday, October 09, 2011

### Brief Playoff Meanderings

* There have been eighteen postseasons in which the Division Series has been held (I’m counting the 1981 playoffs between the half-season winners as Division Series). 2011 set the new record for the most aggregate games played in the round, with nineteen. The maximum is twenty, and had the Rays managed to take an additional game from the Rangers it would have been reached. The previous high was eighteen, which occurred in 1981, 2001 and 2003.

The record for most total games played in the postseason (since 1995; in this case I’m excluding 1981 because the LCS was only a five-game series at that point) is 38 in 2003--two LDS went four and the World Series went six, but all other series went the distance. The ALCS and NLCS are both well-remembered (I can just say Grady Little or Aaron Boone and Steve Bartman and you’ll remember the circumstances).

No other postseason has come particularly close; the runner-up is 2001, which saw 35 total games played despite each LCS only lasting five games. The fewest games played in a post-season is 28 in 2007--every series was a sweep except for the two involving Cleveland, who beat New York in four in the ALDS then lost to Boston in seven in the ALCS. To put 2007 in perspective, every series from here on out in 2011 could be a sweep, and the total games played would be 31.

A natural follow-up question is “What is the expected number of postseason games?” If you assume that each game is a 50/50 proposition (equally matched teams, no home field advantage, no variation in team quality from day-to-day, etc.), then it’s very straightforward to estimate series length with the geometric distribution.

For a five-game series under those assumptions, there is a 25% chance for a sweep and a 37.5% chance for a four or five game series. For a seven-game series, there is a 12.5% chance for four games, 25% for five games, and 31.25% for six or seven games. Thus, the expected length of a five-game series is 4.125 games, the expected length of a seven-game series is 5.8125 games, and the expected number of games in the postseason is 33.9375. 1997, 2002 and 2004 all met expectations with 34 games.

However, if one compares the expected series lengths to the observed series length in the divisional era (1969 and foreward), he will find that five-game series do not conform to expectations:

Five-game series tend to be resolved in fewer games than one would expect assuming an equal probability of each outcome. The difference is statistically significant by reasonable standards. The average is just 3.86 games. Assuming that one of the teams has a .716 expected winning percentage comes close to minimizing the error assuming the geometric distribution framework:

I’m presenting this as a curiosity, and I’m certainly not suggesting that we should assume that the assumptions I described are useless when thinking about the Division Series. And on the other hand, seven-game series since 1969 conform almost as well as one could hope for:

There is a slight tendency for series to be resolved more quickly than one would expect, but it isn’t particularly significant, and the average of 5.75 is not far off the expected 5.81.

*What I’m going to say here is not in any way novel; many fans, both sabermetrically-inclined and not have expressed the same opinion over the years. But there were two instances that I considered so egregious in the Arizona/Milwaukee game give that I can’t help but comment on it here.

I have always thought that many managers are way too eager to make substitutions that sacrifice offense for baserunning or defense or the pitcher’s slot in the lineup, but I’m not sure I’ve ever seen a better display of it than in the aforementioned Game Five. In the eighth inning, Arizona trailed 2-1 with runners at first and third and two out. Chris Young drew a walk to load the bases and advance Miguel Montero from first to second, bringing Ryan Roberts up with the bases loaded.

At this point, Kirk Gibson decided to pinch-run for Montero, sending Collin Cowgill in. Montero occupied the #4 spot in the order, while Roberts was #7. Thus, it doesn’t take a rocket scientist to realize that, with an additional inning to go, there was a pretty good chance that Montero’s vacated spot would come up to bat again, and barring Arizona scoring at least two runs and holding Milwaukee in the bottom of the eighth, it would come with the Diamondbacks still needing a run (when I say needing a run, I mean it in the sense that Gibson apparently considered, since I would never say you don’t “need” more runs at any point in the game).

One would have to evaluate the marginal value of Cowgill’s baserunning very highly to see that as a winning move, especially considering that Montero would be off with contact given that their were two outs. Of course, as it played out, Roberts grounded into a fielder’s choice, and Montero’s spot did come up in the ninth, with the game now tied but runners at the corners and two outs. Henry Blanco hit into a fielder’s choice, and Arizona did not mount a threat in the tenth before allowing the game-winning run in the bottom of the frame.

The second move was not nearly as egregious, but it was still quite puzzling to me. With a 2-1 lead in the top of the ninth, Ron Roenicke summoned his closer, John Axford. The pitcher’s spot was due up fourth in the bottom of the ninth, so he double-switched Axford into Rickie Weeks’ #5 spot since he’d made the last out of the eighth.

Given that Roenicke wanted to make a double switch, Weeks was the only obvious candidate to be replaced--removing Braun or Fielder would be worse, especially since they were closer to coming to the plate, and Nyjer Morgan’s second spot was due up sixth in the bottom of the ninth. (One could make a case that Morgan would be the best candidate, but given that he got the walkoff hit in the tenth it wouldn’t be an argument that would fly over well with the “results not process” crowd).

What I find interesting about the double-switch for the home team taking the lead into the top of the ninth is that the only way the batting order matters at all is if Axford surrenders the lead. Thus, while you preserve Axford’s ability to pitch the tenth without sabotaging your offense in the ninth, you also know that if he does so, it will be only after he yielded a run in the ninth. You know that you will “need” runs if the #5 spot ever comes to the plate again.

Of course, this all worked out for Roenicke, since Axford pitched a 1-2-3 tenth, Morgan got the game-winning hit, and the #5 spot never batted again. And Roenicke does apparently like to bring Counsell in as a defensive replacement for Weeks, so if Weeks is going to come out of the game anyway, the double switch is the way to do it.