THE BOOK--Playing The Percentages In Baseball

I don’t think “most people” think in terms of “half a run a game.” I really think the majority of fans are still way behind in this type of thinking.

What would you think the average fan would say as the number of runs per game lost by batting your pitcher cleanup?

There is little doubt, I think, that the average fan (and commentator, manager, coach, etc.) would overstate the cost/penalty of batting the pitcher 4th.  Whether they could couch it in terms of runs per game, or how they would couch it, I have no idea.

Tango is right in that whenever I run various lineups through my sim, which incorporates things like base running ability, the pitcher sac bunting a lot, and the like, I usually come up with no advantage to batting the pitcher 8th.

If it were me making the decision, I wouldn’t spend more than a few seconds on the issue as I think it is as much a tossup as a tossup can be.

Tango, let’s assume that you pinch hit for the pitcher a little earlier when he bats 8th or higher (which I think you could make an argument that that will be the case), such that the total number of PA for the pitcher at the end of the season is the same whether you bat him 9th or 1st.  How does that change the numbers?

Hmmm… very interesting thought.

Let’s see if we can work this out.  I’ll use Table 63 in The Book, which shows the number of runs scored with 8 typical batters (for their slots), plus the pitcher.  Put the pitcher in the 9th slot, and this team scores 4.835 runs.  As leadoff hitter, this team scores 4.774 runs.

This table also presumes that the pitcher gets 65% of the PAs for his slot.  This means in the 9th slot, he gets (using Table 45) 65% of 3.86 PA, or 2.51 PA.  And in the 1st slot, he gets 65% of 4.80, or 3.12 PA.

So, it should not be terribly surprising that this team will score less, since I am giving the pitcher more PA!  Instead, I should be giving him 2.51 of the 4.80 PA in the leadoff slot or 52% of the PA for that slot.

The question therefore is how many runs would the team score if I give the pitcher 52% of the PA in the leadoff slot, and give 48% to a regular hitter. 

In Table 61 in The Book, I said that a team of nonpitchers would get 5.25 runs per game, and a team of 8nonpitchers plus a pitcher (in the 9th slot) would score 4.61 runs and an in 1st slot they’d score 4.51.

Now, let’s try to take it home.

Pitcher bats 9th 65% of the time (gets 2.51 PA)
.65*4.61 + .35*5.25 = 4.83
(matches The Book)

Pitcher bats 1st 65% of the time (gets 3.12 PA)
.65*4.51 + .35*5.25 = 4.77
(matches The Book)

Good, we’ve found a working shortcut here.  Here’s the payoff:

Pitcher bats 1st 52% of the time (gets 2.51 PA)
.52*4.51 + .48*5.25 = 4.87

They score more often with the pitcher first than last (giving him 2.51 PA in either case)!  Even if this shortcut is not good enough, it at least point to the strong possibility that if you give a pitcher a fixed number of PA (rather than a percentage for that slot), that they will end up scoring the same number of runs either way!

Fantastic!  Great idea MGL.  I’m not really setup to run this, but I’ll add it to my todo pile.

"They score more often with the pitcher first than last (giving him 2.51 PA in either case)!”

Now that is a fascinating frickin’ result!  It might not matter where you bat the pitcher as long as you take him out when it is his 3rd turn at bat, or what have you…

What would the following strategies be worth in terms of runs added to the ledger (obviously, question applies in the NL only):

Visiting Team: Bat pitcher spot in one of the first three spots using a ‘pinch hitter’ and then exchange that player in the first inning’s bottom for the scheduled starting pitcher.

Home Team: Let a reliever pitch the top of the first inning, then put the pitcher spot in one of the three first spots in the batting order and pinch hit in the bottom of the first, afterwards the regular starting pitcher takes over.

Would this be worthwhile?

BTW: very annoying advertising on the screen’s bottom (flash animation making noise when touched by the cursor).

One thing that I have wondered… if you have the kind of team where the leadoff hitter gets on base pretty regularly and your #2 hitter often sacrifices, would it make sense to bat the pitcher in the #2 slot?

On that note, nothing frustrates me more than a pinch hitter brought into the game to bunt when it should be a pitcher doing that.

#6/vj:

What you suggest for the visiting team would actually not be permitted under the rules.

3.05(a):  “The pitcher named in the batting order handed the umpire-in-chief, as provided in Rules 4.01(a) and 4.01(b), shall pitch to the first batter or any substitute batter until such batter is put out or reaches first base, unless the pitcher sustains injury or illness which, in the judgment of the umpire-in-chief, incapacitates him from pitching.”

In other words, you can’t pinch hit for the pitcher in the top of the first.

I recall reading in an old Sports Illustrated or Baseball Digest (from the early ‘70s, I think) that a numbers person had suggested almost exactly what you are suggesting:  the starter pitches 2 innings or so (until his spot comes up in the batting order), and the “second starter” pitches about 5 innings in the middle of the game, batting once and then being lifted for a pinch hitter the second time around, followed by either a mop-up reliever or a “fireman,” depending on what the situation dictates.

#8, you have apparently not read The Book and/or have not frequented this blog much.  In The Book (and from time to time on this blog) we talk about the “pitcher never hits” strategy, or at least the “pitcher never hits unless the leverage is low” strategy, which by far and away results in the single biggest gain one can achieve from a non-conventional strategy.

#7, I don’t know if you are aware of this, but pitchers in general are by far and away worse bunters than position players (who are called to bunt).  That might not be because they “get the bunt down” any better.  It is because when they do get a bunt down, they actually occasionally run hard and leg out a base hit or force an error AND when they have two strikes after attempting to bunt, they are good enough hitters to swing away.

#9:

Yes I have and yes I do.  Sorry--I was not intending to slight anybody. 

I just wanted to bring up that I had heard that strategy discussed quite a while ago.  I managed to find the article (by Frank Deford, about Earnshaw Cook) in the Sports Illustrated archive from 1972:

http://vault.sportsillustrated.cnn.com/vault/article/magazine/MAG1085860/index.htm

Alt_n, thanks for the link.  Absolutely fascinating read.  Maybe Cook was the true father of sabermetrics and not Bill James.  That is some revolutionary stuff for over 35 years ago!  What is hard to believe is that 35 years later lots of teams and in fact most managers and coaches wouldn’t know what the heck he (Cook) was talking about.

A couple of silly things in the article, but that could be misstatements from the writer (Deford). That happens all the time.  For example:

“Any .500 team that adopted real percentage baseball would, he claims, automatically become an even-money bet to make the World Series.”

Or maybe that is correct back in 1972....

BTW: very annoying advertising on the screen’s bottom (flash animation making noise when touched by the cursor).

I put the ad in the least intrusive spot on the page, an ad that barely gets clicked (we have yet to hit 100$ on those ads, and they’ve been running for well over a year I think).  And there are no other ads anywhere (the Amazon link notwithstanding). 

I hope that whatever level of annoyance that this site has exceeded, by placing the ads there, has been more than balanced by whatever else this site offers.