Does RRR's Bunting Philosophy Win Games?

On last night's broadcast, BA and Rock noted that the Brewers have the most sacrifice bunts of any team since the All-Star Break.  Everyone has noticed that the Brewers scoring has been anemic lately.  Losing Weeks is certainly a blow, though a good case can be made that Roenicke's small ball ways are reducing the total number of runs the Brewers are scoring each game.

Having read through Dan Levitt’s 2006 article "Empirical Analysis of Bunting," for my work on aggressive base stealing before the season, I thought I would revisit some of the points for Roenicke's newfound obsession with bunting.

I believe Roenicke's been selectively using the bunts, but he might not be customizing the general small ball strategies to his roster OR he's doing it exactly right for the stellar pitching his getting from his staff.  It's like he's "Playing the Hot Hand" only "Playing the Hot Strategy."

I haven't seen Braun or Fielder bunt and Morgan's certainly cut down his bunting over the last few days after going on a binge (my brother noted that he's still showing bunt a lot, but that might now be a little game simply to pull the infielders in).  The bunts, for the most part, are coming from the bottom of the order where runs are less likely to be scored.  That's flat out traditional small ball - guys that suck at hitting need to have a man at second to get an RBI.

My personal problem with that is that the bottom of the order has been hitting well recently and the pitchers on this team are actually pretty good hitters (for pitchers).  Having Gallardo sacrifice with zero outs and a man on first and second last night was a pretty tough pill to swallow.  Is Gallardo especially likely to get a hit?  Maybe not, but by giving up an out there entirely, he dramatically reduced the expected runs the Brewers would score while notably increasing the probability they would score at least one run.

"xx-" = 1st and 2nd occupied, 3rd base empty

Expected Runs - NL
Lead off Hitter at the plate:
Gallardo HR: --- with 0 outs = 0.542 (+3 runs scoring = 3.542)
Gallardo singles, scoring run from 2nd base: xx- with 0 outs = 1.526 (+ 1 run scoring = 2.526)
Gallardo bunts runners over: -xx with 1 out = 1.336
Gallardo strikes out:  xx- with 1 out = 0.868

A normal run-scoring single means an increase of 1.2 expected runs over a bunt.  A successful bunt means an increase of 0.56 expected runs over an unproductive out.

Probability of scoring at least 1 run - NL
Lead off Hitter at the plate:
Gallardo bunts runners over: -xx with 1 out = 0.669
Gallardo strikes out:  xx- with 1 out = 0.428

A successful bunt increases the probability of scoring at least one run 27%!  That's a 56% relative increase in the chance of scoring.

So when you look at a situation like having Gallardo bunt last night, taking the bat out of a capable hitters hands could cost the team 1.2 expected runs, but increases the chance of scoring 1 run 27% of the time.

The impact of both outcomes is substantial so it's a big decision.  And that's where we move into the area of strategy (game theory lite, if you will).  Is the big inning more important or is scoring a single run more important.

Taking a page out of many previous strategy writers, the only run that matters in a baseball game is the winning run.  Whether that's the 7th run in a 7-6 victory or the 1st run in a 9-0 victory,the only thing that matters is scoring one more run than your opponent.

Say the Brewers are up to bat in the bottom of the 5th inning with a 2-0 lead.  The starter is cruising and We all know they have an absolutely dynamite setup-man and closer.  Let's say that Roenicke rationally believes that the opponent has a 40% chance of scoring 1 run, a 50% chance of scoring 2 runs and only a 10% chance of score 3 runs or more for the remainder of the game. Getting that third run across is now the only thing that matters.  The 3rd run provides them an enormous boost to the Brewers chance to win the game.

If Roenicke plays for a big inning, what's he really gaining by trying to make it a 4-0 lead in the bottom of the 5th inning?  That 4th run is all but worthless.  A sacrifice bunt as early as the bottom of the 5th inning makes a lot of sense here, because it's the 3rd run that wins the game.  You  have Gallardo bunt the runners over at least 9 times out of 10.

Roenicke's small ball may be frustrating in that it leads to a lot of low scoring games for the offense; however, given the way the Brewers pitchers have been throwing, the small ball strategy may very well be maximizing his team's chance to win a given game.
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