The Wisdom of Earl Weaver

Former Baltimore Orioles manager Earl Weaver1 was known for two things: his temper (he was ejected from more games than any manager in Major League Baseball history and was once ejected from both games in a double header) and his dislike of bunting.  Weaver believed2 that "if you play for one run, that's all you get."  Rather than play for a run at a time by stealing or bunting, Weaver conserved his outs and won 1480 career games primarily with "pitching, defense and the three-run homer."  Weaver's unconventional approach was the precursor to the Moneyball3 movement, made popular by the best selling book and the success of the Oakland Athletics (about whom the book is written).

This essay focuses on the merits of bunting.  Specifically we'll examine when bunting results in a squandered out, and when it improves an offensive team's chance of winning the game.


1. Earl Weaver managed the Baltimore Orioles on two non-consecutive occasions (1968-1982 and 1985-1986), making him Baltimore's baseball equivalent of Grover Cleveland (who was the President of the United States from 1885-1889 and again from 1893-1897).  Weaver was elected to the Hall of Fame in 1996.

2. Weaver, Earl and Pluto, Terry (2002) Weaver on Strategy: Classic Work on Art of Managing a Baseball Team (revised edition).

3. Lewis, Michael (2003) Moneyball: The Art of Winning an Unfair Game.


Mathematical Modeling

At any point, a baseball game can be described by the difference in the score, the half-inning, the number of outs and the runners on base.  After each plate appearance, the situation changes.  In the case of a successful bunt, the number of outs increases by one, and the base runners advance.  Does this change increase or decrease the offensive team's chance of winning the game?  A simple (although data-intensive) way to answer the question is to collect many games worth of data and determine how often a team in each situation won the game.

For example, suppose that there is a runner on first base with one out in the top of the third inning of a tie game:

Score Difference: 0
Half-Inning: Top 3rd
Outs: 1
Runners: 1st

A successful bunt changes the situation to:

Score Difference: 0
Half-Inning: Top 3rd
Outs: 2
Runners: 2nd

Using data from every game between 1979 and 19904, we can estimate how likely it is that a team in each situation wins.  In those 12 seasons, there were 3152 games in which the game was tied in the top of the 3rd inning, and the visiting team had a runner on first with one out.  The offensive team won 1490 of those games, or 47.27%.  Similarly, there were 1880 games matching the post-bunt situation, of which 861 (45.80%) were won by the offensive team.  So a bunt in these circumstances reduces the offensive team's chances of winning and should not be attempted.  The value of a successful bunt can be determined for any situation by similar reasoning.


4. Data available at http://www.philbirnbaum.com/probs2.txt, or directly from RetroSheet.


Results

In the results that follow, we assume that all bunts are successful.  Therefore, we only consider cases in which there are runners at first base, second base, first and second base or first and third base.  (Other base runner situations involve squeeze plays in which a runner from third base attempts to score on a bunt.  These are far less certain than typical sacrifice bunts.)  Furthermore, because bunting occurs primarily in close games, we restrict attention to games in which the score differential is within three runs.

The change in probability of winning for the offensive team attributable to a successful bunt is given in the following tables.  Each table represents a different combination of base runners and outs.  Situations in which bunting decreases the offense's chances of winning are given in red; situations in which bunting increases the offense's chances of winning are in green.  Differences which are significantly non-zero are highlighted.

Runner on 1st, No Outs:

    HALF-INNING
    1 2 3 4 5 6 7 8 9+
    Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot
M -3 NA -2.7% -1.4% -2.8% 0.8% -1.9% -3.4% 1.5% -1.3% 0.4% 1.2% 2.9% -6.1% -4.7% -9.7% -1.9% -3.6% -3.7%
A -2 NA 1.6% -2.0% -3.6% -5.4% -1.1% -4.7% -3.0% -4.1% -2.9% -4.4% -2.5% -1.3% -8.1% -5.1% -4.4% -4.7% -4.6%
R -1 NA -3.2% -2.7% -1.8% -2.7% -2.8% -1.6% -6.3% -3.0% -0.4% -3.1% -3.0% -2.0% -6.5% -2.2% -3.9% -3.9% -3.7%
G 0 -1.0% -2.1% -0.2% -3.5% -0.6% -1.9% -1.8% -1.8% -2.5% -0.6% -2.5% -1.4% -1.1% -2.4% -1.2% 0.1% 0.3% -1.0%
I 1 -2.1% -2.0% -0.8% -2.4% -4.1% -0.9% 0.6% 0.4% -6.1% 1.4% 0.3% -1.5% -2.8% -1.4% -0.4% 0.8% -2.4% NA
N 2 4.0% -0.2% -2.8% -2.8% -5.4% -0.2% -1.7% -1.8% -1.3% 3.2% -0.4% -1.3% -1.0% -0.9% 1.8% -0.5% -2.5% NA
  3 -2.6% -2.0% -2.5% 1.8% 2.3% 0.6% -2.2% -1.5% -5.8% 4.4% 1.3% -0.1% -1.5% 1.5% -0.6% -0.4% -0.4% NA

Runner on 1st, 1 Out:

    HALF-INNING
    1 2 3 4 5 6 7 8 9+
    Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot
M -3 NA -1.4% 1.8% -3.6% -0.7% 3.3% -4.3% -3.6% 1.6% -3.5% 0.0% -3.7% -2.1% -3.0% -0.6% -1.5% -2.0% -1.6%
A -2 NA -6.0% 1.3% -1.2% -2.3% -8.2% -1.6% -1.6% -1.6% -2.9% -5.2% -6.7% 0.7% -2.1% -3.6% -0.5% -4.8% -5.8%
R -1 NA -2.6% -1.5% -0.4% -1.4% -3.8% -6.1% -5.4% -1.4% -1.6% -0.8% -5.1% -5.1% -1.7% -5.4% -4.1% -6.6% -9.3%
G 0 -2.3% -3.2% -1.2% -1.6% -1.5% -2.7% -1.6% -3.6% -1.7% -1.2% -2.9% -4.9% -1.8% -1.9% -4.4% -3.7% -0.4% -5.7%
I 1 -3.4% -2.3% -2.1% -1.1% -3.5% -4.7% -3.9% -0.8% -4.8% -1.0% 1.0% -0.3% -1.8% -3.9% -0.4% -1.8% -4.1% NA
N 2 -1.8% -2.6% -0.3% 0.4% 0.2% -1.2% 0.2% -1.4% -2.3% 0.6% 0.2% -2.2% -1.8% 1.4% -1.9% -1.1% -2.0% NA
  3 -5.8% -0.8% -1.2% 2.5% -2.2% -1.2% 3.0% -1.7% 2.4% -1.7% -2.4% 1.0% -1.5% -0.8% -2.9% -0.9% -0.4% NA

Runner on 2nd, No Outs:

    HALF-INNING
    1 2 3 4 5 6 7 8 9+
    Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot
M -3 NA -7.2% 1.0% -5.5% 3.4% -2.8% 1.9% -10% -6.1% -4.1% 4.1% -0.1% -3.5% -3.0% -3.9% -7.1% -7.2% -5.8%
A -2 NA -1.5% -2.3% -7.9% -0.6% -4.4% -5.7% -2.6% -1.6% -5.6% 1.6% 3.2% 4.0% 0.3% -3.4% -8.0% -4.0% -9.5%
R -1 NA -4.0% -3.3% -6.9% -0.8% 3.4% -8.2% -3.2% -2.0% -5.5% -3.7% -0.2% 1.3% -3.7% -7.1% -11% -1.6% -0.9%
G 0 -0.9% -2.6% -1.8% -1.7% -1.1% 0.7% -1.9% -1.5% -2.5% -2.1% -0.3% -2.6% 0.3% 3.3% -4.2% -4.9% -3.2% 4.1%
I 1 3.1% -0.2% -1.9% -0.2% -4.0% -2.3% 0.7% -4.0% -2.8% -1.5% -3.5% -3.9% -1.4% 0.3% -3.1% 3.4% 0.1% NA
N 2 1.2% -4.9% 4.0% 2.7% -0.9% 8.8% -1.5% 1.1% 1.5% 1.6% -0.3% 2.0% -2.7% 0.4% -2.5% 0.2% 1.8% NA
  3 -3.9% 2.8% 4.0% -0.3% -3.3% 0.1% 0.4% -2.1% -4.4% 3.3% -2.7% 6.5% -0.9% 0.3% -0.2% -2.1% -0.9% NA

Runner on 2nd, 1 Out:

    HALF-INNING
    1 2 3 4 5 6 7 8 9+
    Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot
M -3 NA 0.2% 5.0% -0.9% -3.4% 0.1% -0.6% -5% 0.3% -3.7% -6.9% -10% -3.9% -0.1% -2.3% -7.4% -1.1% -4.2%
A -2 NA -4.6% 6.4% -3.9% -1.7% -2.3% -3.0% -1.2% -5.9% -2.3% -3.8% -2.8% 0.8% -4.2% -4.4% -11% -4.9% -4.7%
R -1 NA 0.1% -3.3% -3.8% -5.1% -4.3% -4.8% -6.5% -5.9% -6.6% -4.3% -5.4% -3.3% -4.9% -11% -7% -8.6% -13%
G 0 -1.8% -3.2% -1.9% -0.4% -4.8% -5.2% -7.4% -8.0% -3.2% -2.3% -2.7% -5.3% -1.3% -6.7% -7.6% -11% -10% -6.9%
I 1 1.1% -4.5% -0.6% -2.7% -4.6% -7.4% -5.5% -0.7% -1.3% -0.9% -10% -2.3% -2.1% -4.0% -2.4% -3.8% 2.7% NA
N 2 -4.3% -3.4% 0.2% -4.5% 2.0% -1.3% -0.2% -1.3% -1.3% -4.2% -2.6% -4.1% -2.0% 0.1% -3.2% -3.2% 1.1% NA
  3 -7.0% -7.3% -0.4% -2.1% -4.2% -0.4% -0.6% 1.0% 0.1% -5.0% -0.1% 0.9% -1.1% -1.0% -1.7% 0.4% -0.3% NA

Runners on 1st and 2nd, No Outs:

    HALF-INNING
    1 2 3 4 5 6 7 8 9+
    Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot
M -3 NA 6.9% 15% -11% -0.5% -3.9% -13% -5% -2.8% -0.8% -2.9% -9.5% -2.1% -4.4% -5.0% 2.9% -2.9% -12%
A -2 NA 0.7% 2.7% -5.1% -6.9% 0.5% -3.4% -6.3% -3.8% -1.6% 7.2% 0.2% 2.6% 1.2% 1.7% 2.6% -5.3% 4.2%
R -1 NA -9.3% 1.4% 7.6% -3.3% -2.5% -2.0% 4.3% -6.3% 3.9% 1.6% 1.2% -1.7% -6.5% -3.4% -7% 10% 2.1%
G 0 0.8% -1.2% -2.0% -1.4% 11% 1.2% 3.1% -2.7% -1.9% 3.9% -2.9% 8.4% 4.0% -4.3% 2.0% 1.8% -1.9% 0.5%
I 1 0.5% -2.8% -0.2% -7.5% 7.4% -1.0% 2.2% -4.6% -1.2% 2.5% 8.1% -1.9% 3.8% 0.5% -5.6% 5.2% 0.1% NA
N 2 -2.6% 5.3% -6.3% 0.2% -1.4% -1.2% -0.4% 3.4% 3.8% -0.6% 3.0% -2.3% 3.2% -0.5% 0.0% 0.5% -1.0% NA
  3 15% -6.7% -4.3% 0.0% 5.2% -5.1% -0.7% -0.3% -9.5% 0.0% 3.3% 1.4% -2.0% -6.4% 2.9% 0.6% 1.6% NA

Runners on 1st and 2nd, 1 Out:

    HALF-INNING
    1 2 3 4 5 6 7 8 9+
    Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot
M -3 NA 17% 8.9% -11% 7.8% -0.7% -7.2% -6% -2.9% -4.9% -9.0% -8.1% -6.9% -0.5% -7.1% -7.1% -2.2% -7.4%
A -2 NA 2.0% -5.6% -6.8% -1.6% -1.1% -1.5% 0.4% -10% -6.1% 2.8% -4.8% -7.9% -8.2% -6.0% 2.8% -6.1% -3.3%
R -1 NA -5.4% -11% 3.9% -3.4% -9.0% -12% -5.7% -11% -5.4% -12% -13% -11% -6.0% -5.3% -7% -1.5% -17%
G 0 -5.6% -4.0% -4.7% 2.0% -0.5% 4.3% -4.5% -0.3% -6.6% -0.6% -6.8% 1.2% -1.2% -1.7% -4.9% -3.7% -9.0% -8.5%
I 1 4.5% -4.9% -3.8% -3.3% -1.1% 1.5% -4.6% -1.5% -0.8% -3.7% 0.2% -3.4% 1.4% -1.4% -1.8% 0.5% -1.6% NA
N 2 3.7% 5.6% 2.6% 3.8% 2.5% -3.5% -1.0% -0.2% 0.8% -0.4% -1.4% 0.6% -0.9% 1.9% -1.3% -3.5% 0.2% NA
  3 7.2% -5.0% 1.1% 2.4% -2.0% -4.4% -0.6% 1.6% -0.9% -1.4% -1.2% -0.8% 3.5% -5.4% -2.6% 0.1% -2.2% NA

Runners on 1st and 3rd, No Outs:

    HALF-INNING
    1 2 3 4 5 6 7 8 9+
    Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot
M -3 NA 16% 26% -8.2% 1.0% -3.1% -1.8% -3% 6.1% -3.7% -4.8% -16% -3.7% 8.5% 3.3% 1.5% 1.2% -8.4%
A -2 NA 4.3% 0.8% -13% -6.2% 5.3% 3.2% -12% -1.6% 2.3% 1.2% 2.9% -6.1% -3.4% -3.5% 1.3% -12% 9.5%
R -1 NA -11% -8.8% 5.2% -5.8% -2.4% -12% -18% -3.7% 4.3% -5.3% 1.7% 4.6% -7.2% -13% -15% -1.2% -5.2%
G 0 -1.0% -4.0% -1.9% -5.5% 3.9% -12% -3.6% -8.2% -0.7% 1.2% -6.8% 6.4% 1.8% -6.0% -6.8% -4.0% -11% -4.2%
I 1 -1.7% 1.4% -5.2% -9.7% 12% 2.3% -6.2% -11% -1.2% -1.3% -0.3% -1.8% 4.4% -5.6% -4.3% 6.2% -1.7% NA
N 2 -2.5% 6.8% -9.2% 0.8% -1.6% -8.5% -2.8% -2.2% -4.1% 1.2% 1.4% 1.0% -2.7% -6.6% -3.1% -1.5% -1.2% NA
  3 17% 7.9% -3.1% -3.3% 2.7% -4.8% -1.2% -5.5% -9.0% 0.2% -0.9% -0.3% 2.2% -5.9% -1.1% -0.7% 1.7% NA

Runners on 1st and 3rd, 1 Out:

    HALF-INNING
    1 2 3 4 5 6 7 8 9+
    Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot Top Bot
M -3 NA 12% 2.8% -13% 5.3% -6.1% -5.8% -10% -6.6% -7.2% -8.1% -20% -13% -8.4% -8.4% -4.0% -1.5% -10%
A -2 NA -0.9% -9.2% -7.6% 0.4% -5.7% 1.0% 2.7% -5.9% -13% 0.6% -5.3% -3.7% -11% -3.5% -3.0% -4.3% -2.5%
R -1 NA -13% -7.6% -3.1% -9.7% -7.8% -14% -16% -16% -2.3% -14% -16% -6.1% -11% -12% -13% -4.6% -29%
G 0 -6.7% -4.3% -10% -6.7% -7.7% -3.9% -12% 0.4% -8.9% -4.8% -10% -4.8% -8.2% -11% -17% -9.8% -15% -18%
I 1 2.6% -6.6% -6.7% -10% -4.7% -3.2% -9.2% -8.1% -2.5% -7.0% -0.5% -1.1% -5.8% -1.2% -2.1% -3.1% -2.5% NA
N 2 0.8% 3.2% 0.6% 2.0% -0.9% -6.3% -2.2% -1.8% -6.7% -3.0% -1.0% 0.9% -0.1% -2.5% -3.8% -4.8% -2.7% NA
  3 -3.6% -13% -5.0% 3.1% -2.3% -6.7% -1.0% 0.4% 0.6% 1.9% -0.2% -1.0% 0.9% -4.4% -3.2% 0.2% -4.3% NA

 


Discussion

In general, bunting is a losing strategy, as evidenced by the prominence of the red entries in the tables.  Of the 960 situations examined, bunting reduced the offense's chances of winning in nearly three-quarters (718) of them.  Bunting improved the chances of winning in 238 (24.8%) cases and resulted in no change in four (0.4%).  However, there do appear to be game situations which suggest bunting as an appropriate strategy.  Bunting is more effective when there are no outs than with one out.  Likewise, bunting is more advantageous with two runners advancing than with just one.  Neither of these conclusions is surprising.

Apart from counting outs and runners, bunting is most appropriate late in a close game.  In particular, when the home team can advance the winning run with no outs, bunting is a good idea.  Similarly, when the offensive team leads by one or two runs late in the game, bunting increases the chances of scoring an insurance run (and therefore increases chances of winning the game).  Since bunting generally reduces the expected number of runs scored, it is only appropriate when a single run matters.  Therefore bunting early -- especially to advance a single runner -- is seldom desirable.

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