Take a Pitch; A Walk Can Win a Game
By Keith Glab
Little Leaguers everywhere are taught that “a walk is as good as a hit.” Of course, we know that a walk isn’t quite as
good as a hit. A walk is tied with a Hit by Pitch for the least positive thing a batter can do at the plate. But it is positive.
Perhaps what coaches are trying to convey with that axiom is that “a walk is soooo much better than an out.”
The way I approach this issue is to take a historically obvious walking situation and show how the walk is possibly to
the advantage of the offense, rather than the defense. In 1998, Mark McGwire hit primarily in front of Ray Lankford, a
competent yet unspectacular hitter. Mark drew 162 walks that year, but only scored 25% of the time when he was on
base, on par with his career average. Does this mean that he should have been swinging away more often in an effort
to hit more homers and drive in more runs?
Let us begin to answer this question by analyzing one of the most obvious situations to want your slugger swinging
rather than walking: runners on 2nd and 3rd with 2 outs. Based solely on 1998 numbers, McGwire had a 12% chance
of singling, 4% chance of doubling, 0% chance of tripling, 14% chance of homering, and a 70% chance of making an
out, assuming he swings away and does not walk. Let’s say that a single is guaranteed to score both runners. This
means that if he does not walk, McGwire has a 16% chance of driving in two, a 14% chance of scoring three, and a 70%
chance of ending the inning with zero runs scored.
If McGwire walks, the bases are loaded for Mr. Lankford. In 1998, Ray had a 14% chance of singling, a 6% chance of
doubling, a less than 1% chance of tripling, a 5% chance of homering, a 15% chance of walking or being hit by a pitch,
and a 59% chance of making an out. Let’s assume again that a single scores two, and that the plodding McGwire can’t
score from first on a double. The cardinals now have a 15% chance of scoring 1 run, a 14% chance of scoring two, a
less than 1% chance of scoring three, a 5% chance of scoring four, and a 59% chance of inning the inning without
scoring. Here’s a summary in chart form:
Runs Scored McGwire Swings McGwire Walks
0 70% 59%
1 0% 15%
2 16% 20%
3 14% <1%
4 0% 5%
Avg. Runs .74 .75
So when a player having a historically great season walks in front of a player having a good season in a situation that
traditionally begs for the defense to walk him, the team’s odds of scoring go up by 11% while the average number of
runs scored in that inning remains about the same. Keep in mind that we obtain these numbers without even
addressing the following factors:
1. Players hit slightly better with the bases loaded than with runners just on 2nd and 3rd
2. McGwire is not going to hit as well when he expands his strike zone
3. If Lankford keeps the inning alive, there is more potential for further scoring than if McGwire clears the bases.
The reason that the value of McGwire’s walks are not represented in his runs or RBI totals is that the players in front of
him generally score the runs, while Lankford gets credited with the RBIs. In fact, if McGwire walks and the Cardinals
score, there’s an 87.5% chance that McGwire does not score on Lankford’s at-bat. So McGwire has helped increase
the Cardinals odds of scoring, but does not receive any traditional credit (R or RBI) for it.
Now that we’ve examined a situation where the defense is quite likely to pitch around or even want to walk a superstar,
let us turn to the situation that McGwire receives the majority of his free passes from: 0 on, 0 out. This situation occurs
24.3% of the timea, though for a #3 hitter like McGwire, the percentage will be lowerd (the situation is unlikely to occur in
his first at-bat of the game).
It’s difficult to map the inning’s hypothetical scoring from such an early stage, but we do know that on average, a leadoff
man reaching first base increases the odds of scoring from 25% to 30% (an increase of 5%), and increases the
average number of runs scored in that inning from .461 to .813 (an increase of 76%).a We also know that the average
player hits 20 batting average points higher with a runner on first base than with the bases empty, and 4 BA points
higher not leading off an inning rather than leading off an inningb. (Being a left-handed pull hitter, Ray Lankford
probably takes greater advantage of the right-side hole created from holding a runner at first than the average hitter
would, but we can disregard that for our purposes here). So here’s what we have so far:
1. Even a great hitter like McGwire is at a disadvantage when leading off an inning. (This is why leadoff hitters who can
succeed in that role are so valuable). He goes from a .299 hitter to a .295 hitter.
2. Hitting with a man on first increases Lankford’s batting average by (at least) 20 points, from .293 to .313. (Again
proving the worth of an effective leadoff hitter, but also showing why players will often have breakout seasons when
hitting AFTER a great hitter, not just before.) McGwire has just walked to bring up a player with a better chance of
getting a hit than McGwire did.
3. I don’t have statistics showing situational effects on slugging average, but if we assume that it’s about the same as BA
effects, McGwire’s slugging average drops from .752 to around .744, and Lankford’s goes up from .540 to about .580.
McGwire’s SLG is still 22% higher than Lankford’s. But…
4. If, on average, the number of runs scored in an inning increases by 76% when you put the leadoff runner on first
base, wouldn’t you want a hitter who’s only 22% worse than McGwire up in that situation, rather than having McGwire
swinging at pitches out of the strike zone?
I suppose the question at this point is, “fine, if McGwire’s walks are so darn valuable here, why isn’t he scoring more
runs per time on base?” Two fairly obvious reasons:
1. If McGwire is forced out on Lankford’s fielder’s choice, he can’t score a run. However, he’s still improved the team’s
chances of scoring over making an out to the tune of 6.7% and .102 average runs (0 on, 2 outs) to 30% and .813
average runs (runner on 1st, 1 out)a . Whether McGwire or Lankford is forced on the play has more to do with luck than
one player’s ability to score runs.
2. As previously stated, McGwire comes up with no one on and no one out less than 25% of the time. He comes up with
a runner on first about 34.3% of the timea, meaning that when he walks in those instances, the runner(s) on base
advance. Now I don’t suppose that I need to expound on how runners who advance without a loss of an out are more
likely to score, but I will point out that McGwire will only get credit for an RBI walk about 2% of the time. Again, he helps
his team score with nothing to show for it in the boxscore.
So, having explored the issue from a couple of different angles, we see that in the majority of instances a walk to a
superstar benefits the offense, even in those instances traditionally thought of as pitch-around situations. This brings
up the question, “then when is walking a superstar beneficial to the defense?” I can think of three instances:
1. The hitter behind the superstar is uncharacteristically bad
AKA: the Santiago Scenario. Rarely is there a case when one hitter is SO much better than the one behind him outside
of the #8 hitter in NL games. But if there is such a case, it’s the Bonds/Santiago situation from 2002. Let’s rerun our
initial table with runners on 2nd and 3rd, two outs:
Runs Scored Bonds Swings Bonds Walks
0 63% 68%
1 0% 6%
2 26% 17%
3 11% 6%
4 0% 3%
Avg. Runs .85 .70
In this table, I assumed that the relatively speedy Bonds does score from 1st on a double. Regardless, the team
probably does have a better chance of scoring with Bonds swinging away in front of Santiago (keeping in mind the three
points made earlier about why the walk is slightly more valuable than this table shows). However, we cannot just say
that all of Bonds’ career walks are foolish, since usually someone of Jeff Kent’s caliber is hitting behind him. It has only
been for the past two years that we can really question the value of his walks. Even now, we can’t say that Bonds
should just swing at everything within reach, because of
2. The lefty/righty advantage
There’s a reason that managers stagger their lineups. In the case of Bonds and Santiago, Bonds has hit approximately
100 OPS points better over the course of his career versus right handed pitchers than he does versus southpaws (95,
actually). Similarly, Santiago has hit 102 OPS points higher versus southpaws than versus the rightiesc. This makes it
more advantageous for Bonds to swing away or expand his strike zone versus righties. Versus southpaws, he is
certainly better off taking the walk.
3. Runner on 3rd, one man out
In this situation, a team is likely to score 69% of the time for an average of .98 runs scored in the remainder of the
inning. With runners on first and third with one out, the team is expected to score only 63% of the time, but for an
average of 1.115 runsa. So assuming the batter at the plate is equal to the one on deck, you would walk him if one run
is devastating, and otherwise you would pitch to him. If the batter at the plate is a superstar, and the one on deck is “a
competent yet unspectacular hitter,” you’d be a fool not to walk the superstar.
Why is this so? Well, with a runner on 3rd and one out, a ground ball generally scores a run. With runners on 1st and
3rd and one out, a ground ball generally ends the inning. We do need to consider the on deck hitter’s propensity for
grounding into double plays, but generally speaking this is a great situation for a defensive walk. (Note: this also applies
to runners on 2nd and 3rd with one out). The only other situations where, on average, you decrease the offense’s
odds of scoring with a walk, are with a runner on 2nd and no outs, and with runners on 1st and 3rd with none out. But
in each of those cases you increase the average number of runs scored by so much that walks in those situations are
precarious outside of the 9th inning. There is no situation where the average number of runs scored in the inning
decreases with a walk.
Wrapping this all up, a player who avoids outs is tremendously valuable to any team. It is extremely rare to find a player
who is so far better than the rest of his teammates that he would be foolish to take a walk. Even in the most extreme
case of all time, Barry Bonds with crap behind him, there are only certain situations in which he may be better off
expanding his strike zone than walking. Even then, the improvement is a marginal one.
Yes, it sucks. We would all like to believe that walking all the time won’t win you games, because it’s more exciting to
watch an elite hitter such as Bonds hit than walk. Just as we’d all like to think that stealing bases is an integral part of
an offense because they’re so fun to watch. Just as we’d like to believe that when hitters strike out it’s much more
detrimental than a ground out, since we’d rather see a ball put in play. But we cannot let ourselves confuse what is
exciting to watch with what is beneficial to a team.
Homework Assignments
1. (Re)read the Babe Ruth comment in Bill James’ New Historical Abstract.
2. Find as many players as you can that have led the league in runs scored or RBI’s more than five times. Next, pick
any two other offensive statistics, such as hits, doubles, walks, homers, slugging average, etc. and see how many
players you can find who have led the league more than five times in those categories. Compare, contrast, and then
compose an essay on which group of stats you believe to be the most independent of variables outside of a player’s
control.
3. Give me feedback on this essay.
Appendix
What follows is an expected runs scored chart based on data from the 2000 season. I chose to site data from the
1959 and 1960 seasons because it was the pioneer for such analysis, a much more reliable source than this 2000 data
(Rob Neyer Message board), and included the % of time each situation occurred. Notice that in this chart, runs scored
are higher, but the situations’ relationships to each other are similar. Actually, according to this data, it is even more
beneficial now for the offense to take a walk than it was 40 years ago. Feel free to rerun any calculations using this
data instead:
Bases Occupied Expected Runs % Probability of Scoring
0 1 2 0 1 2
Empty 0.57 0.31 0.12 .30 .18 .08
1st 0.97 0.60 0.27 .45 .29 .15
2nd 1.18 0.73 0.33 .64 .42 .22
1st,2nd 1.63 1.01 0.48 .66 .44 .24
3rd 1.52 1.00 0.41 .86 .67 .28
1st, 3rd 1.92 1.24 0.52 .88 .66 .29
2nd, 3rd 2.05 1.50 0.64 .85 .71 .29
1st, 2nd, 3rd 2.54 1.70 0.82 .89 .69 .34
Endnotes
a These statistics come from play-by-play data gathered by George Lindsey from 373 games and 27,027 total
situations during the 1959 and 1960 seasons. Surprisingly, Pete Palmer later developed a computer simulation to test
this data throughout baseball history, and most of the data remained constant throughout the years.
b This data is from the Elias Sports Bureau from American League hitters in the years 1984, 1986-1988, 1990 and
1992, totaling 464,057 non-pitcher at-bats.
c These lefty/righty splits come from the Yahoo!Bigleaguers.com website, and actually only run since 1987. Both Bonds
and Santiago had some at-bats in 1986 that would no doubt alter the numbers slightly.
d Barry Bonds only came up with none on/none out 20% of the time in 2002
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