When managing a baseball team, a manager has to decide how to run the offense. In a prior post, I gave a little bit of an overview of two major offensive strategies: big ball and small ball. Big ball is an offensive strategy where the team depends on big hits and a few innings where multiple runs are scored. Stolen bases, sacrifices, and strategic outs are not major parts of this type of strategy; rather a team will forgo a seemingly more sure single run to go for a curvy number on the scoreboard.
In small ball, however a team will go for the more certain single run over the chance of getting more runs in an inning. A team that uses this strategy will use sacrifices, stolen bases, and strategic outs to score a runner on base instead of depending on solid hits and home runs. A team that has a lot of weak hitters in their lineup is more likely to use this strategy since runs will be at a premium.
I also alluded in that earlier post that big ball is the better strategy. Stolen bases actually have a negative correlation with runs scored whereas home runs, on-base percentage, and slugging have a very strong correlation with runs scored. One of the questions that may have come to mind if you read that post is “Don’t stolen bases improve a team’s chances of scoring runs? How come increasing the number of stolen bases for a team also decreases the number of expected runs for that team?”
In short, the reason for this is that a missed stolen base decreases expected runs scored. With a runner on first and nobody out, for example, a team can expect to score 0.941 runs per inning. If that runner successfully steals second base, the team has a runner on second and nobody out and can expect to score 1.170 runs. However, if they are caught stealing, the team has nobody on base and one out, and the run expectancy is down to 0.291 runs.
How often must a team successfully steal a base to break even? In other worse, how often must a team be successful in stealing a base to make it worth it? To research this, I used the chart on this website (http://www.tangotiger.net/re24.html) to determine run expectancy given different situations. I used the 1993-2010 matrix since that is the most relevant information on that website. Since stealing home almost never happens, I will not look at that and instead look at situations with runners on 1st base, 2nd base, and on both 1st and 2nd base. Here are the different scenarios (note: when I look at scenarios with runners on 1st and 2nd, I consider getting the lead runner out as being "caught stealing"):
Exp. Runs Stolen Base Caught Stealing
0 Out, 1st Base 0.941 1.170 0.291
0 Out, 2nd Base 1.170 1.433 0.291
0 Out, 1st & 2nd 1.556 2.050 0.721
1 Out, 1st Base 0.562 0.721 0.112
1 Out, 2nd Base 0.721 0.989 0.112
1 Out, 1st & 2nd 0.963 1.447 0.348
2 Out, 1st Base 0.245 0.348 0.000
2 Out, 2nd Base 0.348 0.385 0.000
2 Out, 1st & 2nd 0.471 0.626 0.000
The next step is to consider the net gain in expected runs when a stolen base is successful and the net loss in expected runs when a stolen base is unsuccessful:
SB, Net Gain CS, Net Loss
0 Out, 1st Base 0.229 (0.650)
0 Out, 2nd Base 0.263 (0.879)
0 Out, 1st & 2nd 0.494 (0.835)
1 Out, 1st Base 0.159 (0.450)
1 Out, 2nd Base 0.268 (0.609)
1 Out, 1st & 2nd 0.484 (0.615)
2 Out, 1st Base 0.103 (0.245)
2 Out, 2nd Base 0.037 (0.348)
2 Out, 1st & 2nd 0.155 (0.471)
Based on this information, we can determine how successful a stolen base attempt must be for a team to break even.
Break Even
Stolen Base %
0 Out, 1st Base 73.95%
0 Out, 2nd Base 76.97%
0 Out, 1st & 2nd 62.83%
1 Out, 1st Base 73.89%
1 Out, 2nd Base 69.44%
1 Out, 1st & 2nd 55.96%
2 Out, 1st Base 70.40%
2 Out, 2nd Base 90.39%
2 Out, 1st & 2nd 75.24%
In short, a team must be very successful at stealing bases to make it worth it. A 50% stolen base success ratio won't cut it. A 75% stolen base success ratio just barely cuts it. I don't have any hard numbers to back up how often each of the nine scenarios above come up. I'd argue, though, that the vast majority of stolen base attempts occur with a runner on 1st. The simple average necessary stolen base percentage for scenarios with runners on 1st is 72.74%. For simplicity purposes (but also since it is a reasonable ratio), we will determine that 72.74% is the magic ratio.
So how does this translate to real life baseball? To determine this, I have looked at the league leaders in stolen bases for each league for each year going back to 1980. I also took a simple average of the net gain for each stolen base when there is a runner on first (0.1637 runs) and a simple average of the net loss for each each caught stealing when there is a runner on first (-0.4483 runs). In that time, there have actually been four players (1981 Rickey Henderson, 1993 Chuck Carr, 1995 Quilvio Veras, and 2001 Juan Pierre) who have lead the league in stolen bases and have actually hurt their team with stolen base attempts. None of them materially hurt their team (Rickey Henderson cost his team 0.70 runs, Chuck Carr cost his team 0.37 runs, Quilvio Veras cost his team 0.25 runs, and Juan Pierre cost his team 0.09 runs), but we're talking about league leaders here. If you lead the league in stolen bases, one would expect the player to also add value to his team. No wonder Chucky hacked.
The vast majority of players, however, added runs for their team. How many runs did each player add? The answer is not much. Most baseball statistic gurus would argue that a player adds one win of value to a team when they add 10 runs to their team. Only one player, 1986 Vince Coleman, added over 10 runs for his team in a year by stealing bases (he stole 107 bases, got caught stealing 14 times; he added 11.24 runs for the team). After that, however, not a single player added a full win for their team. Rickey Henderson came closest in 1988 when he added 9.39 runs of value for his team. On average, league leading base stealers added about 4.39 runs for their team over the course of a year. For some players, this could be seen as a nice bonus. For example, Mike Trout had a spectacular offensive season in 2012. He also stole 49 bases and got caught 5 times, adding 5.78 runs of value for his team. Jose Reyes was on the list, Ichiro Suzuki was on the list, Carl Crawford was on the list, and Brian Roberts was on the list. For these players, they don't make a Major League career by stealing bases; it's just a nice little bonus.
For some players, however, their major asset is speed on the basepaths. Vince Coleman would have never been a Major Leaguer if it wasn't for his base stealing prowess. Tony Womack was a terrible player without his speed. Chone Figgins, Eric Young, Quilvio Veras, and Scott Podsednik weren't everyday players without their speed. The question that should really come to mind for these players is "Why were they everyday players?"
There are other ancillary reasons that a speedy player adds value to a team. They likely have more range in the field, they may be able to take an extra base on a hit, and may be able to run out a few ground balls for hits. However, let's look at Tony Womack in 1997. In 1997, Tony Womack led the National League with 60 stolen bases. He actually only got caught 7 times, so his success rate was about 90%. Because of his prowess on the basepaths, he added 6.68 runs for the team. Their other middle infielder for the team that year was Kevin Elster. He lost about 0.90 runs on the basepaths by stealing 0 bases and getting caught twice. However, he did get injured fairly early in the season and got replaced by Kevin Polcovich. In 1997, Polcovich stole 2 bases and got caught stealing twice. That is equal to about -0.57 runs. So, on the basepaths, here's how the three players ranked:
Tony Womack 6.68 runs
Kevin Polcovich -0.57 runs
Kevin Elster -0.90 runs
However, in 689 plate appearances in 1997, Womack hit 6 home runs. In 164 plate appearances in 1997, Elster hit 7 home runs. In 279 plate appearances in 1997, Polcovich hit 4 home runs. Extrapolating the home run total over 689 plate appearances may be unfair since it is unlikely Elster or Polcovich would have continued hitting home runs at that rate (if they had, Elster would have hit 29 home runs in 689 plate appearances and Polcovich would have hit about 10 home runs in 689 plate appearances). To be relatively conservative, let's say Elster would have hit 20 home runs in 689 plate appearances and that Polcovich would have hit 8 home runs in 689 plate appearances. A home run adds approximately 1.40 runs (source: http://www.tangotiger.net/runscreated.html); there is one automatic run since the player scores. There are also additional runs added for players on base, so in the end, it works out to about 1.40 runs.
In 689 plate appearances in 1997, Womack hit 6 home runs and added 8.4 runs for the team in that year. Think about that for a second. Tony Womack, one of the speediest and weakest hitters of all time, provided more runs for his team in 1997 with the long ball than with base stealing. If Elster had hit 20 home runs in 689 plate appearances in that same year, which is a very reasonable projection, he would have provided 28 runs for his team with the long ball. If Polcovich hit 8 home runs in 689 plate appearances in that same year, again a reasonable projection, he would have provided 11.20 runs for his team with the long ball. So here are the home run contributions for each player
Kevin Elster 28.00 runs
Kevin Polcovich 11.20 runs
Tony Womack 8.40 runs
When combined with base stealing statistics, here are the contributions for each player:
Kevin Elster 27.10 runs 2.71 wins
Tony Womack 15.08 runs 1.51 wins
Kevin Polcovich 10.63 runs 1.06 wins
When
it comes to on base percentage, they were essentially equal; Womack had
a .326 OBP, Elster had a .327 OBP, and Polcovich had a .350 OBP.
Womack was actually weakest in this category, and Polcovich was the
best. Using my Eq. run statistic, .024 OBP points is equivalent to 0.133 eq. runs / game. We have to divide this by 9 since the eq. run statistic assumes a team of 9 of the player instead of one of the players' run contributions. Then we multiply it by 155 games, which is the number of games Womack started in 1997. Polcovich added about 2.29 runs over Womack and Elster in OBP. That brings the difference down to about 2 runs, or about 0.2 wins over the course of a season, between Womack and Polcovich.
Here's the messed up thing; Womack, who was just barely better than a utility infielder on a below-.500 team, he was an all-star, he finished 9th in Rookie of the Year voting, and 24th in MVP voting. Polcovich didn't. He actually only played one more year in Major League Baseball, and it wasn't as a starter. Womack played until 2006, averaging under 4 home runs a year and with a .317 on-base percentage. He was just barely better than a utility infielder whose Major League career ended one year later in 1997 and he got worse over time. Again, it just shows how terribly inaccurate people who talk about winning with "small ball" is important.
In short, there is a negative correlation between stolen bases and runs scored because a runner caught stealing gives up more runs than a runner stealing a base gains. Even the best base stealers have a very minimal impact on a game, however. Only one league leading base stealer since 1980 (Vince Coleman) added a game's worth of value to his team.
SACRIFICE BUNTING
So we can come to the conclusion that stolen bases don't win many games. How about sacrifice bunting? A good small ball team has a lineup of players who can bunt. But is that smart?
The answer isn't an across-the-board "yes" but it also isn't an across-the board "no". In the first scenario I'll look at, I'll consider a situation with a runner on 1st and nobody out. In this situation, a team can expect to score 0.941 runs. An unsuccessful sacrifice bunt will leave a runner on first with one out, a situation that will decrease the expected run value to 0.562 runs. A successful sacrifice bunt, on the other hand, will decrease the expected run value to 0.721 runs. In addition, the best information I found stated that a sacrifice bunt works about 76% of the time. Taking that into account, a team with a runner on first and nobody out would expect to see its expected run value decrease from 0.941 runs to 0.683 runs if they decide to sacrifice bunt with the next batter up.
It doesn't sound great. Even if a sacrifice bunt works, the expected run value goes down. Why would any team do that? The answer is that having the next batter swing away could work against them. A player with a .000 OBP, for example, would always want to sacrifice bunt in that situation since 0.721 runs is still higher than 0.562 runs.
But how often would the next player up need to get on base to make it so refusing the sacrifice is a smart option? To determine this, we realize that having a runner on 1st and 2nd with 0 outs yields an expected 1.556 runs. Again, having a runner on 1st with 1 out yields an expected .562 runs. The equation I need to solve is 1.556x + .562(1-x) = .683, where x is the break-even on-base percentage. Solving this shows that a player with an OBP of above .122 should swing away in this situation. Obviously, the real answer isn't that simple; an extra base hit, a single where the runner takes 3rd, and a double play are possible when swinging away. For the sake of this calculation however, I will say that the prospects of getting more than a runner on first and second with one out, along with the prospect of a bunt double play, is offset by the prospect of a double play. Therefore, an OBP of about .122 sounds about right.
I ran a very similar analysis with the same situation but instead of having a runner on first with no outs, I have a runner on first with one out. The expected runs in this situation is 0.562. With an unsuccessful sacrifice bunt, the expected runs goes down to 0.245. With a successful sacrifice bunt, the expected runs goes down to 0.324. With a successful hit, the expected runs goes up to 0.963. Using all of these factors, I found that the break-even OBP is down to .110.
How about the suicide squeeze? There are a lot of situations where this comes up, but to keep this post from becoming even longer than it already is, I'm going to look only at a situation with a runner on 3rd and 0 outs and a runner on 3rd and 1 out. I am also going to assume that we are looking at a situation in a game where a pitcher will throw the ball to first if the bunt works to get the out. Finally, the best evidence I could find says that a suicide squeeze only works about 68% of the time.
A team with a runner on 3rd with nobody out can expect to score approximately 1.433 runs in that inning. A successful suicide squeeze will score 1 run and leave the bases empty with one out, which leaves a team with 1 sure run and a run expectation for the rest of the inning of 0.291 (for a total of 1.291 runs). An unsuccessful suicide squeeze will get the out at home but the batter will reach first. A team with a runner on 1st and one out can expect to score 0.562 runs. Using the 68% success ratio, a team that decides to use the suicide squeeze sees its expected runs decrease from 1.433 runs to 1.058 runs.
Playing big ball, a team will go for a hit. To be conservative, I'll say the only hit that will happen is a single to score the run and leave a runner on first. A team that gets a hit in this situation will see its expected runs go up from 1.433 runs to 1.941 runs. A team that doesn't get a hit would still have a runner on 3rd with one out, which would still yield about 0.989 runs. The break-even on-base percentage is .072. Most weak hitting pitchers will still have a higher on base percentage than that.
With a runner on 3rd and one out, however, the squeeze play becomes a lot more reasonable. With a runner on 3rd and one out, a team can expect to score .989 runs. An unsuccessful suicide squeeze will lower that to 0.245 runs and a successful suicide squeeze will actually increase it to 1.112 runs. A suicide squeeze attempt will still lower the expected runs to .834, but it's not a huge dropoff. A successful single will increase expected runs to 1.562. If a hitter only hits singles, he needs a batting average of about .381 to make it so that a suicide squeeze is not a good idea. However, this is certainly not all-encompassing. Most players won't have a .381 batting average or even a .381 on-base percentage, so it would seem that a suicide squeeze is the right decision most of the time. However, as a I stated above, a suicide squeeze attempt will still lower expected runs. If you include doubles, home runs, triples, errors, deep fly balls, soft ground balls, etc., swinging away will still be the right decision for the average hitter. Still, it would make sense to use the suicide squeeze with a below-average hitter.
But What If You Only Need One Run? Is Sacrifice Bunting Smart Then?
Obviously, there are situations where you are really going after one run. If you are down by one run late in a game or if you are tied late in a game, getting one run should be the goal, either to keep the game going, to take the lead late, or to win the game. Having a runner on 3rd with 0 outs may yield an average of 1.433 runs, but does anything beyond 1 really matter in that situation? I suppose it could, but for the sake of this argument, we will look at situations where only one run is needed.
First we will look at sacrificing with a runner on first. With a runner on first with 0 outs, a run will score about 44.1% of the time. An unsuccessful sacrifice bunt will lower that to 28.4% while a successful one will decrease it to 41.8%. Using the same ratio as above, a sacrifice bunt attempt will lower the odds of scoring a run from 44.1% to 38.6%. Having runners on 1st and 2nd with 0 outs, however, will increase the odds of scoring a run to 64.3%. Using these assumptions, a player needs a .284 OBP to break even. Outside of most pitchers and a few select everyday players, most players will have an OBP above .284 so forgoing a sacrifice bunt in this situation doesn't make sense.
With a runner on first with one out, a team can expect to score about 28.4% of the time. An unsuccessful sacrifice bunt will lower it to 13.5% while a successful sacrifice bunt will lower it to 23%. Therefore, a team that decides to sacrifice bunt with a runner on 1st and one out will lower their odds of scoring a run from 28.4% to 20.7%. Having runners on 1st and 2nd with one out will raise the odds of scoring a run to 42.9%.
The break even on base percentage in this scenario is then .244.
Now let's look at the suicide squeeze. With a runner on third and nobody out, a team can expect to score about 85.3% of the time. A successful suicide squeeze will increase that to 100%. An unsuccessful suicide squeeze will decrease it all the way to 28.4%. Going for the suicide squeeze in this scenario lowers the odds of scoring one run from 85.3% to 77.1%. A successful hit using big ball will score the run. An unsuccessful non-sacrifice at-bat will lower the odds of scoring one run to 67.4%. The break even batting average is .298, but also remember in this case that a long fly ball would produce the same result as a hit and a well-placed ground ball would produce the same result as a hit. So, I suppose instead of batting average, we could say that a formula of (hits + long fly balls + well placed ground balls) / at-bats would have to be .298.
With a runner on third and one out, a team can expect to score about 67.4% of the time. A successful squeeze will increase that to 100% and an unsuccessful suicide squeeze decreases it to 13.5%. That means that going for a suicide squeeze in this situation will actually increase the odds of scoring a run (100% x 68% success rate = 68%, which is already higher than 67.4%). Obviously, it's not as simple as that; the defense will play with the infield in. If the infield is in, the team will likely have to swing away no matter what, since a sacrifice bunt will almost never be successful.
In conclusion, small ball may sound nice in theory. However, in pretty much all cases, it costs more runs (by forgoing a curvy number and instead settling for 1) than it gains.
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