image credit to zimbio.com
By Lincoln Floyd

As I was watching the Rangers game last night I couldn’t help but be overwhelmed with the thought that baseball is a funny game. Despite being around for well over 100 years, there is still so much we don’t know about the game. So many different things happen over the course of a baseball game that we can’t keep it all straight.

To those who know me (or follow me on twitter) it is pretty obvious I am a numbers guy. I like having tangible evidence to help keep my perception in line with reality. The numbers help me understand the game at a deeper level. Fortunately for me, no sport produces the amount of data that baseball does. I know the game is more than numbers, but the numbers are important. Almost every MLB team has a well-staffed analytical department for that very reason. The numbers DO matter.

Another reason baseball is so unique from other sports is that there isn’t a clock in baseball. There are no 15-minute quarters, or 24-second shot clocks in baseball. Each team has 27 outs to score more runs than the other team. An out is one of the most precious commodities in baseball, and thus should be protected fiercely.

I said all of that so that I could say this: I really hate sacrifice bunts. I am aware that bunting is part of the game. I am aware that people have been doing it for over 100 years. I am aware that most of the “old school” baseball types like the idea of a player “sacrificing” himself for the good of the team. Trust me, I get it.

The problem I have with sacrifice bunting is that it is proven to not be the most effective way to score runs. It isn’t a wild mathematical theory that may or may-not be true. There is a large body of evidence based on decades of data that show sacrifice bunting is almost always a bad idea.

Below is a simple chart known as the “Run Expectancy Matrix.” This chart was compiled based on data from the 1993-2010 seasons. You may ask why this matrix doesn’t encompass a broader range of historical data? The reasoning behind that is context. Baseball is a very cyclical sport in that there are clear-cut offensively dominated periods, and pitching dominated periods. By starting the data in 1993 we are looking at what amounts to a very offensive friendly era. These changes are due to a myriad of factors like mound height, strike zone, size of the stadium, and much more.

But back to the chart. The 3 columns on the left represent all of the different possible scenarios involving base runners. The top row represents how many outs a team has. The decimal numbers in the chart represent how many runs an average team is expected to score based on the situations.

For example a team with 0 outs and a runner on 2nd is expected to score 1.170 runs that inning. But if that same team is batting with 1 out and a runner on 2nd they are expected to score only .721 runs in that inning.

Like I said, this matrix is compiled based on what has actually happened in baseball over this time period. This isn’t what someone thinks will happen; this is real, tangible data. This simple chart pretty much sums up my feelings about the sacrifice bunt.

Let’s look at the scenario that came up in the game last night. In the bottom of the 5th inning, Ian Kinsler led off with a double. So the Rangers had a runner on 2nd base with 0 outs. Their run expectancy for the inning was 1.170 meaning Texas was expected to score at least 1 run in the inning.

Elvis Andrus, the Rangers #2 hitter stepped to the plate. Lineup optimization is an argument for another time, but a guy hitting in the #2 slot in any lineup should be capable of driving in runs. (In his book, “The Book--Playing The Percentages In Baseball” Tom Tango actually advocates the #2 slot should be the best hitter in the entire lineup)

Instead of swinging away, Elvis Andrus laid down a sacrifice bunt. It can be debated who actually called for the bunt, but that is beside the point. Elvis “sacrificed” himself so Ian Kinsler could move 1 base closer to home. Sounds pretty solid huh?

Instead of just saying “that is the way baseball is played,” let’s look at the handy Run Expectancy Matrix and see how the run expectancy changed. With a runner on 3rd base and now 1 out, the run expectancy is .989. So the sacrifice bunt actually DECREASED the likelihood that Texas would score a by .181. This is not a large number by any stretch, but it is a 15% drop in run expectancy. In the case of last night’s game, this decrease became relevant as Josh Hamilton and Adrian Beltre both flew out to center field to end the inning, stranding Kinsler at 3rd base in an inning that on average should have netted at least 1 run.

This is also the case when a runner is sacrificed from 1st base to 2nd to avoid the double play. With a runner on 1st and 0 outs a team is expected to score .941 runs while a team with a runner on 2nd and 1 out is expected to score only .721 runs. These differences are even larger (23% decreased run expectancy), and again, this is real.

Now there are two sides to every coin. Some times late in games it is ideal to play for only 1 run. There is an entirely different run expectancy matrix that deals with the probability of scoring only 1 run. In these extreme scenarios, sacrifice bunting CAN be a good idea.

The batter at the plate also matters when a team is thinking about sacrifice bunting. If it is a very weak hitter, sometimes the team is better off choosing to have that hitter bunt as opposed to swinging away. That is an extreme case though. It would require a VERY poor hitter to make sacrifice bunting a good idea in the scenarios I discussed.

None of this is groundbreaking data. It isn’t like I whipped out my calculator and waded through decades of data after the 5th inning last night so I could write this piece. This doesn’t even scratch the surface on all the data out there regarding sacrifice bunts. There are tons of books and articles out there that a person can read to better understand these concepts. To see this and other run expectancy matrixes you can click here.

People who don’t like advanced analytics are quick to discount anything involving numbers claiming, “The game is more than math.” I totally agree with that sentiment. The game is more than math. But in this instance, the math is pretty cut-and-dry. By sacrificing outs to move runners, teams are hurting their odds of scoring runs in most instances. You wouldn’t knowingly take worse odds to win the same prize in Vegas because your gut told you to, would you?

I know not everyone will agree with me on this. That is part of the beauty of baseball. This is just one aspect of the game that is cause for much debate, and I love that. 

Thanks to the enlightening conversation in the comments section, it became relevant to include the run expectancy chart for scoring a single run at any point in an inning. This chart is included below:
chart credit to Tom Tango of tangotiger.net
As you can see, based on the 1993 - 2010 data, in the situation the Rangers were in during the 5th inning of Wednesday's game, the odds they would score one run with nobody out and a man on 2B were 0.637, or 63.7%. By implementing a sacrifice bunt, and putting Kinsler on 3B with one out, the odds of scoring just one run increased to 67.4%, or a 3.7% increase. 

Another common situation is the bunt with nobody out and a man on 1B. If the bunt is successful, the odds of scoring just one run move from 44.1% to 41.8%, a decrease of 2.3%. 

Not factored into this table is the odds that a bunt attempt is even successful. As was seen Alberto Gonzalez's attempt in Thursday's game against the Mariners, it is not always an automatic that the sacrifice bunt will be placed successfully. This is one of several variables that must be weighed in these situations, including the quality of the hitter, and the game situation. Sometimes all these variables can stack up to make the sacrifice bunt worth the 3.7% increase in the probability of scoring one run, and sometimes they don't.

Lincoln Floyd is a Shut Down Inning staff writer. You can email him at Lincoln.Floyd@shutdowninning.com or reach him on Twitter @SDILincoln. 


04/12/2012 1:12pm

Good stuff man

04/12/2012 1:25pm

I've never understood using the sacrifice bunt to get or extend a lead. It's nice to see some numbers that support why that doesn't make sense. I would put myself in the "pro-bunt" group which seems to separate Rangers fan on Twitter, but even I don't like when Kinsler starts the game by getting on base, and we sacrifice our 1st out to move him over into scoring position.

I would like to see a similar matrix that broke down the percentage in each of these situations that at least 1 run is scored. This clearly shows that bunting decreases your expected run total, but does it increase your chance of getting at least 1 run? I would expect that it would and could justify bunting late to tie up a game when down by just 1 run, but you'll never be able to justify having Andrus bunt in his first at-bat of the game.

04/12/2012 1:43pm


I haven't looked for an online version, but such a chart does exist. In "Baseball Between the Numbers" the baseball prospectus team references a separate chart that deals with these 1 run situations. The data changes slightly, but it is still overwhelmingly against the sac bunt. The entire book is fascinating reading.

04/12/2012 1:26pm

Awesome Lincoln. Sure makes you think about the strategy of the game.

04/12/2012 1:30pm

I think it comes down to line-up construction and trusting Elvis. Wash would never make MY bunt, if he doesn't trust Elvis then he shouldn't bat him 2nd.

04/12/2012 1:37pm

I think Dan hits it on the nose, if it's Michael Young in the 2 spot and not Elvis we aren't talking about a bunt there. Elvis is not your prototypical RBI guy and with no outs, I can see the move there to allow Hamilton and Beltre the chance to get Kinsler home from 3rd.

04/12/2012 2:44pm

I have two things to comment on in this well written article: 1st) A Run is the most precious commodity in baseball not an out. 2nd) I completely believe the situation last night warranted a sacrifice bunt. Elvis is currently batting a whopping 125 (3/24), so with a runner standing on second he has a one in ten chance of moving him over or possibly scoring from second; with the bunt to move him to third all Josh has to do is hit a sacrifice fly ball to score Kinsler from third—a much better option in that scenario of getting the run home. While Michael Young is currently hitting 250, based on his history he would probably get the swing away signal from 3rd; especially with Hamilton and Beltre batting behind him; the hope being that the Rangers are in store for a possible big inning. All that being said; the Rangers pitching staff (concerns for Nathan aside) has been shut down in this short lived season, Millwood was pitching a gem, and the game appeared to be headed toward another close game where one run would make all the difference. Sacrificing (weather bunt or fly ball) is all about the situation. There is an argument to be made in football at all levels to not kick in any situation as well, but we know that is not always the realty. With Wash at the helm expect some small ball to be played—especially with our pitching staff. Now I will get out of the way and let you young Matrix guys continue the discussion.

04/12/2012 4:08pm


1. I agree runs are more precious than out. I said commodity because both teams start out with the same amount, and how they "use" them varies. But your point is valid.

2. My only problem with that, is if Elvis is going to be the 2 hole, he needs to execute like one. While sacrificing Ian over to 3rd may (I don't have the single-run expectancy chart in front of me) have increased the likelihood of scoring 1 run, I would argue that the 5th inning is too early to play for a single run.

All very good points. This is why I love baseball. Starts some great discussions.

04/12/2012 5:50pm

The way Elvis hit the ball his last at bat (although right at Smoke) should be some indication that he is coming around, but I just do not think he will ever be more than a 270 lifetime guy...if that. So is the answer shift him to 9th, move Young to 2nd? I think I like that a bit more as well.

04/12/2012 3:42pm

We just sac bunt so in the later innings the threat of a sac bunt will alter defensive alignments, therefore giving us a greater chance at getting base hits which leads to more runs (and run on sentences).

04/12/2012 11:38pm

Haha, oh tk. Well written article Lincoln. I need one of these analytical jobs where I crunch baseball stats all day.

04/14/2012 2:10am

Nice article. I would like to see the probability of scoring 1 run chart split by each batting position. I'm sure the odds of scoring 1 run with a player on first are better when the player at the plate is the 4th batter than the 8th. I'm wondering if there would be a significant difference when the player bunting is 9th, which could change the 3.7% increase.

04/14/2012 3:40pm

My question would be in the quality of the data itself. I'm not saying it isn't good data but there seems to be an assumption that a sac bunt is the only outcome of a player bunting. Corollary is that the manager is depending upon the batter to sacrifice himself with no other possible outcome. You mentioned one ingredient which is the quality of the batter but to truly be able to suss this out you would have to measure many variables:
* quality of the defense being faced in defending the sac bunt
* ability to sacrifice against this particular pitcher versus attempting a traditional at-bat.
* groundskeeper's bias that day (ty cobb seemed to think this had value anyway)
* probability for the offense (batter+baserunners) to get a different result from bunting the ball
* effect of not being able to convert on the attempted bunt
* effectiveness of the bunting batter against this (type of) pitcher in bunt situations, non-bunt situations
* probability of this batter getting on base this particular time otherwise (slump? hot streak?)
* probably some stuff i missed

This is probably what most people mean when they say "the game is more than the math". You seem to want to go too far and to break it down into a science that you can get out your cue card to decide for you. Managers should not manage a baseball game like a black jack game. They should manage it like a dynamic entity, more like a poker game.

04/29/2012 9:08pm

Ok, here's the problem with this math. The point of smallball is to maximize the chances of getting a smaller number of runs. You trade the possibility of multiple runs for the possibility of one run. So now there's less of a chance of a monster 8 run inning and more of a chance of 1 run. This reduces a mathematical property called "variance" which basically is a measure of how "swingy" your random variable (in this case, the runs in each inning) is.

The problem with looking at run expected value is that there is only one run in a game that's important: the one that puts your score ahead of the opponent's. The EV of a runner on 1st and 2nd with no outs is 1.556, how much of this statistic is artificially inflated by times where the pitcher is just off? One 6 run inning and 3 0 run innings perfectly (ok, I rounded) explains this EV. But how often are those 6 runs important? What if you win by exactly 6? You only needed one run and you took a very real chance to get 0 runs in exchange for not sacrifice bunting and getting 1. What are the exact odds of scoring runs (any amount greater than 0) given each of these situations? How do they correlate with the relevant statistics of the batters at the plate? (OBPS, BARISP)

I'm not saying I'm in either camp but there are very real times where you're nursing a 2 run lead where you will gladly take a 75% chance of scoring one or two runs over a 30% chance of scoring 4-5. However the expected value of sac bunting here is lower (.75-1.5) than the expected value of not (1.2-1.5) This data isn't bad or anything, just incomplete.

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