When to Pinch Run?

Over the past decade, a tremendous amount of progress has been made in quantifying if and when managers should do everything from sacrifice bunt to issue an intentional walk, but one area that has been (at least to my knowledge) overlooked is when to pinch run. One of the main reasons pinch running hasn’t been investigated to the same degree as these other strategies is that there are a lot of moving parts to look at- how much more valuable is the pinch runner than the previous runner? Will removing the starter hurt the team’s defense? What’s the opportunity cost of losing an available bench player? While the answers to each of these questions are needed for a complete analysis of when to pinch run, there is one question we can answer relatively simply- how often can we expect the pinch runner’s spot in the order to come up again later in the game?

The more often a pinch runner can be expected to have to come to the plate, the less appealing pinch running is likely to be, as the players who are most often removed for pinch runners are generally very strong hitters (or catchers), and pinch runners are generally light hitters.

Take for example the White Sox-Twins game on April 9th of last year. Tied in the bottom of the 8th inning, the White Sox elected to have Mark Teahen pinch run for Paul Konerko following Konerko’s 1-out single. The next two White Sox hitters went down in order, and two innings later Teahen stepped to the plate in the bottom of the 10th with men on first and second and one out. Teahen grounded into a 6-4-3 double play and the White Sox went on to lose in 11 innings.

To look at how often a pinch runner’s spot in the order can be expected to come up, I used retrosheet data and looked at all American League games over the past two seasons, tracking all the times a pinch runner was used in close games (what I defined as a game within three runs and in the seventh inning or later) and then how often that spot in the order came up again. I limited the sample to only American league games so as not to have to deal with the complexity of tracking double switches, so this analysis may not be applicable to National League games.

Here is the average number of times the pinch runner’s spot in the order came up after pinch running:

(Click for clear view)

I filled the squared where the sample sizes were extremely small, but as you can tell from some of the round numbers, sample sizes in the 7th inning were also pretty small. There are some other anomalies in the chart. With more data I expect we would find that pinch runners used by the home team when down by 1 would be more likely to hit later in the game than those used when the home team was down 2 and 3 runs. But for the purposes of this post, the above numbers should suffice. If there is interest, I can add years to the data to come up with more reliable numbers.

So are pinch runners being used effectively?

For a pinch runner to be used effectively, the value of the pinch runner on the base-paths + the difference in the defense between the pinch runner (or whoever enters on defense) and the previous player – the opportunity cost of using bench players must be equal or greater to the run difference of the two players at the plate multiplied by the number of times that spot in the order is expected to come up again.

For now, let’s ignore defense and the opportunity cost of losing an available bench player and just focus on how much is gained on the base-paths and lost at the plate by looking at an example Angels fans became very familiar with last season- having Reggie Willits run for Hideki Matsui.

To estimate the relative run values of having each player on base, I took each player’s BSR ratings for the the year in which the pinch running occurred (2010 in this case) and the two years prior, and divided the baserunning total by a best estimate of times on base (hits + walks + intentional walks + HBP). I used a standard 3/4/5 weighting scale to give more weight to more recent performance (using this method will likely overstate how valuable having a player who is often called upon to pinch run, as they will be on base more than the total given by hits and walks, but this method will also likely understate how bad players who are often get pinch ran for are, so the bias should be minimal).

Using this method, I calculated Willits as being .027 runs above average per time on base and Matsui as being .008 runs below average. From these values, the Angels expected to gain .035 runs by bringing Willits off the bench to run.

How much do they stand to lose at the plate?

Using the same weighting procedure, Willits’ wOBA comes to .265 and Matsui’s is .361, giving us a difference of .096. Converting this difference to runs gives us a run difference of .083 runs per PA.

To find the point at which pinch running and not pinch running yield the same expected value is given by .035 = .083*(expected number of future PA). Solving the equation, when a pinch runner can be expected to bat .42 more times a manager should be indifferent between using Willits as a pinch runner or leaving Matsui on the bases.

Going back to our chart, the change should be made for all situations listed in the 9th, extra innings, and for home teams in the 8th inning.

Of course, the expected number of times the pinch runner’s spot in the order will come up is based on situations in which a pinch runner was actually used. By not using a pinch runner, teams that trail in the game may decrease the chances they score a run in that inning, thereby decreasing the chances the spot in the order comes up again. Even taking this into account, I think this analysis is worth while, as gives us a rough guide as to when pinch running may be a good idea, and when it is in the team’s interest to let the slower runner stay on base.

From this analysis, it appears that teams are already pinch-running fairly optimally, as very few pinch runners are used in the 7th inning, with an increasing number as the game goes on.

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22 Responses to “When to Pinch Run?”

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  1. Bryce says:

    Why would you limit yourself to cases where a pinch runner was used when determining whether the spot would come up again? Is there much difference between the odds that a spot will come up again when the guy was/wasn’t removed?

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    • Frank says:

      That was my first thought too. You gain a very much larger sample size that way and probably get a better estimate of times a spot in the order would come up for the rest of the game based on inning and # of outs.

      Doing both analyses, if sample sizes afforded statistical confidence, might be able to tease out some of the MLB managers biases towards pinch running (for example, a lower value for # of future plate appearances for a line up spot seen by the actual pinch running sample than the value for # of future plate appearances for the spot from the overall sample might reflect their affinity to do so when weaker line up spots are due up).

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  2. williams .482 says:

    one thing that UBR leaves out which I think is extremely important to this analysis is SB/CS. If, for example, Willits running for Matsui includes trying to steal second, that changes the equation farther in favor of pinch running (or it would if Willits were actually good at stealing bases).

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    • chuckb says:

      Yes, you’d need to add SB runs per time on base as well.

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      • Cidron says:

        agreed. pinch runner on 1b, takes off and steals second, perhaps following it up with a steal of third…. that has to factor as well, as the steals, and new runner placement will open holes in the infield that weren’t there (in an attempt to hold the runner close).

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  3. TK says:

    this is super interesting, I must say. I’m sure there are a hundred variable people will bring up, but one I’ll bring up is that the player that comes in to pinch run doesn’t have to hit if his spot comes back around. Another bench player can be used to pinch hit for him.

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  4. walt526 says:

    Interesting model. It seems to me that something else that the manager needs to take into account is whether or not it would be helpful to have the would-be pinch runner available to pinch hit for a pitcher later in the game. In an era of 12+ pitching staffs, benches are not all that deep. If a team has to pinch hit early for the starting pitcher, then it’s not conceivable that their pinch runner is also their 3rd or 4th best pinch hitting option.

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  5. chris6789 says:

    Very interesting — what I’ve often wondered is why among the pool of marginal starting pitchers (the #4 or #5 starters on most teams) there isn’t at least one with speed who provides extra value to his team as a pinch runner on days when he’s not starting. Having one of your team’s SPs pinch run would effectively eliminate the cost of using a bench player.

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    • david says:

      in theory it’d be great, but i wouldn’t want an inept pitcher running the bases in a high leverage situation–no matter how fast he may be.

      plus, if he gets hurt the manager is screwed. pitchers are delicate as is.

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      • Cidron says:

        as an example, I offer up these three words. Chien-Ming Wang. Good pitcher, until he tried to run the bases one day. Hasn’t been the same since. The way pitchers, even marginal ones, are coddled, you (as a manager) don’t want anything to do with getting him injured.

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    • williams .482 says:

      Clay Buchholz was used like that once, fast as he is, it was really not pretty. He made some not so clever decisions and got himself thrown out at home. Add in the risk of injury as said above, and it is really not worthwhile.

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    • Bhaakon says:

      Pinch running has such a small marginal benefit, I can’t imagine it being worthwhile unless the runner is bad and the pinch runner is great. If the manager’s bringing in a guy who is only around average (and I can’t see many pitchers being much better than that) then what is the point? There are only so many Bengie Molinas around the league (zero, actually, but you know what I mean).

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  6. Ben says:

    This doesn’t seem to take in account differential fielding value. For example, if the Orioles use Felix Pie to pinch run for Luke Scott late in the game, they also get whatever the advantage of having Pie play LF over Scott. This formula seems to only work when pinch running for a DH, otherwise it becomes far more complicated taking into account fielding (presumably though, a hitter who is slow enough to be pinch run for is likely to be below league average defensively).

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    • BillWallace says:

      Right, this is what the Giants did last year. If Burrell got on base in the 5th inning or later they’d have Schierholtz run for him and it combined as a defensive switch.

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    • adohaj says:

      In the article he noted that he would ignore defensive differences

      “For now, let’s ignore defense and the opportunity cost of losing an available bench player “

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    • Bhaakon says:

      The problem is that a hitter who is slow enough to be pinch run for has a good chance of not playing the same position as the speedster, so it may not be that easy to calculate the difference. Not many pinch runners are playing 1B or C.

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  7. GiantHusker says:

    This goes to prove the old adage: if you can’t be accurate, at least be precise.

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  8. chuckb says:

    Good work here. As you point out, the defensive complexities make this a little trickier and, as I said above, I think SB runs per time on base should be included but this is a good starting point.

    Thanks for doing this.

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  9. gdc says:

    The opportunity cost for bench player usage is more important in NL rules since the light-hitting utility guy you use as a PR might still be good enough to PH when the pitcher’s spot comes up. I would guess that PR’s are used less in the NL apart from the defensive sub switch mentioned above for that reason.

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  10. Reichert says:

    This model is lacking. Let me give you a scenario…

    Mike Pelfrey of the Mets gets on in the third. You can pinch run for him, or let him stay in the game. He’s already thrown 90 pitches, per usual.

    My opinion…you leave him in. As an ace, that’s what you have to do.


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  11. I’m still learning from you, as I’m trying to reach my goals. I definitely enjoy reading all that is posted on your blog.Keep the stories coming. I enjoyed it!

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