A Look at Run Expectancy and Stolen Bases in 2011

TORONTO, CANADA - SEPTEMBER 7: Jacoby Ellsbury #2 of the Boston Red Sox is caught stealing by Kelly Johnson #2 of the Toronto Blue Jays during MLB action at the Rogers Centre September 7, 2011 in Toronto, Ontario, Canada. (Photo by Abelimages/Getty Images)

There are just three requirements essential to the modern, fulfilled ballpark experience:

1. The hot dog

2. The mustard

3. Tom Tango's run expectancy table.

On occasion you can certainly forgo the hot dog and mustard. Maybe it's because you are watching your carbs, or because the buns aren't steamed enough, or because the mustard isn't French's, but in any case, you absolutely always need that Run Expectancy table.

I've found that a handy screenshot of the table in your phone can be enlightening in a great number of ways during the course of a game, but especially in its capacity to illustrate the value of the stolen base. For example: According to Tango's table, a simple steal of second base with no outs begins with an RE of .941. After the stolen base, the RE then changes to 1.170 with runner on 2nd, no outs. The gain in RE, then, is +.229 runs (1.170 - .941 = .229). But a steal of third with two outs is only worth around +.037, just a fraction of that steal of second base with no outs. This is an extreme example, of course, but it helps illustrate that the value of a SB varies with its context.

Certainly there are metrics out there that offer a much more sophisticated effort into quantifying individual baserunning achievement in a general sense, but I wanted to isolate RE strictly as it applies to the SB and CS.Using retrosheet data I've added up the gains* in run expectancy for each stolen base by individual baserunners in 2011:

NAME SB RE_SB
Michael Bourn 61 11.563
Brett Gardner 49 7.641
Coco Crisp 49 8.231
Cameron Maybin 40 7.501
Drew Stubbs 40 7.456
Ichiro Suzuki 40 6.545
Matt Kemp 40 7.595
Emilio Bonifacio 40 7.492
Jacoby Ellsbury 39 7.051
Jose Reyes 39 7.363
Elvis Andrus 37 6.122
B.J. Upton 36 6.908

(For this table and the rest of this article I am using the Run Expectancy numbers generated from 1993-2010 retrosheet data with an assist from the Chances Is blog. The values will differ slightly from those in the Tango link.)

Generally the results are as you'd expect: more stolen bases, more added RE. But there are a few cases where the SB total does not match the RE total. One particular discrepancy is that between Ichiro Suzuki and Matt Kemp, both of whom stole 40 bases in 2011, and yet Kemp leads Ichiro in RE by a full run. Part of this is attributable to the fact that 35% of Kemp's SB's took place with no outs compared to only 22% of Ichiro's. This makes sense as stealing earlier in the inning naturally provides the offense behind you with more opportunities to drive you in. In other words, more outs = less RE:

#Outs
0 1 2
RE Added Stealing 2nd 0.243 0.159 0.102
RE Added Stealing 3rd 0.272 0.270 0.031

But just as the benefits of stealing early in the inning may be larger, so are the risks:

#Outs 0 1 2
RE Lost Caught Stealing 2nd -.640 -.444 -.240
RE Lost Caught Stealing 3rd -.883 -.603 -.342

Which brings us to the second part of the equation-- the loss of run expectancy when caught stealing. While Matt Kemp preferred stealing earlier in the inning than Ichiro, he also apparently preferred getting caught earlier in the inning as well. With a success rate of just 78%, Kemp erased 5.181 RE from his final tally on the season, while Ichiro's mistakes removed just 2.883 RE with an 85% success rate. The result of all this leaves Suzuki with a greater net result of RE on the season:

NAME SB CS SB% RE_SB RE_CS RE_TOTAL
Michael Bourn 61 14 81.3 11.563 -8.38 3.183
Coco Crisp 49 9 84.5 8.231 -3.901 4.33
Brett Gardner 49 13 79 7.641 -6.283 1.358
Matt Kemp 40 11 78.4 7.595 -5.181 2.414
Cameron Maybin 40 8 83.3 7.501 -3.74 3.761
Drew Stubbs 40 10 80 7.456 -5.445 2.011
Ichiro Suzuki 40 7 85.1 6.545 -2.883 3.662
Emilio Bonifacio 40 11 78.4 7.492 -5.252 2.24
Jose Reyes 39 7 84.8 7.363 -3.16 4.203
Jacoby Ellsbury 39 15 72.2 7.051 -6.317 0.734
Elvis Andrus 37 12 75.5 6.122 -5.884 0.238
B.J. Upton 36 12 75 6.908 -5.424 1.484

It may be a dead horse at this point, but this is just one more way to appreciate the damage of the CS. I've highlighted two cells I found particularly interesting in that regard. Elvis Andrus and Jacoby Ellsbury, both notorious speedsters, had nearly eliminated all run expectancy gains made with their stolen bases by getting caught at least 1/4 of the time last season. This sort of recklessness on the base paths allows a more cautious runner like Jose Reyes, and his 85% success rate, to climb to the top of the standings in total RE.

The problem was not exclusive to just Andrus and Ellsbury, however, as most of the SB leaders lost somewhere around 60-70% of their gains in RE with the CS. In fact, the league as a whole lost more RE than it gained in SB attempts. If only baserunners could carry with them a screenshot of their own, one which could remind them of the potential gains and losses in RE-- something they could reference immediately before they made that decision to run. Something like..

Added RE when: STARTING BASE STATE 0 outs
1 out
2 outs
Stealing 2nd “1--” 0.243 0.159 0.102
Stealing 2nd “1-3” 0.203 0.234 0.092
Stealing 3rd “-2-” 0.272 0.270 0.031
Stealing 3rd “12-” 0.302 0.256 0.048
Stealing 2nd and 3rd “12-” 0.505 0.490 0.140
Stealing Home “--3” 0.095 0.305 0.738
Stealing Home “1-3” 0.085 0.351 0.728
Stealing Home and 2nd “1-3” 0.328 0.510 0.830
Lost RE when:
STARTING BASE STATE 0 outs
1 out
2 outs
Caught Stealing 2nd “1--” -0.640 -0.444 -0.240
Caught Stealing 2nd “1-3” -0.860 -0.831 -0.512
Caught Stealing 3rd “-2-” -0.883 0.603 -0.342
Caught Stealing 2nd , Safe at 3rd “12-” -0.558 -0.575 -0.464
Caught Stealing 3rd, Safe at 2nd “12-” -0.828 -0.606 -0.464
Caught Stealing 3rd “12-” -0.613 -0.708 -0.464
Caught Stealing Home "–3” -1.155 -0.873 -0.373
Caught Stealing Home “1-3” -1.289 -0.964 -0.512
Caught Stealing Home, Safe at 2nd “1-3” -1.130 -0.862 -0.512
Caught Stealing 2nd, Safe at Home “1-3” -0.555 -0.093 +0.488

No need to thank me, Jacoby. I still owe you for the free taco.

[*There are a few circumstances that require special consideration. The first of which is the completion of a strikeout or a walk occurring on the same pitch as a stolen base. I treated these as two separate events in one. They may be related, though I did not want to assume that they were and therefore could not punish the baserunner for the new out-state and the changed run expectancy. Similarly, I did not award the baserunner the added RE from the new baserunner in situations where he has stole third on the ball four. For these situations I simply modified the starting base/out RE to 'pretend' the strikeout or walk had occurred before the stolen base.

Secondly, there was the issue of double steals, and how to distribute the credit between the individual baserunners for the ultimate change in RE. In these cases I made adjustments to the RE in the starting and ending base/out states to create two parallel universes: one which pretended that the trailing runner stayed put, and another where the lead runner stole his base before the trail runner ran. I did not divide up lost RE on double steals where a CS had occurred.]

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