When sabermetrics was first coming into prominence -- after the unholy sacrifice of human fetuses to the Dark Powers but before the burning of the Jack Morris effigy -- many of the first steps centered around out avoidance. On Base Percentage, cherishing all twenty-seven outs, and other things that I learned from Brad Pitt. This mindset led to a lot of people yelling very loudly about sacrifice bunting and -- to a lesser extent -- base stealing.

I have been in that crowd yelling and if you're reading this, there's a good chance you're at least aware of where the line has been drawn. More recently, a little bit of grayscale has been added to the debate by using numbers instead of platitudes. The results suggest that bunting will almost always reduce run expectancy but can increase run probability when used in certain situations. Which makes sense, as it sometimes makes sense to sacrifice the likelihood of a big inning for a better chance to score the lead runner.

There's still every reason to think that the sacrifice bunt is overused by managers and actively taking runs off the board, but the relative scale is probably not huge. Much the same way that voluntarily spending $13M on Vernon Wells is unlikely to matter all that much, but just why would you do that on purpose?

So, like bunting, stealing bases should get the same more nuanced look if we want a real answer about how the strategy should be appropriately deployed. The obvious answer is that successful steals are good and unsuccessful steals are bad, so teams should seek to maximize their rate of success. There is also a mist of conventional wisdom floating around the topic -- getting into scoring position, getting to third with less than two outs, etc.

Using Tangotiger's Run Expectancy Matrix (1993-2010 environment) it is possible to get a gauge of the relative risk/reward for each base stealing situation. I have done so and encharted the results below.

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*I know that you're not an idiot, but 1-- means a runner on first, 1-3 means runners on first and third, etc. Break even success rate means break even success rate, idiot. If you are successful at a higher rate than the break even rate, you are adding value. If you are successful at a lower rate than the break even rate, you are subtracting value.
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There are also several systematic biases that make the break even success rate not all that definite. The catcher could throw the ball into center field which favors the batting team, outs on the bases do not require the pitcher to increase his pitch count which favors the defending team, etc. As I care most about which situations are the best to steal in relative to one another, this should all come close enough to washing out.*

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All first and second situations were considered to be true double steals with the throw going to third base. So a successful attempt would get runners to second and third and a failure would result in an out and a runner on second. All first and third situations were considered to be only a steal of second base by the runner on first with the runner on third staying put on third.
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Stealing of home was not considered because eminent domain is fucking lame and no one does that anyway.
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Last year, American Leaguers stole 1501 bases in 2002 tries, which is almost exactly a 75% success rate. Of those tries, exactly 1500 came with only a runner on first. So about three-quarters of the time, teams were stealing in a situation where they needed to succeed at least 70% of the time to add run expectancy by this crude metric.

Even if we knock a few percentage points off of the break even success rate to account for defensive miscues, it's still probably fair to say that not a whole lot of run expectancy is going to be generated by stealing bases alone. Still, we have good reason to believe that, from a macro standpoint, attempting to steal bases added more value than it took away. It probably wasn't very much, but it was something.

Like bunting, Run Probability is where the stolen base really shines. There are game situations in which the value of scoring multiple runs becomes much smaller and the value of scoring at all becomes much greater. As you would expect, advancing a single base is of greater importance when your only concern is scoring the lead runner.

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Yes, Run Probability drops slightly with runners at second and third and not first and third. As it is really only the lead runner that we care about, it's not really surprising that trying to advance the second runner with risk of an out is a bad gamble, but you wouldn't expect negative value from advancing a base and removing the force at second. *

*Perhaps what is being observed is the open base at first allowing for the pitcher to be more careful with the current batsman or teams electing to try and turn a double play instead of throwing to home. Who knows. The difference is negligible and if your only goal is scoring the lead runner, you shouldn't be doing that anyway.
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Several things to note here. One is that in both the Run Expectancy and Run Probability charts, a double steal with runners on first and second and zero or one out is heavily weighted in favor of the batting team. This is for the obvious reason that a successful attempt moves up two base runners and gets a runner to third with less than two outs. On a failed attempt, you still get to advance one runner and keep a batter in scoring position.

Last year, AL batsmen came to the plate with only a runner on first base 15378 times and there were 1500 steal attempts (9.75% of all PA). In 5622 PA with runners on first and second, there were 165 attempts (2.93%) and that's with each true double steal being counted as two attempts.

Sure, two base runners means twice the chance that one is Mark Teixeira, but I have a hard time thinking that there isn't value being missed here. Especially late in games when everyone is bunting instead because some nerd with a run probability matrix told them it was fine now.

The 2013 Yankees will have some combination of Derek Jeter, Brett Gardner, Eduardo Nunez, Ichiro Suzuki, and Curtis Granderson in the first few lineup slots almost every night. There will be ample opportunities for double steals and given the numbers above, I would love to see some aggression.

Also, while the raw values on the Run Expectancy chart underwhelmed me, I feel the opposite about the Run Probability chart. Depending on the number of outs, a straight steal of second base increases the likelihood of scoring by 19.6%, 13.4%, or 9.5%. Stealing third can add even more. In a tied or one-run game, that's huge.

Let's imagine a player. As baseball is played by people, let's give a name to this person and hereafter refer to him as Edward Nuno. Nuno can be used off the bench, and given the numbers above, it wouldn't be unreasonable to think of a stolen base increasing the likelihood of a run being scored by 15% or more. Getting caught hurts a lot in this situation, but Nuno can be expected to succeed about 80% of the time.

With all of that considered, we would expect that inserting Nuno and asking him to steal would make a run being scored about 10% more likely. And as we use Nuno when his run is the tying or go ahead run in the ninth inning or later, we can also approximate his run scoring to be worth an increase of 40% in win probability.

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Down one run in the ninth, the probability of winning is around 10% and so scoring to tie the game increases the probability to around 50%. Scoring the go ahead run takes you to around 90% if you are the away team or 100% if you are the home team. As these are the situations in which Nuno would be deployed, any time that he scores a run should increase the odds of winning by around 40%.
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So each time Nuno is used like this, we expect .04 wins (10% increase in likelihood of scoring a run that adds 40% of a win). The Yankees played forty-seven one run games last season. If Nuno was used as described in all of them, then based on the percentages given we would expect an additional 1.9 wins.

So Nuno's contribution to the 2012 Yankees in only 47 games of pinch running would be ahead of Eric Chavez and just behind Alex Rodriguez and Russell Martin by their respective fWARs.

There wouldn't always be a chance to use Nuno and sometimes the base runner would be Brett Gardner already, but you get the idea. Significant value can be added by smartly using pinch runners and stealing bases in late and close situations.

But I'd still probably prefer to send a guy like Nuno to the minors because Jayson Nix can be a replacement level stand in at **several** defensive positions.

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