About a week ago, the Rays went on a little journey through bad baserunning. First, Kevin Kiermaier failed to slide into second while attempting to steal. Then Ji-Man Choi was thrown out tagging up and trying to go to third on a fly ball to left field.
These baserunning blunders were upsetting. But more upsetting was the discovery, made while discussing the plays with my fellow DRaysBay writers, that I could no longer do basic algebra. Arithmetic was hard for me, too.
I was trying to calculate the necessary expected success rate to break even on asking Kiermaier to steal second, and first I was getting a 60% value that I knew was too low. Then I “found the problem” and started getting a negative number.
A couple envelopes later I went to bed, still having gotten nothing approaching the right answer. I’m very sorry, Mr. MacFarlane.
In the morning, everything made a lot more sense, and I was able to math again. But the experience pushed me to assemble a very simple spreadsheet, so that I wouldn’t have to do even small amounts of math on the spot ever again.
Here’s the spreadsheet. If you want to use it, click File, and make a copy for yourself.
Let’s talk about the calculation.
Run Expectancy Tables
The guts of a baserunning break-even calculation is really the run expectancy, or RE24, table . Basically, looking at the 24 base-out states (eight possible configurations of base runners times three possible configurations of outs makes 24 states), and seeing how many runs have historically scored following each state, we can assign a run expectancy to each state.
For instance, according to the RE24 table published in the FanGraphs glossary from 2014, with no outs and a man on first, the batting team has gone on to score an average of .831 runs, whereas with the bases loaded and two outs, they’ve gone on to score an average of .736.
“But don’t run environments change?” you ask. “Are these old values the right ones to use today?”
Great point. They do, and depending on how precise you need to be, it may or may not matter. Use whatever values you want. If you want to go deep, Jonah Pemstein and Sean Dolinar made a really great tool that can help you tailor the RE24 table to a specific batter.
The Break Even Point
For evaluating baserunning decisions, what we really care about is the change in run expectancy. Let’s walk through a calculation.
Say there’s a man on second base with nobody out, and the batter hits a fly ball. Let’s suppose it’s to the edge of the warning track in left field. It’s going to be caught, so our starting base-out state is really one out, with a man on second. That has a run expectancy of .644.
If the batter tags up and runs to third, he can either get their safely, or he can be thrown out.* If he gets there safely, there will be a man on third with one out. That has a run expectancy of .865. If he’s thrown out, there will be nobody on, with two outs. That situation has a run expectancy of .095.
*Yes he might draw a throw wide of the bag that goes into the dugout, allowing him to score. That doesn’t happen very often. This version of the calculation ignores that possibility. A future better spreadsheet might include it. If I make it, I’ll share it.
So, putting those together, we have an addition of .221 expected runs on a success, and a subtraction of .549 expected runs on a failure. Now let’s do algebra, solving for x where x is our runners chance of making it safely to third.
.221*x - .549*(1-x) = 0
.221*x -.549+.549*x = 0
.77*x = .549
x = .71
Meaning that a runner has to be able to make it safely 71% of the time to justify trying to tag up. Do you figure that Ji-Man Choi can tag up and run to third on a flyball to left, 71% of the time? Me neither.
So there it is. It’s an easy calculation, but it’s easier to have a spreadsheet handy so that you don’t have to make any calculations. Feel free to grab this one and use it whenever you please.