You guys remember Highlights Magazine? Are those still around? For those who might not be familiar, Highlights was a kids magazine federally required to be provided in the waiting rooms of doctors' offices. They had lots of little puzzles, which would inevitably be colored on, plus some mini comics. Goofus and Gallant was one of those comics. The premise was that there were two juxtaposed brothers: Gallant, who would always make the polite, safe, self-sacrificing choice in any given situation, while Goofus would always act rudely and rashly with a distinct lack of concern for others. Example:
"Gallant carries the meat cleaver slowly and carefully back to the kitchen where he places it in its slot in the cutting block."
"Goofus capers wildly about the living room with the knife in his hand, creating a scene that would make Lizzy Borden recoil."
You get the picture. This came to mind last night in the eighth inning as we discussed in the game thread whether Erick Aybar's decision* to steal third base with one out in a tied ballgame was wise or foolish. There were advocates on both sides of the argument, and it's true that those in favor of the move were vindicated in hindsight, as Aybar's stolen base allowed him to score on a play that would not have occurred had he still been standing on second base.
*I will be referring to this as Aybar's decision throughout this piece. I sincerely believe that Erick made the decision to run rather than Scioscia calling the play. If you'd like, you may feel free to assign any credit** or blame to Scioscia instead.
I would like to look at this play a little more closely without using hindsight. Was this a good decision based on the information available at the time? I argued last night that it was, and I live by the code of xkcd (I have experience both as the guy at the computer as well as the object of his ire), so I'd love to offer some proof of my conviction. You may not be swayed by it, and I may very well be doing the math completely wrong. Please feel free to comment and correct me if I am.
Let me set the scene. For those who didn't see the game or haven't looked at the play-by-play, there was a key moment in the bottom of the eighth inning. The game was tied at three. Erick Aybar led off the inning with a single, and then advanced to second on a wild pitch despite Mike Scioscia and Efren Navarro collaborating to keep him at first (seriously, those bunt attempts were awful). Navarro's eventual pop out left Aybar at second with one out. Matt Joyce came up to pinch "hit" and the Astros countered with Joe "Becky/Margaret" Thatcher. Thatcher sagely pitched around the slugger Joyce until Matt worked a 3-1 count. It was then that our beloved Admiral decided that the Death Star's shields were down and attempted to steal third base. Thanks to speed and body contortion, Aybar arrived safely at third and then scored on Daniel Robertson's sacrifice bunt.
Was Aybar's attempted steal a good decision or was it too high a risk?
I certainly understand the impulse to label it as too risky. Aybar was already in scoring position, and he has good speed, so he likely would have scored on any base hit past the infield. The Angels would have had at least two chances to get that hit. An out at third immediately removes any imminent threat to score, leaving the bases empty with two outs. Conversely, if Aybar arrives at third safely with one out, he can score in any number of ways including a sacrifice fly or well-placed ground-out. He also has double the opportunities to score on defensive miscues like wild pitches or errors.
When it comes to questions like these, I love to use a tool called the WPA Inquirer. It's a bit of a blunt instrument since it doesn't take into account all the details of the situation (such as the upcoming batters or the stadium or the pitcher, just to name a few), but unless one of those factors is an outlier, it will give you a good idea of how a play will affect the probability one team has of winning the game under two different scenarios. I will also be using the Fangraphs Win Probability chart from last night's game to fine tune my settings as much as possible.
According to the chart on Fangraphs, the Angels win probability after Navarro's pop-up was 64.9%. Using the WPA Inquirer, the closest I can get to that is 64.8% if I use a 4.0 run environment. I then compared two scenarios to that baseline; one scenario assumes Aybar was caught stealing (bases empty in the bottom of the eighth inning with two outs and a run differential of zero). The other scenario assumes Aybar's steal attempt was successful (same inning/run setting, only with a runner on third and one out ) I don't take Joyce's walk into account, since I don't think it factors into Aybar's decision. The numbers shake out thusly:
|Scenario||Outs||Base Situation||Angel's Win Probability||Change in win probability|
|Start: Aybar at second base||1||- 2 -||64.8%||--|
|Scen 1: Aybar thrown out||2||- - -||52.4%||-12.4%|
|Scen 2: Aybar steals third||1||- - 3||74.1%*||+9.3%|
*Note that this matches up pretty well with Fangraphs, which shows a 75.1% chance for the Angels to win after Aybar's steal. The difference is most likely due to Matt Joyce's walk, which occurred on the same play as the stolen base and would increase the Angel's chances slightly.
You can see that Aybar getting thrown out is, as we suspected, a pretty big deal. The Angels lose 12% to their win expectancy. There is a bit of a saving grace in that the Angels are the home team, so they still have one extra out to play with. But let's be honest, the Angels with two outs and no runners on base are about as threatening as an overweight chihuahua. Assuming neither Trout nor Pujols is up, of course.
On the other hand, Aybar stealing third is a pretty big boost to their win potential. They go up by over 9% because of all the new ways he can score. The question then becomes what is the break-even rate for Aybar's steal attempt? To think of it a different way, if Aybar is successful Z% of the time on this attempt, the risk will have been worth it. Solve for Z. (I know, you were told there would be no math.)
Here is what I did to calculate this (please skip this if algebra makes your eyes glaze over):
(Scen. 2 change in win prob. x Z) + ((Scen. 1 change in win prob. x (1 - Z)) = 0 which gives:
(.093 x Z) + (.124 x Z) - .124 = 0
Once you do the
magic math, this gives us 57% as Z. Even though there is a quite a bit of downside to the stolen base, there is also quite a bit of upside. Enough to where Aybar only has to be successful 57% of the time to make that a worthwhile gamble.
There are other calculators for the value of stolen base. According to this analysis of the value of a stolen base, the break-even calculation for our scenario gives us a value of 69.5%. One key difference is that this calculation uses run expectancy while my previous calculation uses win expectancy, and I think that's where the large discrepancy comes into play. Aybar getting caught not only decreases the chance of the Angels getting one run, but it also greatly decreases their chances of getting multiple runs, which is important throughout most of the game. In the bottom of the eighth inning, however, the Angels likely only need one run to win, and stealing third with less than two outs greatly increases the chances of getting that one run.
Whether we use 57% or 69.5%, we still need one more piece of information. What were Aybar's chances of making it to third base safely? That piece I linked above gives a way to calculate the likelihood of a runner being safe based on pitcher delivery speed and runner speed. I didn't time Thatcher or Aybar, so unfortunately, I don't have that data at my fingertips.
Thanks to Baseball Reference, what I do have is Aybar's stolen base rates (72% overall for his career, 75% of third base), Thatcher's stolen base rates (80% stolen base success against, 83% of third base), and Jason Castro's caught stealing numbers (base runners steal successfully against him 74% of the time, and 83% of the time when they attempt steals of third base). I could go through some more math to try to determine how to average these numbers to obtain Aybar's likely success rate, but it's academic. Each of those numbers is greater than both of our break-even values. So whether you want to use the low rate presented (72%) or an average of the three rates for stealing third (80%) as the likelihood for Aybar successfully stealing, you're going to come up with a number that indicates the gamble was a good play.
As devastating as it would have been to see Aybar get thrown out there, he is a fast runner and Thatcher has a slow delivery. The Angels benefited greatly from a theft of third, both in theory and in reality. The Admiral took a calculated risk, a worthwhile one, and it paid off.
Now let's talk about those bunt attempts by Navarro...