I remember October 27, 2011. It was right before my wife and I finally just got rid of our TV, mostly because we realized we never watched it. But that night, it was on, as it looked like the Rangers were about to beat the Cardinals in Game 6 of the 2011 World Series and claim their first ever World* Championship. In the ninth inning, Neftali Feliz took the hill against the Cardinals, armed with a 7-5 lead. And then… David Freese happened. And Lance Berkman happened. And David Freese happened again.
At the time, I was working for a team, so I did not comment on baseball publicly (I did post a semi-cryptic “Wow!” to my Facebook account after the game was over… I have a feeling my employers were thinking the same thing), but of course, it was a thrilling game. Any fan of baseball had to enjoy that one.
But who really won that game? I don’t mean in the sense of “The Cardinals, you fool!” I mean on an individual player level. Should the game be known as “The David Freese Game” from here to eternity?
Warning! Gory Mathematical Details Ahead!
Let’s pick up the action in the ninth inning, with Jason Motte (and Daniel Descalso) entering the game for the Cardinals. At this point, the Rangers have a win probability of 93.1 percent (all WPA numbers use 2010-2014 as a baseline).
Nelson Cruz grounds out, pitcher to first.
Cruz and Motte combine to produce a ground ball. From 2010-2014, a ground ball with no one on and no one out (in any situation) produced the following outcomes and would have produced the win probabilities in parentheses, given this particular situation:
No runner, one out – 73.3 percent (92.8% win percentage for the Rangers)
Runner at first, no out – 24.0 percent (92.4% win percentage for the Rangers, which is bizarrely lower than the above)
Runner at second, no out – 2.6 percent (95.6% win percentage for the Rangers)
Runner at third, no out – 0.2 percent (94.3% win percentage for the Rangers)
Weighted total: 92.9 percent
Averaging that out, by just knowing that by hitting/inducing a ground ball, Cruz and Motte have changed the win probability 0.2 percentage in favor of the Cardinals. We know that Cruz gets 60.6 percent of that blame (-.0012 wins), Motte gets 39.2 percent of that credit (+.0007 wins). Yadier Molina picks up a spare 0.1 percent (negligible).
We also know that the ball that Cruz hit was fieldable by Motte and we know that batters and pitchers do have some control, although somewhat less over that. The fact that the ball was reachable by an infielder brings the chances of an out to 88.4 percent. Motte gets 40.6 percent of that credit (+.00023 wins) for inducing and Cruz gets 46.6 percent of the blame (-.00026 wins) for hitting the kind of ground ball which is easily turned into an out, we will credit and debit their accounts accordingly. Background noise gets 12.7 percent of the credit (0.00007 wins in favor of the Cards).
Motte the fielder (rather than Motte the pitcher or Mott the Hopple), gets credit for picking up a ball that we already know seems destined for an out and makes a true throw to Albert Pujols at first. At this point, the chances of Cruz being out are actually 100 percent in 2010-2014 (no first baseman dropped a throw from the pitcher during that time), so we don’t give poor Albert Pujols any credit. We give Motte the rest of the credit (+0.00043 wins).
Final Score for the play – The Rangers lost 0.3 percent of win probability (-0.003 wins). Nelson Cruz shoulders a blame of 0.00146 wins as the only Ranger involved on the play. Members of the Cardinals, mostly Jason Motte (.00136 wins), got the job done; with a helping hand from dumb luck (0.00007 wins). There are some residual credits for Yadier Molina, and there should probably be a little something for Albert Pujols.
The Rangers win probability stands at 92.8 percent, down 0.3 percent from where it had been.
Mike Napoli walks
This one is much easier to diagram. We know that after the play, there is a runner at first with one out, a win probability of 93.7 percent for the Rangers, up 0.9 percent from before.
Final score for the play – Napoli gets 64.2 percent of that (+.00578 wins), Motte gets 33.9 percent (-.00305 wins), Yadier Molina doesn’t frame well and gets hit with a 1.0 percent penalty (-.0009 wins), and dumb luck gets 1.1 percent (.00099 wins).
David Murphy grounds into a fielder’s choice, shortstop to second base. Mike Napoli out at second. Murphy to first.
This one is more complicated. With a runner on first, one out, a ground ball is a dangerous thing for the offense. There are a lot of inning-ending double plays that can happen (this happened 32.4 percent of the time from 2010-2014.) Then again, it could go through for a single and then there are two on with one out. That’s not a bad situation to be in.
Weighted total: The Rangers now have a 92.5 percent win probability—knowing that it’s a ground ball—a change of 1.2 percent.
Motte again gets 60.6 percent (+0.00728 wins) of the credit for inducing the grounder. Murphy takes a 39.2 percent penalty (-0,00472 wins) for beating the ball into the ground like that. Yadier Molina picks up 0.1 percent of the credit (again, we’ll just call that residual).
Daniel Descalso at short was able to get to the ball and throw to Theriot covering, so we’ve gone from a 73.3 percent chance (from him not letting the ball get into left field) of at least one out to a 100 percent chance.
Descalso gets the credit for getting to the ball, and throwing it to Ryan Theriot at second, and Theriot gets credit for catching the ball. Now, we know that there will be at least two outs in the inning, and there is the potential for a third (69.0 percent of the time, the double play is completed in a situation like this, which would be a 92.4 percent win probability for the Rangers) and the potential (31.0 percent) for a runner on with two outs (94.0 percent win probability for the Rangers—which means that with two outs, instead of one, their win probability has actually gone up), leaving the Rangers’ win percentage right now at 92.8 percent.
Descalso did his job, getting the ball and the throw over (99.5 percent of the work), Theriot did his job by catching the throw (0.5 percent of the work). By doing so, those two have somehow decreased the Cardinals win expectancy by 0.3 percent (small sample size for ya!). We’ll excuse Napoli from any blame, because there was likely little that he could have done.
But now it’s Theriot’s job to complete the double play. We haven’t done this one before, but in situations where a potential double play ball has been hit, it’s a contest between the pivoting middle infielder and the runner at first.
Using the same strategy as we have before (using a logistic regression), we find that the pivoting middle infielder gets only 15.5 percent of the credit for turning the double play (or blame for not turning it) and the batter gets the other 84.5 percent. Avoiding the double play means that the Rangers now have a 94.0 percent chance of winning the game, up 1.2 percent from a moment ago when this was an uncertainty. Murphy redeems himself to the tune of +0.01014 wins and Theriot has to swallow a -0.00186 penalty. (You can’t quiet the riot!)
Final Score on the play – Murphy actually comes out ahead on the play, losing credit for hitting a ground ball, but the fact that avoiding the double play was so valuable means that he got it back.
I guess that here we could start giving credit or blame to Texas manager Ron Washington. It would be Washington’s call on whether to let Adams hit for himself or to send someone up (but who would actually send a pitcher to hit for himself in a high leverage situation like this? Oh…) I guess you could even make a case that Rangers general manager Jon Daniels might even get some blame here because he should have had a better pinch hitter on the roster than Endy Chavez. We will refrain from all of that.
Chavez and Motte conspire to hit a fly ball, which with two outs and a runner at first usually means the end of the inning. Just knowing that it’s a fly ball, we know that there’s a 75 percent chance of an out, and but because of the chances that it’s a home run or extra base hit, the Rangers win percent goes to 97.0 percent for the moment, an improvement of three percentage points.
Chavez gets 42.6 percent of the credit (+0.01278 wins), while Motte gets 51.2 percent of the blame (-0.01536 wins). Luck gets the 6.2 percent left.
Chavez did not hit the ball out of the ballpark, which brings our Ranger win probability to 94.4 percent, a drop of 2.6 percentage points. The fact that it wasn’t a home run—which is a far greater reflection on Chavez (78.8 percent of the blame, -0.020488 wins) than on Motte (19.7 percent of the credit, +0.00512 wins)—and the rest going to the dumb luck bin.
The fact that it was a catchable ball is more to do with the batter and pitcher. Fly balls in the left field area are caught 85.4 percent of the time, and the fact that it is so catchable is 48.1 percent batter (so the batter gets 41.1 percent of the out), 32.5 percent pitcher (27.8 percent of the out), 19.4 percent league background noise (16.6 percent of the out), and 5 percent butterscotch ripple.
Berkman gets the final 14.6 percent of the out by catching the ball. (Rangers win probability is now 92.4 percent meaning that they all split up a 2 percent drop in Ranger win probability).
Motte actually nets out a loss of 0.004 wins on the play, mostly because he gave up a fly ball and the fact that it didn’t leave the park had little to do with him. He did allow a fly ball that was very catchable, but for the most part, Chavez got himself out.
Final Score – Cardinals 10, Rangers 9
So Many Moving Parts…
This was supposed to be longer. I had plans to do everything from the ninth inning on in that game, all the way through to *spoiler alert* David Freese’s home run in the bottom of the 11th. You can see how far I got. It’s a tribute to how many moving parts there are in baseball, and if we’re going to have a full accounting of who did what, we’re going to need a lot of bandwidth to do it.
I know that there are plenty of people out there who are wondering why I chose win probability. It has the unfortunate property of being a stat that is heavily influenced by the context of what’s going on (some would call that its greatest strength), but I think it’s the best story-telling stat that we have, and sometimes it’s nice to tell a story. This methodology could be adapted to fit a linear-weights type of model. One just needs to figure out the linear weights for each step along the way and pro-rate the credit out properly. The nice thing is that this system gives us a more fine-grained idea of what happened than the double-accounting system of everything being credited to the batter and pitcher, simultaneously. In this system, if an event is much more a matter of the pitcher doing something, then the batter shouldn’t take all of the credit. We can also measure a little more directly the contributions of luck. Have some teams gotten luckier than others in their outcomes?
But if there’s a lesson in this one, it’s an appreciation for how many things have to go right even in the space of a half inning. Not everyone got involved, but if Theriot drops the throw from Descalso on the force out, the course of Ranger history probably changes. But he didn’t, even though he didn’t turn two. Even in a half-inning where the win probability didn’t change all that much, there’s a lot to unpack. And this goes on all season long.
Thank you for reading
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