Cleveland was ahead by 1 run in the bottom of the 5th, 1 out, runners on the corners. Chance of winning is .776
Runner on 1B attempted to steal 2B.
Choices for Rays was:
Let runner steal uncontested, keep runner at bay, leaving runners at 2B+3B, chance of winning .795
Throw to 2B, allow runner to score
CS means .795
SB means .833
As you can see, the win value of the runner at 3B gaining a base is exactly equal to the win value of the runner on 1B being thrown out. Which makes sense, since the run value of going from 3B to home plate is about plus 0.4 runs, and the run value of the CS is about minus 0.4 runs.
Of course, this ONLY makes sense if the CS was a guaranteed out. Otherwise, having the runner steal 2B and the runner scoring would be a disaster play.
End result: catcher should NOT have attempted to throw the runner out, and he got lucky to breakeven on that play.
I am not looking at EVERY bases empty scenario. In the bottom of the 2nd, with Yanks ahead by 3, Aaron Judge was IBB with the bases empty (!). There were two outs, so maybe it's not so bad?
Let's go to the tape!
Aaron Judge is worth about 0.13 runs above average in a random PA, which means he's worth about 0.013 wins per PA. In this particular instance, the leverage index is 0.22, so his leveraged-wins impact is .013 x .22 = .003 wins
(Click to embiggen) The win expectancy for an average batter in this situation is .810. With Judge batting, that goes up a bit by .003 to .813.
An IBB puts the win expectancy at .817.
So, it's still a bad call to IBB Judge in this situation.
If instead of him being a .475 wOBA batter he was instead a .630 wOBA batter, then that's the breakeven point to walk him. Bonds at his best was around .540. So, no, you can't walk him here, which is why he doesn't get walked here.
With one out in the fifth inning of San Diego’s 6-4 victory over the Reds at Petco Park, Padres first baseman Jake Cronenworth hit what appeared to be an RBI groundout to second base. Tyler Wade scored from third. Fernando Tatis Jr. advanced to second. Machado was due up. Ho hum.
But Cronenworth made a signal toward the plate for a catcher’s interference ruling. Sure enough, home-plate ump Cory Blaser made the call, leaving Shildt with an intriguing decision.
On catcher’s interference, the batting team is allowed to accept the result of the play rather than the base that the batter would otherwise have been awarded. Almost always, when catcher’s interference is declined, it’s because the play resulted in a hit, anyway.
But on this occasion, Cronenworth made the inning's second out. He also plated a run. It left Shildt with these two options:
1. Decline the interference, take the out and the run and a 2-0 lead
2. Accept the interference, with Wade returning to third, leaving the bases loaded with one out for Machado and a 1-0 Padres lead
So, what to do? (For all the charts below, click to embiggen)
From that standpoint, we see that bases loaded, one out is worth 1.590 runs, while runner on 2B with 2 outs, and banking the runner is worth 1 plus 0.325 runs. The difference is what we care about, and the difference is a whopping 0.265 runs in favor of taking the run, and out, off the board, and putting those two runners back on the bases.
Adding .265 runs is equivalent to adding almost .03 wins. However, run expectancy is a proxy for win expectancy. And as a proxy, it works well. Until it doesn't.
Next, we consult our win expectancy, specific for that half-inning, the bottom of the fifth. And, well, we get something different. The typical home team, up by 1, with the bases loaded and 1 out, has a .799 chance of winning. But, give up the runner on 1B to an out, and plate the runner on 3B for a run, and the win expectancy will go up to .811. In other words, we lose .012 wins by loading the bases (at least with an average batter batting).
So, quite the turnaround here. In a random situation, which is what the Run Expectancy is talking about, we gain almost .03 wins by keeping all our runners on base. But from a Win Expectancy scenario specific to the bottom of the 5th home team up by 1, and we lose .01 wins. That's a .04 win difference, all depending which method you use.
Now, the next step should be to consider who is batting, future HOF Manny Machado. All these charts, they all work nice when everything is average. Run Expectancy assumes an average inning and an average difference in score and average batters and runners and pitchers. While Win Expectancy uses the specific inning and score, it still assumes average players all-around. I will leave this particular step to an Aspiring Saberist.
What I want to do instead is look at EVERY half-inning and score, to see when bases loaded is preferred, and when trading two runners for an out and a run is preferred. Here is that chart, and we'll have alot to talk about here.
The top line is the batting team score. Plus means they are ahead and minus means they are trailing. The left column is the inning, split by top/bottom.
The darker the orange (the more negative the number), the more it favors putting the run and out on the board. The darker the purple (the more positive the number), the more it favors keeping the runners on the bases.
Purple = bases
Orange = out + run
In the play in question, bottom of 5th, batting team ahead by 1, we can see the value of -0.012, which means it favors putting the run and out on the board, to the tune of .012 wins. This is the Machado scenario, but with an average batter, not Machado, batting.
Ok, now let's look at specific overwhelming choices, where the identity of the players doesn't matter. The biggest is bottom of the 9th, game tied. In this case it should be obvious: plate the run for the walkoff win. That's a .171 win difference over loading the bases. But that was too obvious.
A high one is bottom of the 9th, batting team down by 1 run. In this case, it should be almost as obvious that you put the run and out on the board for a .078 win gain. When you are down by 1 run in the bottom of the 9th, the most important runner is the one that ties it, and the next important runner is the one that wins it. That third runner, the one on first base, that runner is irrelevant. So in this case, you are gaining the run and losing an out, but you are (effectively) only removing one runner from the bases.
On the flip side is bottom of the 9th, batting team down by 2 runs. Suddenly, all three runners are important. That first runner, he's really irrelevant on their own. He's only important if the second runner can also score. Scoring one, without the other, is irrelevant, since in that case, instead of losing by 2 runs, you lose by 1 run. Therefore, in this scenario, it should be quite obvious: load the bases, keep the extra out. This is a .182 win gain.
If you need rules of thumb, here they are:
when batting team is down by at least two runs, take the interference and load the bases
when the batting team is ahead by at least two runs, decline the interference and plate the run
in-between: consult the chart, but if it's close, consider the identity of the batter (like in the play in question, with Machado)
We can look at the win expectancy to make the call, if you want to be more objective. That game was in the top of the 10th, with one out, and a runner on 2B. Getting a run-scoring single adds .26 wins, while a first-and-third single adds .10 runs (over and above the first-and-second default scenario). Let's say therefore a single would add +.18 wins. An out drops it by .09 wins. So, the breakeven is getting a basehit 33% of the time (which is a wOBA of .300).
To think of it more simply: an IBB is typically win-neutral. Whether the batter gets an IBB or is allowed to be pitched normally, the end result is typically the same. So, all that Cabrera has to be thinking is if he can match his true talent wOBA. Assuming he's .400, that's what he needs to be hitting. And getting a hit 45% of the time is a .400 wOBA. So, if Cabrera thought in the moment: I can get a hit here at least 50/50, I am swinging: then tip of the cap for being faced with a situation that you likely never prepared for, and your instincts took over.
Having earlier looked at it league-wide, the focus now will be to control for the quality of batters and pitchers when shifts happen. I will further limit it to bases empty.
From 2018-2021, the quality of LHH being shifted upon has been about 26 points higher than the LHH not being shifted (ranging from 22 to 30 points). In 2022, nothing really has changed, with a 31 point difference. In terms of the actual performance, from 2018-2021, the wOBA worked spectacularly well on LHH: based on the quality of batters with a wOBA of .347 with bases empty and unshifted, those batters ended up with a wOBA of .321 when shifted. So that's a 26 point drop. In 2022, we have 50 point drop. (This improvement in defense did not carry over with runners on base.) In other words, an extra 24 point gain in performance for the defense, over and above the gains we've come to expect of them.
As for RHH, from 2018-2021, shifts were not really based on quality of batting. The shifted RHH were only 11 points higher than the unshifted. So, whatever reason the clubs had didn't work at all, with an egregious result of 27 points higher with the shift than unshifted. In other words, the exact opposite of the success they had with LHH.
But in 2022, that has changed. The quality of batters being shifted is still the same, but now the clubs are having success, with a 10 point drop in wOBA with the shift, than unshifted. So, that's a change from +27 in wOBA before 2022, to a 10 point drop in 2022. Or a 37 point turnaround. That's an astounding turnabout. They've also seen an improvement with shifting with runners on base as well.
Essentially, the entire drop in run scoring can be attributed to the improved results on shifting on LHH and the spectacularly improved results on shifting on RHH. Whereas RHH shifting was actually INCREASING score before 2022, now in 2022, the clubs have figured it out, and shifting on RHH decreases run scoring as well.
As for why this has happened: I haven't looked yet, but maybe an Aspiring Saberist will get there first.
I’ve posted on Twitter some data. I wrote a chapter in The Book on the topic. Plenty of othershavechimed in, all concluding the same thing. Times Thru Order effect is real, and it does not take a backseat to a pitcher that is mowing down his opponents.
I’m here to offer a possibility that under a specific situation, maybe there is an overriding concern. We’ll get there in a sec. Here’s a data chart, and I’ll explain what it is. (Click to embiggen)
All the data is from 2010-2019, courtesy of Retrosheet. Chart on the left is regular season and chart on the right is the post-season. The columns from -1 to 9 refers to the strikeout - walk differential for the first 18 batters faced. -1 means more walks than strikeouts. 9 means 9 or more strikeouts than walks. All the others are exact counts. Walk is really walks + hit batters, with IBB removed. Snell was a “9”, meaning the best.
The columns “1” and “2” means 1st time and 2nd time through the order. The data is wOBA. Now, don’t pay too much (or any) attention to those two columns. Those are selection biases and we’ll learn nothing from them.
The column we care about is “3” meaning the performance 3rd time through the order. Since we selected our strikeout-walk differential based on the first 18 batters faced (in-sample), we are interested in what happens after that (out-of-sample). And that is the third time thru the order.
Now, let’s start with the regular season. We notice that the wOBA gets progressively lower, the more the strikeout-walk differential. That’s really an issue of bias, because the better pitchers will be part of the higher differential groups disproportionately. So, we expect that value to behave as it does based strictly on the quality of the pitchers in each of those groups.
Now, the right thing for me to do is to look at the actual quality of pitchers in there. I will leave that to the Aspiring Saberist. What we can do instead is use this as a baseline of sorts as we now turn our attention to the post-season chart.
First, we’ll notice that in the post-season, third time through, with the strikeout-walk differential at 5 or less, the performance is roughly the same. Since the post-season is made up of good pitchers to begin with, we don’t expect the progressive drop we saw from the regular season.
That said, then the fun happens. We see a big drop at a strikeout-walk differential of 6. Then a huge drop at 7. And all by its lonesome is a .214 wOBA with a strikeout-walk differential of 9+. Now, we are only talking about 9 pitchers (all huge names, as you’d expect: Cole and Kershaw twice each, Kluber, CC, Max, Stras, Verlander). And they totalled just 49 plate appearances. One standard deviation is 71 wOBA points. If we assume a .300 level talent, that’s only 1.2 standard deviations.
But, 49 sounds like a lot, and if the non-data folks want to hang their hats on something, it’s that one. That in the post-season, when a superstar pitcher is mowing down batters, they went out to pitch at a better-than-Mariano level.
And to give them more ammunition, we can combine the strikeout-walk differential at 7+ (so those last three lines). That’s 341 batters faced at a wOBA of .259 (meaning Mariano level). And one standard deviation is now down to 27 points. Which is actually 1.5 standard deviations.
Therefore, I will give them that as a reasonable possibility. Just like we DID find evidence that a pitcher’s talent level does improve in the 9th inning when he’s going for a perfect game, maybe there is a brief change in talent level for a pitcher, who is at the highest level, pitching at an even higher level, and on the greatest stage, the post-season.
That said, these star pitchers did not pitch at the level that their first 18 batters suggested, that they were “unhittable”. The best you can see is that they pitched like an average Mariano Rivera. Which is of course great. And naturally, you don’t pull Mariano Rivera from a game.
But everything I’ve said comes with a degree of uncertainty. You can make the argument that Blake Snell third time through drop in performance gets cancelled out by what we saw, and so we had an average Blake Snell. And you don’t pull an average Blake Snell.
Or, all of this is really grasping at straws, that the regular season provides so much data that we can conclude that Snell was losing effectiveness all the while our eyes were lying to us.
Anyway, the floor is open to the Aspiring Saberists.
Back in March of 2017, I presented preliminary research that showed some massive inefficiency in shifting RHH.
Focus on the wOBA with RHH v Shift, with no runners on, and the 43 point gap.
Now, I have not controlled for the batters, pitchers, fielders. But SOMETHING is going on. Whether only great RHH are being shifted and/or bad pitchers and/or bad fielding teams.
OR, it could also be a massive inefficiency in fielding alignments with RHH, with regards to shifting. Basically, if you put the SS and 3B too close to each other, and you don’t have the 2B covering up enough of the open spot the SS abandoned, you are basically being very inefficient in the fielding alignment.
I have finally controlled for the batters and pitchers. And there’s a 38 point gap since 2015. Here’s what I did:
As earlier, I looked only at bases empty situations
I tabulated wOBA for each combination of batter+pitcher over the 2015-2020 time period
I broke up their matchups whether with a shift or with a standard fielding alignment
They had to face each other at least once in each of the two situations over the time period
Each matchup was weighted by the Harmonic Mean
I found the difference in wOBA with the shift minus without the shift
I then figured the weighted average by bat-side, by using each batter-pitcher matchup’s Harmonic Mean
(Reminder: a shift is 3+ infielders to one side of the bag.)
Here’s how it looks by bat-side. For LHH, we have 19,334 weighted PA. With no-shift, the batter-pitcher had a .341 wOBA. With the shift, the SAME batter-pitcher had a .317 wOBA. That’s a 24 point drop because of the shift. These batter-pitchers faced the shift 49% of the time. Shifting LHH is a good thing for the defense.
For RHH: 18,676 weighted PA. With shift: .364. Without shift: .326. Difference: 38 point gain with the shift. These batter-pitchers faced the shift 42% of the time.
I thought maybe some RHH deserved to be shifted, that maybe those shifted over 50% of the time are “obvious” candidates” while those shifted less often are the ones bringing up the average. No dice. Across the board, regardless of how often a RHH was shifted, they had a huge gain with the shift.
My point from March 2017 remains: why are clubs shifting RHH at all?
On an 0-2 count, with a runner on 1B, and 2 outs, the run expectancy is 0.14 runs.
If the runner is CS, that puts it at 0
If the runner gets a SB, and the batter is now at 1-2, that puts it at 0.22 runs.
So, with an average batter, you gain .08 on success and lose .14 on failure. You need to be successful 64% of the time.
Now, I said with an AVERAGE batter. What if it was Mike Trout? The best hitter in the league adds 0.10 runs per PA in an average situation. More with a runner on base, less with 2 outs.
***
Interlude:
In order to have that .14 runs, what does that mean? Well, it means that the runner on 1B, and all future batters, will score an average of 0.14 runs. Sometimes it will be 0, sometimes 1, sometimes 2 or more.
79% of the time, the batter is out, ends the inning, and so 0 runs score.
17% of the time, the batter gets on base without pushing the runner home. When that happens, we expect 0.4 runs from those runners, and then another 0.1 runs from all future batters. That's 0.5 runs.
4% of the time, the runner scores, with the batter also scoring (via HR, so that's 2 runs), or the batter is on second or third (so worth another 0.3 runs, plus the runner or 1.3 runs). Let's say overall, this is an average of 1.6 runs.
Add it up:
17% x 0.5 runs
+ 4% x 1.6 runs
= .15 runs
So, based on this back-of-envelope calculation, we're pretty close. That's how the run expectancy works.
***
On an 0-2 count, with a runner on 1B, and 2 outs, now we want to know the run expectancy with Mike Trout batting. Since Trout has entered an 0-2 count 984 times in his career, we can somewhat reasonably rely on this data. His OBP is .280, but once you add in his ROE, he's safe 29% of the time. So he makes an out 71% of the time.
21% he gets on base without scoring the runner, which we know is worth 0.5 runs.
8% he scores the runner, and half of those he scores himself, and the other half he's on base. That's an average of 1.65 runs.
Add it up:
21% x 0.5 runs
+ 8% x 1.65 runs
= .24 runs
So, Mike Trout is worth +0.09 runs with a runner on 1B and 2 outs.
***
Now, let's go back to the beginning, and replace the average batter with Mike Trout.
On an 0-2 count, with a runner on 1B, and 2 outs, the run expectancy is 0.14 runs with an average batter, or 0.09 runs more with Trout, or 0.23 runs.
If the runner is CS, that puts it at 0. HOWEVER, Trout starts the next inning. And that is worth about +0.08 runs. So, a CS does not put you down to 0 runs, but 0.08 runs.
If the runner gets a SB, and the batter (Trout) is now at 1-2, that puts it at 0.32 runs.
So, with Trout, you gain .09 on success and lose .15 on failure. You need to be successful 63% of the time.
***
In other words, it's the same thing. And therefore, having Trout batting with an 0-2 hole with a runner on 1B is worth about the same thing as Trout starting a clean inning, and leaving the previous runner on base.
***
This is all logical and back-of-the-envelope math. If someone wants to run an OOTP simulation (pick it up in the 8th inning if you can), I'd love to see those results.
When the Marlins made their comeback against the Cubs in the 2003 playoffs, I described how WPA worked on a play by play (and in the case of the fan, pitch by pitch) basis. A couple of weeks ago, I described Layered Hit Probability, all the various layers we have to go through in order to explain the how/why that a play happened.
?Sam Miller lays it all out with what we are up against if we try to go to the ultimate, and describe all the baserunning and fielding involved in a play. And he makes the salient point:
To give credit on all of them means building statistical systems that can make assumptions that hold true in as many cases as possible -- and that don't require hours (and that don't rely on personal opinions) for each of them.
What Sam did is identified what we call Action Events. At every Action Event, we stop the play, and understand the landscape. We identify what is the run potential (actually win potential) at that point in time. Then we fast forward to the next Action Event and ask the same question. And we capture that change, and assign that change to the change agent(s) between the two Action Events. And on and on we go, much like I described with the Marlins/Cubs, but far more in-depth, as Sam has done. With the key point that we make sure it all adds up, as Sam showed.
And once we have it all broken down for all plays in an inning or a game or a season, we can tally it all. You can see it in the Cubs/Marlins:
The tally:
Prior + SS = +.076
Prior + Alou = +.051
Remlinger = +.001
Remlinger + Fielders = -.016
Dusty = -.017
Fan = -.031
Prior = -.051
Gonzalez = -.184
Farns + OF = -.271
Prior + OF = -.476
Manager = -.017
Fan = -.031
Pitchers = -.368
Fielders = -.502
TOTAL: -.918 (.018 – .936 = .918)
And the kicker is going to be, that once we have a Statcast WAR, that we may be able to explain the PLAYS, we may be introducing a bunch of random variation into a PLAYER. We'll be taking three steps forward on explaining baseball, but we may be running in place in explaining a baseball player. This is why FIP has such a strong footprint, taking the bird's eye view in explaining a baseball player. You have to be careful in conflating the IDENTITY of the players involved in a play, with the INFLUENCE of the player (as opposed to the effect of random variation). And this gets into the bittersweet symphony of explaining baseball, which I tried to describe in this two-part thread from a while ago.
?In the top of the 5th, with the Nationals down by 3 runs, Strasburg (the batter) had runners on 1B, 2B, and 0 outs. The question was whether to PH for Strasburg, after he pitched only 4 innings. A PH would add 0.1 to 0.2 runs in that situation. Probably closer to 0.2 runs, given that the manager was intent on having Strasburg bunt even to the point of striking out. Let's say 0.16 runs.
Strasburg gives up runs at 75% of the league average. If you want to argue that in the post-season, he's better, I'll grant you that his TALENT is at 65% of the league average. So instead of giving up 4 runs per game, he gives up 2.6 to 3.0 runs per game. So he saves 1.0 to 1.4 runs per 9 innings, or .1 to .15 runs per inning. Pitching two innings, that means he'd save you .20 to .30 runs. Let's say 0.24 runs.
Method 2: Runs Earned v Runs Saved
So, it's fine to let him bat there, right? Well, after I tweeted that out, Bill James reminded me that in this case, a run saved is not worth a run earned. He is right, and I guessed it was 8 runs per win for the batting team and 12 runs per win for the pitching team. So, that works out .16 runs / 8 runs per win, or 0.02 wins for the PH and .24 runs / 12 run per win, or 0.02 wins to keep pitching Stras. Breakeven.
Method 3: Runs Earned v Runs Saved (more thoughtful method)
That was my initial guess. But, we can do better.
?
Those scores you see are from the perspective of the home team (AT THE START OF THE HALF INNING, more on that in a bit). And the home team was up by 3 runs in the top of the 5th. If the Nationals score a run, that run changes the win expectancy from .848 to .762, meaning a change of .086 wins. On the flip side, in the bottom of the 5th, keeping a run off the board isn't as impactful, with an impact of .938 - .893 or .045 wins. In other words, a run earned is worth TWO runs saved.
Method 4: Even more specific
This is a high level view. I did it the better way next. I looked at all games where the top of the 5th started with the home team up by 3, and I checked the change in win expectancy in the top of the 5th and bottom of the 5th of those games. And it showed a similar 2:1 effect (9.45 runs per win in the top and 20.2 runs per win in the bottom).
So going back to my numbers, the .16 runs earned for the PH is .16/9.45 or .017 wins. And the .24 runs saved for Stras is .24/20.2 or .012 wins. This gives a clearer edge for the PH. Note I did not even consider that there were two runners on base, with 0 outs.
Method 5: The right way
Finally, I did it the RIGHT way: I did not start at the top of the inning, but I looked at games where it was the top of the 5th, runners on 1b, 2b, and 0 outs. The runs per win in that case was all the way down to 4.6. And so, the .16 runs for the PH is now worth .035 wins. But hold on! Looking at THOSE games, for the bottom of the 5th inning and bottom of the 6th inning (where the score could be that the defense is down by 3... or down by 2 or even tied or ahead!), the runs per win is now 13.4. In other words, a run earned is 3x a run saved! Anyway, so the .24 runs saved is now worth .018 wins. And so, that makes it very clear that we want a PH here, even if Stras is a great pitcher.
Method 6: Simulator by an aspiring saberist
At this point, that's alot of math and theory. Ideally, someone will run their simulator out there and see how well all this holds up.
Batting team gains .020 wins if safe, loses .102 if out
Breakeven: 84%
In other words, if you are at least 90% sure the runner will be safe, you SEND him:
.718 x .90
+ .840 x .10
= .730
Home team (defense) win expectancy goes from .738 to .730 in this case
And if you are at best 80% sure the runner will be safe, you HOLD him, otherwise:
.718 x .80
+ .840 x .20
= .742
Home team (defense) win expectancy goes from .738 to .742 if you send him when you are at best 80% sure.
Why the high breakeven?
The difference between this situation, and most others, is that you do NOT want to make an out at home with 0 or 1 outs. That's because of the power of the potential sac fly. So, that's why you have to be really really sure that the runner will be safe. At least 84% sure. That's Tim Raines trying to steal a base, that's the confidence you need.
And when a runner is thrown out by this much, you know that it was not an 84% chance of being safe. The only way for Altuve to be safe is if the relay was not perfect. And with two guys throwing, that probably sets it at 50% chance of that happening. With two outs, this is the ideal send. With 0 or 1 out, it is not.
?A couple of days ago, I laid out a series of tweets as to how to do a quick analysis of The Intentional Walk. Ben went the extra mile and did it the right way.
Runner is about 75 feet from 3B. Taylor Sprint Speed is 29 ft/s, meaning he needs 75/29 = 2.6 seconds
Cain will have to make an almost 200 foot throw. He has a somewhat below average arm at 85 mph. Here's where we need to leave the world of mph and enter the world of feet / sec. 85mph is 125 ft/s. That's at release. The ball will slow down in flight. Roughly speaking, it'll lose 10% every 60 feet.
In this case, we'd do 200/60 = 3.33, and 0.9^3.33 = 70%. So at arrival, the speed of the ball is 70% of 125 ft/s or 88 ft/s. So the average speed of the ball in flight is about 106 ft/s. And so, a 200 foot throw will get there in about 200/106 = 1.9 seconds. (It's not this straightforward, but it's close enough.)
The exchange time (pickup to release) for a throw is about 0.5 to 0.75 seconds, which means that the ball would have reached the VICINITY of 3B in 2.4 to 2.65 seconds. It would have been close if the throw was on target. Which of course, it might not be.
How successful would Cain have been? Probably 60% if the throw is on target. And maybe it's on target 70% of the time? So, about 40% of the time he gets the runner maybe?
In the meantime, it would allow the batter to reach second base as the tying run. But, there were two outs! Making the third out at thirdbase is a cardinal sin for baserunners. Which makes it very appealing for the defense.
Bottom of the 8th, 2 outs, down by 2 runs. Our choices are:
runners on 1B and 3B (our baseline)
or
runner on 2B and 3B
end of inning
So, our baseline is a win expectancy for the Nationals of 15.8%.
If Cain went for it and missed, then the win expectancy is 19.2%.
If Cain got the out, then the win expectancy for the Nats is 7.1%.
In other words, the tradeoff is that the Nats gets +3.4% if Cain doesn't hit the target in time, or the Nats are -8.7% if Cain gets Taylor to end the inning.
All Cain has to do is make the play 28% of the time. That is:
28% of the time, the Nats lose 8.7%
72% of the time, the Nats gain 3.4%
And that's breakeven.
Remember, we guessed that Cain would have gotten Taylor about 40% of the time, and he only needed to get him 30% of the time.
?It's the bottom of the 8th, two outs, your team is up by 1, with runners on first and second. Walking Trout essentially means placing a runner on third base. In a random situation, giving up an automatic triple with 2 outs and bases empty means giving up about 0.35 runs, or 0.035 wins. But in this situation a walk is adding 0.075 wins. It also assumes an average batter coming to bat behind him. Which Ohtani decidedly is not.
What would Trout do otherwise? Well, Trout is a career +500 runs in 5000 PA kind of guy, so he adds, in a random situation, +0.10 runs per PA, or +0.01 wins per PA. In THIS situation, the Leverage Index is close to 5, so those 0.01 random wins becomes +0.05 wins if Trout was allowed to bat.
So, even if Ohtani was an average batter, the walk is not recommended.
Now, what does The Book say? We have a table that shows all the possible situations that you could consider the IBB. And the above situation is not one. We make it clear in The Book that with two outs and trailing, the pitching team should never advance the lead runner.
What would I have done? I'd have been scared, and told my pitcher to keep throwing away, with no hope that Trout would chase anything. He'll prima facie "earn" his walk, and I wouldn't have guys like myself second guessing... myself.
?I think I answered this in a blog post recently. I can't remember right now, but it goes something like this: assume the three outfielders get 10 plays per game, while the three non-1B infielders get 13. By handedness, instead of the LF getting 3 plays and the RF getting 3 plays, you can probably swap the worse fielder in one spot for each batter, so that the worse fielder gets 2 plays and the better gets 4 plays. Something like that. By abandoning a position, you turn the 1.4 outs per 2 plays into 0 outs per 2 plays. That's a net impact of over 1 run. If instead it's the infielder you do it too, you probably have a similar impact.
Maybe it's a bit more, but then you would realign all your fielders to maybe close part of the gap. Let's call it 1 run.
But if you remove TWO fielders, it'll get exponentially greater. Now, all the hiding that leverage allows starts to diminish. Losing the 2nd fielder is probably another 2 runs. A third fielder probably adds 3 more runs on top of that.
Anyway, without putting much effort or thought, that's basically the blueprint. You can work it out for yourself as to the impact of losing each fielder to see what happens.
?It's bottom of the 5th, Saunders is on second, Jays down by 1, with 1 out. Pillar hit it deep to the RF line, for a likely out, but ended up as a double. Saunders ended up on third.
Let's check the win expectancy. Before Pillar, Jays had a .437 chance of winning. If this was a fly out, he'd have to go back to 2B for a win expectancy of .384. Had he tried to tag up, it would have put Saunders at third, with a .390 chance of winning. Right there, you can see why even thinking for a tag up is a bad idea. With only a .006 win gain, the runner has to be far enough from 2B, but close enough to come back for a fly out.
We'll keep going. On the batter reaching 2B, we should end up with a run, meaning a win expectancy of .593. Instead we have runners on second and third, for a win expectancy of .542. That baserunning play cost .051 wins, or more accurately a potential of .051 wins. Carrera bailed him out.
Mathematically, there were three choices:
play for the tag up, meaning .390 win% on an out, and .543 on a hit
play to score, meaning .384 win% on an out, and .593 on a hit
worst of both worlds, meaning .384 win% on an out, .543 on a hit
If there was less than 10% chance of there being a hit, you do option 1, and play for the tag up. If there was at least 10% chance of there being a hit, you do option 2, meaning be pretty close to third base. Option 3 is not an option.
?MGL said something that I've never thought about:
...when the batting team is behind by at least 2 runs, the defense never plays the infield in. When the batting team is up by any number of runs or behind by 1 or tied game, the infield almost always plays up.
Now, you should know that as impressive of a saberist that MGL is, he couples that with bench-manager-level of knowledge of baseball. If ever you would put a saberist as a bench manager, it would be MGL.
So, this is cool then. With runner on 3B only and 1 out:
When batting team is down by 2 or more, the OBP for that PA is .330.
When batting team is up, the OBP for that PA is .400!
This is consistent with MGL's observation, that the defense will play in to keep that runner from scoring, at a cost of letting the batter reach base. So, the defense plays in when the batting team is ahead, trying to keep that runner from scoring on an out, even if it means letting the batter reach base on a hit or walk. And the defense plays back when the batting team is down by at least 2 runs, more worried about keeping the batter from getting on base than keeping the runner from scoring.
How does it affect the bottom line, the change in run expectancy? With batting team down by 2+, change in RE is +.014. With batting team up, change in RE is -.028 runs. Therefore, the defense is playing REALLY SMART by allowing a .400 OBP!
And this points to the idea that maybe the defense is playing too far back when down by 2+, and as MGL later noted to me, that maybe in the early innings, they should play in more in these situations.
I should also note that there are a few exceptions that stood out to these rules: batting team down by 1 or tied, and in the first inning, and behaviour is like down by 2 (play back). But down by 1 or tied and in the 2nd or later innings, and behaviour is like up by 1 (play in).
?Well, well, well. The NFL is changing the touchback rule on kickoff so that it goes back to the 25 yard line. Since the breakeven point is right around the 20 yard line, the returning team is HIGHLY incentivized to do a touchback. You can't just automatically give one side 5 yards and expect nothing to change. Well, they will change. The kicking team is now incentivized to kick it short enough to not allow a touchback to begin with.
See, if the touchback was the 10 yard line, the kicker would simply do one thing: kick it as hard as he can. If the touchback was the 40 yard line, the kicker would simply do one thing: make the trajectory a high enough launch angle so that distance is "sacrificed", a sacrifice that benefits the kicker. At 20 yards, there was harmony.
How does this apply to fielding shifts in baseball? Well, if a hitter is smart, he (a) wants the fielders all to one side and (b) he would continually poke the ball or bunt the ball to the open side. But if the fielders see the batter adjusting, the fielders will suddenly play defense normally. In which case the huge advantage for the batter disappears. Which forces the batter to now pull the ball more, forcing the fielders to shift more, which allows the batter to not pull as much... until we have harmony. The batter therefore doesn't want to do this too much. He has to hit suboptimally (not always bunt) to keep the fielders to continue to play suboptimally! It's just a matter of how suboptimally the hitter is to maintain the oppositions suboptimization. Weird, I know.
Indeed, the NFL can make the rule so that the defense decides on what the touchback line is! A team can say "touchback to 40", in which case the kicker will "bunt" it (i.e., high short kick). A team can say "touchback to 20", in which case the kicker will "pull" it (long straight kick). Basically, letting the defense call the touchback line is just like fielders positioning themselves on a baseball diamond!
?Long (long, long) time Straight Arrow commenter GuyM has a sensational article over at BPro.
But why do umpires shift their error rates at all, unless it is to lend a helping hand to the underdog? The answer is, because they know (more or less) what’s coming. Umpires are changing their decision rule on close calls—“lean ball” vs. “lean strike”—based on the likelihood that the pitch will actually be a strike. With two strikes, they know the pitcher will usually throw outside the zone, and they know the hitter will typically swing at anything close—so guessing “ball” on any taken pitch is the percentage play. By adjusting their decision rule at each count to reflect their prior knowledge of the true distribution of pitches, they make better guesses and fewer mistakes. In short, umpires are Bayesian, not compassionate.
As I'm reading down this list, ?I was thinking "I'd like to see this one". That was on the first one. And the second. And the third and fourth... all, without exception, is exactly what I'd like to see. I can't even think that I'd prefer to listen to one over the other. They are all right up my alley. So, whoever over at SABR choose these presenters, you did a fantastic job. And of course, the presenters themselves have chosen terrific questions to answer.
I do hope that the rest of the public will get to see these presentations in some form at some point in time.
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