Clutch Up Part 2
Baseball's Monty Hall Problem
Cover Photo: NY Post
Part 2: Baseball’s Monty Hall Problem
There’s a famous demonstration of how counterintuitive probability can be called “the Monty Hall problem”. It’s common in statistics and business; it was even on a TV show (albeit a TV show about math) and in Hollywood scripts for awhile.
Here’s the riddle: Imagine a game show where a contestant tries to find a prize hidden behind one of three doors. So: One door has a car behind it. The other two have goats behind them (which is what they do on Let’s Make a Deal, originally hosted by Monty Hall).
Suppose the contestant chooses door number one. But before opening door number one, the host (who knows where the car is) opens door two to reveal a goat. The host then gives the contestant a choice: The contestant can stick with door number one or switch to door number three.
What are the odds that the car is behind door number three? Most people think it’s 50/50. After all: There are two doors left, one has a car behind it, the other a goat…that has to be 50/50, right? Perhaps counterintuitively: No, it’s not a 50/50 choice at that point. There’s actually a two-thirds probability that the car is behind door number three; the contestant should switch doors (unless he’s really into goats).
If you’re thinking “what, why?”, you’re not alone. But it is actually true that switching doors gives you a two-thirds probability of winning. Here’s the matrix:
This math is irrefutable1.
Why is this true? It’s because the first choice of doors was random, but the second choice of doors wasn’t. Because when the host opened either door two or three to reveal a goat, he specifically chose a door that had a goat behind it. Remember: He knows where the car is. He won’t open the door with the car behind it – his choice isn’t random. When he opens a door, he essentially pools the win probability of doors two and three. The odds shifted because you gained knowledge.
So, if you’re ever on Let’s Make a Deal and find yourself in this situation, don’t think “switch doors, don’t switch doors…it’s all the same.” It’s not. One strategy is superior to the other.
Now let’s apply that knowledge to baseball. It’s counterintuitive to switch from a higher run-scoring strategy (TTO) to a lower run-scoring strategy (anything else). But the data we have suggest that a certain lower-scoring strategy is better in high-leverage situations. Basically: The optimal strategy changes because you’ve gained knowledge.
A run in the first is worth the same as a run in the ninth only in the very abstract. The difference is that in the first inning, you don’t know how many runs you need to win the game. For this reason, it makes sense to optimize around the three true outcomes approach, which maximizes total run scoring across the season. But when the game is late and close, the game has literally changed: The team has gained knowledge. They now know that they only need a run (or two) to win. At that point, the best approach is to switch to a strategy that gives you a high probability of scoring one run (or two), even if it gives you a lower probability of scoring many runs. This is baseball’s Monty Hall problem2. When you’re late in a game – when you’ve gained knowledge – you can use that knowledge to identify when switching from the TTO approach to what we’ll call the “Tony Gwynn” approach gives you a better chance to win. The Padres appear to have the same approach in all situations, and that might be the single biggest reason why they struggle in clutch situations.
Clutching Up
What all this means is that ”Clutch” performance is more of a byproduct of a particular approach to hitting than a separate skill. Which makes us wonder: If a player can alter the approach between TTO and the “Tony Gwynn” approach, should we consider that player clutch? And if he can’t, could he be considered not-clutch?
Maybe! And there’s at least one Padre who seems to be the definition of not-clutch:
No, that isn’t Nola. That is Jacob John Cronenworth. What stands out is the almost unbelievable strikeout rate: 34.6% in Late & Close situations. The technical term for that strikeout rate is “crap”. And it’s not hard to see how it happened:
Here is Crone’s 2-strike approach in 2023.
This was Jacob Cronenworth trying to hit the ball to the Moon. This is a swing designed to sacrifice contact for power and launch angle. But the thing about Crone is we know he has the ability to shorten up. There are innumerable examples from earlier in his career but there’s an obvious choice to showcase:
Courtesy: Fox Sports MLB
This was Jake Cronenworth trying not to make an out. That swing was short, his head was down, eyes locked on the ball to the point of contact. It was the biggest hit of his life. It was the highest leverage moment the Padres have been in for 25 years. This was Jacob John Cronenworth clutching up. Only 9 months ago.
There’s strange irony that the clutchest player of all time is the ultimate Padre, Tony Gwynn, who was a bright spot in a grim era when the team’s owners underinvested in the team. Now, ownership is spending big, but the team is achieving historic futility in clutch situations by eschewing Mr. Padre’s approach.
Implications
It’s tempting to look at this information and assume the Padres are making a systematic error, giving incorrect weight to runs in high-leverage situations. It’s more likely they know exactly how valuable a change in strategy in those at bats would be, but just aren’t set up to hit a different way. Maybe if you told, say, Manny Machado it’s strategically superior to shorten up and channel Tony Gwynn in certain AB’s he’d say “Yeah, I know, but this is how I hit.” Aside from Cronenworth it’s very hard to say whether Padres hitters can switch between a TTO approach and the “Tony Gwynn” approach. Heck, maybe even Crone can’t revert back to his old swing. What we know for sure is that the Padres struggle with late and close hitting, and that they appear to take the same TTO approach in every at bat. This is what underlies the 0-8 record in extra inning games. This explains the unreal 5-15 record in 1 run games. There’s also probably been bad luck to have had so many close games, but that bad luck is leveraged by a rigid TTO approach that is poorly suited to the late and close situations. Maybe the implication of all this is that at the deadline the Padres should be looking for a high contact bat that they can insert in the right situations in late and close games to provide the “Tony Gwynn” approach when there’s a situation where TTO is the inferior strategy. Or maybe, if it’s possible, they should let players who are capable shorten up and pursue contact when the moment calls for it.
Last Word
Our last word on TTO: the TTO strategy maximizes runs scored across the course of a season, but makes a team more vulnerable to losing streaks due to the boom or bust nature of the scoring outbursts. It also makes it harder to win late and close games. In other words the TTO strategy is more vulnerable to bad luck: the team might win some blowouts but lose most of the close ones, and that’s exactly the pattern we see from the Padres. This stretch typifies the season:
The Padres scored 44 runs in nine games while giving up only 23. That is dominance. Except the record across that incredibly hot stretch was a middling 5-4. On the season they’re 17-11 in blowouts (.607 winning percentage) where they’ve outscored opponents 169-123 (+46), but 5-15 in one run games, and 0-8 in extra innings. They’re getting unlucky, but they’re playing a rigid style that leaves them more vulnerable to bad luck. It’s easy to read all of this as an attack on the TTO approach. But here’s the thing: TTO is probably the right choice. If it’s the case that the Padres hitters are unable to switch between TTO and “clutch” hitting approaches, TTO is the superior strategy on the season as a whole. If you make us choose between only having one or the other, we’ll pick TTO. The purpose of this piece isn’t to attack the Padres strategy, it’s just to help explain the most confusing first half of baseball we’ve ever seen.
Not All Games Are Equal
Fittingly the second half starts with a series against the Phillies who ended the Padres magical 2022 run. These won’t be ordinary games. There’s leverage on these games, because the August 1st trade deadline is coming, and even though at the end of the season all wins count equally, the deadline will force a decision that will significantly affect the team’s makeup for the rest of the season. That’s why the next few games count so much more than others. These next few games are not just about the Padres place in the standings, they’re going to define the team’s destiny: hit the afterburners with trades for win-now pieces, or accept that 2023 is going to fade away, commit to fighting another day…
Nothing Really Good
There’s nothing really ‘good’ about a disappointing first half, but the silver lining might be this: The second half should be a white-knuckle affair. There’s more reason to watch than ever. Perspective is important. We don’t have to win every game. But we might need 90 wins to get to the playoffs. That would require winning 47 of the last 72 games. An easier way to think of it might be that we can lose 25 more games and not die. That’s a slim margin for error, but the task isn’t impossible. This team’s midway through a long flight, and they lost an engine. But they can still land the plane. To do it, and here we mean in the colloquial sense, the Padres are going to need to clutch up.
We still tried though. Here’s a matrix from L2AJ highlighting that in fact there are two different ways to lose if the car is behind the door you picked, and why that makes the choice to switch seem like at 50/50 proposition.
Here is the probability modeling that shows why this matrix is incorrect. Enjoy your migraine.
What made the Monty Hall problem so controversial is how subtle the changes in probability were, your brain didn’t realize a swing in probability had even occurred. But imagine if the game were played with 100 doors instead of three. After you chose one of the 100 doors at random, the host then opened 98 of the remaining 99 doors to show they all had goats. Would it be an easy choice to switch doors then? Similarly in baseball the swing in win probability from switching away from a run maximizing TTO strategy to the “clutch” approach isn’t as obvious because the margins are small; regardless of approach hitters usually make outs. But in other sports it’s readily apparent. A football team with first down on the 1-yard line will usually try to score a touchdown because that’s the strategy that maximizes scoring. But if there are only a few seconds left in regulation and they need 3 points to win they may kick a field goal on first down because of the leverage on win probability for those 3 points. This is uncontroversial in football in part because the swing in win probability is so much more obvious, and because the structure of the sport allows for specialization. But even if we recognize switching approach is strategically sound, we don’t have special teams in baseball.