As I occasionally mention, I worked in finance before I started writing about baseball. One of my early bosses told me something that pretty much everyone in the industry has heard at one time or another. I had just presented a fancy trade that took advantage of about seven different financial instruments to eke out a small profit with minimal risk. He took a long look at my page of notes, scrunched up his nose, and gave me a tip that has stuck with me ever since: “Hedges are for gardens.”
That’s not something you’ll learn in a book. Financial theory is all about reducing variance and then doing the resulting low-risk trade you’ve built over and over. They call them hedge funds for a reason, after all: hedging against loss is a lot of the point. But the secret those books won’t tell you is that this behavior has a logical limit. If I showed you a risk-free way to make a dollar, theory would tell you to replicate that exact trade a billion times. If I showed you a riskier way to make five dollars, theory would tell you to reject it in favor of the first trade and make up the foregone four dollars in volume.
But in the real world, that’s not how things work. As it turns out, you can’t replicate things infinitely. Plenty of the decisions I’d made that reduced variance also reduced expected return per unit of the trade. You can think of it in simplified terms: I’d taken something that would make me four dollars, plus or minus five dollars, and turned it into something that made me two dollars for sure. Two is less than four. If I could select the guaranteed two dollar option twice, that would be clearly better than the risky four dollar option, but my boss pointed out that just doing twice as much isn’t always easy, or even feasible. The better trade, he told me, was the one that didn’t sacrifice quite so much expected value in the name of hedging.
What does this have to do with baseball? More than you’d think. Accepting lower returns in exchange for lower risk is a time-honored tradition across all sports. Whether it’s the running game in football, mid-range jumpers in basketball, or setting up deep and playing defensively in soccer, old school tactics were heavy on risk mitigation. Baseball has tons of these: shortening up to put the ball in play, pitching to contact, sacrifice bunting, letting your starter go seven regardless of how he’s pitching that day. Those strategies are all about minimizing variance around your central outcomes rather than trying for the highest effective value.
A quick survey of other sports is in order. The hedging-obsessed strategies of yesteryear are in full retreat. Football teams probably still run the ball too much and punt too frequently, but passing rates and fourth down conversion attempts have exploded in the 21st century. Three-pointers are at an all-time high in basketball. High-level European soccer teams press high on the field even though the risks of surrendering a breakaway are higher. Hockey teams are pulling their goalies much earlier when trailing, even though that increases the odds of the other team putting the game away with an uncontested goal.
In all of those cases, it’s a math argument. The new strategies might be riskier for any given play, but they’re better in the aggregate. Shoot one three-pointer, and your risk of abject failure – zero points – is meaningfully higher than if you took a shot closer to the basket. Shoot 20 of them in a game, and some of that variance comes out in the wash, leaving you with higher expected points in the end. Sure, you could hedge with the lower-expected-value shots, but there are a limited number of possessions in a basketball game. There’s no “doing twice as much” here. Hedges are for gardens.
Baseball is the same way. Each team only gets to bat 40 or so times in a game. Those are precious chances to score runs, and they’re more or less fixed. The gap between the team that batted most and least times in 2024 worked out to about 2.5 plate appearances per game. Again, there’s no “doing twice as much.” Batting teams just have to try to score as many runs as they can before they run out of outs.
Here’s a thought experiment that will hopefully help explain why this return-seeking/risk-accepting behavior is taking over. Take two hypothetical games. In one, you make two dollars 50% of the time and one dollar 50% of the time. In another, you make eight dollars 25% of the time and nothing the other 75% of the time. The second strategy has a higher expected value and also higher risk of failure on every observation.
Which strategy is riskier over one observation? The zero-or-eight choice, obviously. But let’s say I let you play 40 times, and your objective is to maximize the times where you rack up $55 or more. A one-dollar-or-two-dollar strategy has an expected value of $60 over 40 trials, and very little variance. It gets to $55 a full 96% of the time – excellent! The high-risk strategy? It has a higher expected value but more variance. But here’s the thing: 90.4% of the time, it still gets to at least $55. It gets to $60, the expected value of the low-risk strategy, a whopping 81.8% of the time. If you were to take these two strategies and test them against each other over 40 observations, the high-risk/high-variance strategy would win roughly 81% of the time.
I’m not sure whether that’s intuitive, because my intuition was re-wired by the market long ago. Return scales linearly with the number of trials. Variance scales as the square root of the number of trials. The standard deviation of four trials is only double that of a single trial, but the return is four times as much. Things that feel more failure-prone simply aren’t over a large sample, at least as long as the return is there. That trick – variance not mattering as much in the grand scheme of things when you get a ton of observations – applies to sports as surely as it does to hypothetical games of chance.
An obvious place where baseball has gone the way of prioritizing maximum expected returns over minimum variance? Home runs. Optimizing your swing to hit the ball out of the park means you’re going to fail frequently. The same swings that produce home runs also produce whiffs and weak popups. If you were merely minimizing the chance of failure, you’d swing softly to sell out for contact.
But it’s not just a question of failure against success; not every success is the same. A homer is generally worth many singles. Striking a ball hard and in the air is worth far more than hitting it softly and on the ground, even if both are “successes” when it comes to contact. If you got only one bite at the apple and anything but a ball in play counted as a loss, prioritizing contact would be the smart move. Over a full game, power plays.
On the flip side, pitchers are chasing higher expected returns as well. Fastballs are a classic variance-reducing pitch. They’re in the strike zone more often than their bendy counterparts. Batters make contact with them more frequently. The worst thing you can do as a pitcher is throw a non-competitive pitch. An all-fastball diet minimizes the chances of that failure, and thus reduces variance.
Again, though, reducing variance isn’t the actual goal. The goal is to secure the best outcome. Now that hitters are increasingly trying to hit the ball out of the park (see above), throwing mostly fastballs is a worse bet from an expected value standpoint. What have pitchers done? They’ve accepted the extra risk of a ball, and by extension the extra risk of walks, to make the higher-EV play of hunting whiffs and strikeouts.
The death of sacrifice bunting is another inevitable consequence of the return-over-risk-aversion mindset. Sacrifice bunts are more or less just hedges. They reduce expected scoring in exchange for flattening out the distribution – more one-run innings, fewer crooked numbers. But they’re bad hedges, like the ones I pitched to my boss, so teams are ripping off the Band-Aid and making the highest-value decision.
Another classic risk that teams are increasingly accepting in exchange for better performance is the bullpen game. How many times have you heard an announcer bring up that all it takes is just one guy having a bad outing? It’s true! That happens sometimes. But what’s your alternative? If it’s using a spectacular starting pitcher, yeah, sure, do that. But that’s almost never the alternative to a bullpen game. The alternative is usually a journeyman, or an unproven rookie, someone who is meaningfully worse than all of your trusted relievers on a per-inning basis. They’re less prone to not having it that day, perhaps, but they’re more prone to giving up runs because they simply aren’t as good. You have to wear the risk sometimes, and teams are increasingly just doing it.
I’m not going to go through the math of each one of these situations to show how risk reduction has taken a back seat to return maximization. There are just too many different ways we’re seeing this same behavior to break them down mathematically in a single article. My list almost certainly isn’t exhaustive, either. It’s hard to transform baseball into the black-and-white, extensively defined scenarios where return and variance are easy to measure. My point is merely this: Teams and players are applying this lesson every day. If you’re looking for a broad story of baseball in the 21st century, it’s a relentless pursuit of increased expected returns.
To be clear, this is the story of all sports in the 21st century. It’s inexorable. Now that players and teams have seen the light, they’re not going to suddenly reverse course unless the incentives change. The math is simply too clear.
Now, I’m not saying that you should always make the riskier play. The essential thing about the riskier strategy isn’t that it’s riskier; the return is what matters. It so happens that risk and reward are often paired, but that’s not always the case. Luis Arraez shouldn’t try to hit home runs. Emmanuel Clase shouldn’t abandon his fastball.
Additionally, the right strategy isn’t to never hedge. It’s to hedge only when you’re dealing with few observations and significant consequences to failure, or when the hedges aren’t costing you any expected value. I don’t mind a sacrifice bunt in the bottom of the 10th in a tie game. At that point, you’re only getting a few bites at the apple, and winning by two isn’t any better than winning by one. Humans are overly risk-averse by nature, but that doesn’t mean that the correct amount of risk aversion is zero.
One place where this is obvious is in roster construction. Running out of viable starters would be disastrous, and so teams hedge by over-allocating starting pitchers. Even then, they never seem to have enough, but no one’s coming into a season with just five starters and feeling good about it. Amateur player acquisition is another place where hedging sometimes makes sense. Spreading your money out over more viable players isn’t an automatic decision, but it’s not obviously wrong or even frequently wrong.
This article is getting a bit rambling, no doubt, so let’s wrap it up. The takeaway: Choosing the least risky strategy, on a per-play basis, is often the worst strategy if you want to win the game. If you’re looking to score the most runs (or the most points or goals if we’re talking about a different sport), you can’t go around running scared. The right play is the return-maximizing play almost every time, even if it feels “too risky” in the moment. Keep that in mind, and you’ll have a valuable tool for understanding why teams and players keep changing their behavior.
