Houston Astros insuring their future

Jon Singleton, the living, breathing, 6-foot-2, 225-pound embodiment of just how much smarter the Astros are than your team, was bad last year. He’™s crushing the ball this spring, but who knows? He might be bad forever, and the $10 million steal that the Astros either shrewdly earned or coerced — €”depending on your point of view — €”would be a $10 million waste.

That’€™s what happens when your baseball team is also an insurance company.

Insurance companies lose sometimes. One of the cars crashes. One of the healthy 45-year-old non-smokers dies. One of the insured bonds depreciates.

Insurance companies generally win, though. Travelers, for instance, is worth $35 billion by simply having a different risk tolerance than you have.

The Astros are an insurance company in the sense that the long-term contract that a player signs — €”in Singleton’€™s case, before he is even promoted — €”is the sum of two pieces. It’€™s the fair market value of the contract (or at least fair-market by baseball’€™s unfair-market service time-based rules) plus an insurance component where the player gives up his upside for the downside protection.

It’€™s easy to see why this is a winner for the team. A lot of it is covered in the first section of this article about the Singleton extension. But for a simple exercise, take a player with $2 million in the bank who has a 50 percent chance of being worth $10 million for some future year and a 50 percent chance of only being worth $2 million (all figures in present value, after tax for simplicity).

Would that player sign a contract for $6 million?

This comes down to how the player values each marginal dollar. A general rule (in line with the Kelly criterion, a shaky but generally on-the-right-track theory for investors and gamblers) is that the player will try to maximize not expected wealth, but expected log of wealth, which has each dollar worth marginally less. One million is better than a 50-50 shot at 2 million, for instance.

The expected value of log(wealth) after that season is just an average of logs: (log(12M) + log(4M))/2 = log(6.93M), or $4.93 million over the $2 million he’€™ll already have. Not only would the player be willing to sign the contract for the $6 million midpoint, but he’€™d be willing to sign it for less than $4.93 million.*

There are things that can be changed in the equation that make the logarithmic nature of it have a bigger impact compared to just a straight average. As the player€’s uncertainty grows either with variance in performance or time between now and the year of the payout, the further from the midpoint that number gets. And the lower the initial bankroll is, the further from the midpoint that number gets. (In the extreme case, a player with $0 in the bank under the same conditions would theoretically be willing to sign for $4.47 million by the same equation.)

That’€™s where the Astros come in.

They are hardly the first team to notice that you can lowball your young players. The Rays did this with Evan Longoria and later Matt Moore. The Pirates are making big efforts here too.

Where the Astros are getting their comparative advantage is trying to make that log work for them like no team before them. They’€™re doing it with players who have less of a bankroll, in Singleton’€™s case before he played a single game in the major leagues. And they’€™re doing it far out with players who have incredible variance in performance, reportedly making offers to George Springer, Matt Dominguez and Robbie Grossman in addition to Singleton and the big one in Jose Altuve.

Because the Astros have torn down and rebuilt in multiple phases over the past few years, they have a core of elite prospects whose youth makes such contract guarantees attractive. They also have the quantity, which is just as important as the quality to make this strategy work.

That’€™s how insurance companies make their billions. One of the cars crashes, but most of them don’€™t. One of the 45-year-old non-smokers die, but most of them keep getting at-bats for the Yankees. One of the bonds depreciates, but the market as a whole is generally fine.

Jon Singleton hit .168/.285/.335 last season, but when you have a portfolio of contracts, you’€™ve spread what little risk you’€™ve taken on.

Instead of this being one good contract and one potentially bad contract:

Contract comparison

Year Altuve Singleton
2015 $2.5M $2M
2016 $3.5M $2M
2017 $4.5M $2M
2018 $6M $2M
2019 $6.5M $2.5M
2020   $2.5M
2021   $13M

Club options in italics

You have this portfolio, which looks incredible:

Combined contracts

Year Altuve and Singleton
2015 $4.5M
2016 $5.5M
2017 $6.5M
2018 $8M
2019 $9M

You’€™re not going to produce an Altuve every year or even every couple of years, but with the discounts your players are willing to take, you don’€™t have to produce many. The math will work itself out.

Although since we’€™re talking about insurance contracts, that sounds a lot like what everyone said eight years ago. The math will work itself out. One of these mortgages will go under and we’€™ll have to pay the insurance on the default, but they’€™ll mostly be fine and by probability and making a sufficiently large portfolio, we’€™ll be fine.

That’€™s one of the two worries about this strategy when it comes to the Astros. The insurance companies and other holders of collateralized mortgages didn’€™t realize that their products were so highly correlated, and treating them as pseudo-independent events led to a gross miscalculation of risk.

The correlation is what could bring this down. If there’€™s something about their scouting or internal evaluation process that makes more of these not work out in the long run than would be expected, then these long-term contracts would become more of a burden than a blessing.

The second fear is that players stop taking these contracts either at the direction of the union or because they start to see them as an insult. Or third, an actual insurance company comes in to undercut the team’€™s insurance function by insuring players’€™ future earnings.

But for now, the Astros’€™ roster construction and focus on doubling as an insurance company should give them a competitive advantage at a time in their franchise history when they’€™re dying for one.

* The math also shows why the owner, who say has $100 million, is willing to take this deal. He is also trying to maximize log of wealth, and if it’€™s a sole owner with the $10 million or $2 million coming out of his pocket, (log(90M)+log(98M))/2 = log(93.9M), the owner would have been willing to do it up to $6.1 million but can usually get the player to go to something right above his number.

Zachary Levine is an author of Baseball Prospectus.