A few weeks ago, I asked this question on Twitter: If Mike Trout were willing to sign a 20-year contract with the Angels right now, what would be a fair price? The responses I got ranged from $100 million to $350 million and averaged $243 million. Glenn DuPaul did the heavy lifting to try to answer this, which is great for me, because Less Heavy Lifting is basically my entire goal in life. It’s why I went to college, and it’s why my furniture is made of Nerf. Glenn’s answer: $274 million. OK! He also wrote this, which is probably what I would have written, too, to avoid sounding like a crazy person:

No baseball team (or professional sports team for that matter) would give 20 years of guaranteed money to an athlete (the longest contract in baseball history is Todd Helton's 11-year deal with the Colorado Rockies). There is just too much risk involved. Trout's career could end early for many reasons, including injury or a lost touch with his love for the game.

This is probably the most interesting question raised in DuPaul’s piece. No team wants to give 20 years of guaranteed money to an athlete, unless the price is absolutely right. Is it possible that the price actually would be right? Is the 20-year contract, or something close to it, where baseball is going? The extensions Matt Moore and Salvador Perez signed this winter suggest it might be. Yes, these types of deals are risky. But the actual risk is far, far greater for the 22-year-old. To a team, the risk is a note appended to an actuarial table. To the kid, the risk is three decades coaching at a junior college, walking with a slight limp.

To go further, we need to agree on two things. The first is that humans are inherently risk averse, and that this risk aversion makes them behave irrationally. Here’s where the behavioral economic theory known as Prospect Theory comes in:

Imagine that you have the opportunity to play a gamble that offers a 50% chance to win $2000 and a 50% chance to lose $500. Would you play the gamble? The results reveal that only 43% of the participants were willing to play the hypothetical gamble although its expected value was much higher (+$750) than the status quo of not playing.

To an economist, this is irrational. But it’s also a delusion we’ve all agreed on. There’s a reason insurance companies are willing to sell you house insurance, after all. You’re likely to pay far more to the company than you’ll take out, and they’ll make loads of profits on your irrationality. Except you can handle one kind of loss, the $50-every-month kind. You can’t handle the other kind.

The second point is that the value of a dollar depends on the context.

[21:1] As he looked up, Jesus saw the rich putting their gifts into the temple treasury. [2] He also saw a poor widow put in two very small copper coins. [3] "I tell you the truth," he said, "this poor widow has put in more than all the others. [4] All these people gave their gifts out of their wealth; but she out of her poverty put in all she had to live on."

The richer you are, the less a dollar matters. I don’t mean this in a tax-the-rich sense, but simply in the very real way that we have certain minimum expenses to maintain a basic quality of life. The first dollars we earn go to that quality of life. The billionth dollar goes to our great-grandchildren, and the lawyers that will distribute those inheritances

1. Humans fear risk.
2. The first dollar is the most valuable dollar.

Those two factors explain why the Royals’ 21-year-old catcher Salvador Perez signed away his next eight seasons for the guarantee of just $7 million, and those two factors explain most contract extensions signed by pre-arbitration players that include generous club options, including Matt Moore. Moore signed an extension this winter that guarantees him $14 million over five years and gives the Rays three club options. It’s similar to the contract Evan Longoria signed in 2008, a week after his major-league debut, perhaps the most team-friendly deal ever. Just as no team wants to give 20 years of guaranteed money to a player, no team wants to give five years of guaranteed money to a player who will play for the league minimum and a one-year commitment. And yet, the Rays—the team that can least afford to carry a sunk contract—committed this money to Moore and were pretty universally praised for it. They did it because Matt Moore fears risk, and he knows the first dollar is the most valuable dollar, and so he took a discount. R.J. Anderson:

And so, many will wonder why Moore’s agent, Matt Sosnick, would let him sign this contract—particularly in knowing that four years of arbitration could be realistic? The most obvious answer is that turning down a guaranteed $14 million is tough for any 22-year-old, even those in baseball. Moore was not a big bonus baby, either, meaning this is his first opportunity to set his family up for life. The value of security is subjective. Moore may value it higher than you or your neighbor would.

Moore will be paid about $26 million during the 2017, 2018 and 2019 seasons. PECOTA projects him to produce 8.4 WARP in that stretch. If salaries go up 5 percent per year, Moore projects to be worth more than $50 million over those three years, with the very real possibility that he becomes the sort of pitcher who can produce 8.4 WARP in a single year. And those three years are all club options, so the Rays don’t even face any additional risk beyond their $14 million. Moore gives up a best-case scenario of perhaps $125 million, all so he can guarantee he’ll earn at least $14 million. Moore is rich now, forever.

Moore, of course, has pitched 19 â…“ big-league innings. Longoria had played six games when he signed his extension. Teams have been signing young players to extensions since at least John Hart in the 1990s, but the Longoria, Moore, and Perez extensions are unusually long and locked up players who were unusually young. This is why they work. By the time players reach arbitration, they’re already millionaires. They’re already relatively secure. They can start thinking about their great-grandchildren.

It’s notable that the Royals signed Perez and Alcides Escobar to deals that included club options, but Alex Gordon signed an extension with player options. Escobar has earned a bit more than $1 million in his career. Salvador Perez has earned less than $1 million. Gordon had earned more than $7.5 million and was guaranteed an additional $4.8 million for 2012 even before the extension. He was already richer than almost anybody you know. The Royals simply didn’t have the leverage over him that they had over Perez, or that the Rays had over Moore.

Twenty-one players this winter signed extensions that bought out free agency years. We can divide them between those who had already earned at least $5 million in their careers and those who hadn’t. Of those who had earned $5 million, only Brandon Morrow agreed to a club option. Of those who hadn’t—Nick Hundley, Jonathan Lucroy, Alcides Escobar, Matt Moore, Salvador Perez, Cameron Maybin, Dustin McGowan, Cory Luebke, Andrew McCutchen, Gio Gonzalez, Derek Holland, Ryan Vogelsong, Casey Janssen, Sergio Santos—all did. (Perkins’ figures are a little cloudy; he was right on the border of $5 million, and he agreed to a club option. Santos signed his extension the last week of the season.) The more money players already had, the less willing they were to trade their upside for security.

In general, here’s how we can look at it: when Brandon Wood buys a burrito, and they ask him whether he wants guacamole, Brandon Wood has to ask if it costs extra. Brandon Wood will always have to ask if it costs extra. If Brandon Wood had signed an Evan Longoria contract when he was a top-10 prospect, he would never have to ask if it costs extra, ever again. This is what young baseball players are risking every day before their first big payday. Guilt-free guacamole.

A player’s three pre-arbitration years are the small-market team’s most useful weapon, and leveraging those three years of uncertainty to compel middle-class kids to sign away large portions of their upside is the next way to counter big-market teams’ free agent edge. And baseball’s small markets are where new ideas incubate. It was in small-market Cleveland that the pre-arb extension was popularized. It was in small-market Oakland that the Paul DePodesta was popularized. Small-market teams have to try radical tactics on the margins, and when these tactics work, big-market teams appropriate them. The Rays and the Royals are telling us where contracts are going, and—so far, and especially in the Longoria case—it is working.

The 20-year contract might never be real. There are players for whom a long-and-early extension is probably not appealing at all. (I suspect Bryce Harper, for instance, is the sort of guy who would offer the hypothetical coin-flip scenario above, confident he would win despite the odds.)  But with the smaller signing bonuses that the new collective bargaining agreement seems to portend, longer extensions signed earlier will appeal to both team and player. I’ll be surprised when the next Mike Trout—Bubba Starling, or Francisco Lindor, or Luis Heredia—signs a 12-year extension in his rookie year. But not totally surprised.

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That was a fun article. Thanks!
"Moore will be paid about $26 million during the 2017, 2018 and 2019 seasons. PECOTA projects him to produce 8.4 WARP in that stretch. If salaries go up 5 percent per year, Moore projects to be worth more than $50 million over those three years, with the very real possibility that he becomes the sort of pitcher who can produce 8.4 WARP in a single year."

Here's the thing--if Moore performs at that level, he will get at least one really significant free agent payday. That makes the forgone dollars worth even less from his lifetime baseball earnings. For example, let's say he plays well at Tampa, hits free agency, and signs a 5/70 deal...and is out of baseball at the end of it. His lifetime baseball earnings are still $96 million. The forgone revenue from his arb years and three option years is effectively marginal income ABOVE the hundred million level.

If you look at the Gordon contract you see this pretty clearly--he was willing to give up two seasons of free agency, but that still allows him to get one big payday in his career at age 31. If he doesn't do well, he has the player option to fall back on.

So the logic that is developing is pretty clear, I think--player signs away some excess value in their late twenties for financial security but ensures a single big payday in free agency if they play well/aren't injured. As an aside, if this becomes the standard way of doing business in baseball, WAR purchased in free agency will begin to become more expensive.
One aspect of player income that you did not address is endorsement income...which for a young, popular player can make a significant (I think) addition to his take home pay.

That was the main reason I questioned the sanity of Evan Longoria (and his agent) when he made his deal. Given his pedigree, looks, etc., I think he could be reasonably sure to make up a sizable chunk of the difference between his "normal" salary and the increase during his non-arbitration years from his long term deal.
He would have no value there either if he either (a) got hurt or (b) became Brandon Wood.
"No baseball team (or professional sports team for that matter) would give 20 years of guaranteed money to an athlete"

The only exception to Glenn's assertion that no professional sports team would do this would seem to be Magic Johnson, who signed for 25 years (though it got restructured). Hockey contracts edge up there, but that has more to do, I believe, with their CBA creating incentives for teams to sign players to longer contracts.
Relatedly, I think if we really delve into all the "risks" associated with this type of contract that might make it more or less reasonable, beyond interest and injury (discussed), two things come to mind:

Insurance: I know some MLB teams take out insurance for injury on contracts, and I would have to assume that an insurance policy on a 20 year contract would be significantly more expensive.

Risk/Reward of restructure/labor issues: the labor history of sports suggests that there's at least a decent chance that at some point during this contract, something happens in a labor deal that would have an impact on its value (work stoppage, hard salary cap, what have you). Restructure has tended to happen with longer contracts (see: Magic Johnson, A-Rod almost twice). There's a definite chance if ANY player signs a 20 year deal and becomes a mega-star, that player becomes disgruntled at some and holds out for a more beneficial deal. In that sense, the possible upside of a 20 year contract is probably limited: if it tilts too far in favor of the team, don't expect it to stay that way.
One variable that hasn't been addrssed : renegotiation
demands from the player when their performance exceeds
market compensation standards at the back end of their agreement.
When is the last time that happened in MLB?
It might happen if we start seeing long-term, low AAV contracts...
I was just wondering if teams and players considered this as well. We can call it the "sheffield corollary".

When a player's contract becomes lower than market value, he begins to whine, bitch and half-ass it until he gets a better deal.
Great article, welcome to BP Sam!
Here's hoping the Mariners can lock up Montero and Ackley long term. That would be awesome!

I love this article, I hate insurance companies. Thanks Sam
Really good article...Thanks Sam
Excellent and informative article. Thanks!
I like the meme "guilt-free guacamole". Add it to "Beer and Tacos", and your really... cookin'.
Interestingly, usually when these discussions happen, the prism through which we look at the contract is a "is this good for the team" perspective. Should we assume here that it's good for the player? Would an agent do this deal in a heartbeat? Most probably would, but I'd be curious if Boras would ever agree to a deal like this without the player opt-out clause that seems to be increasingly common.

As a further tangent, I think there comes a point where player and agent interests dovetail. An agreement like this (20 years) might be good for an individual player because it is *rationally* risk averse, whereas an agent can handle these risk pools to maximize contract values because the agent has a large number of clients. The agent and players are faced with different calculations when it comes to Prospect Theory. It's important to note that an economist would consider risk-averse Prospect Theory behavior irrational more in the context of repeated play than as a one-time proposition. Collectively, an agent's risk exposure for trying to maximize value of each contract is lower than for the players for whom he's negotiating the contracts. In this sense, Boras' advice to a player to sit out a year (Drew, Hochevar, etc), or sign a shorter deal (Madson) may be and at times has been better for the agent than the player.
Small clarification, Sam - prospect theory postulates that humans are "loss averse". This is a slightly different than the economic concept of risk aversion, although the difference is probably meaningless for this setting.

That aside: once again, a great piece. Great to have you here at BP.
Sorry, one more clarification: "To an economist, this is irrational."

This isn't true. Behavior that does not maximize one's own utility would be considered irrational, but the assumption of risk aversion is a common one (in many settings, the standard assumption) in economic literature. (That is, risk-aversion is baked into the individual's utility function, if that wasn't clear.)

Again, pardon if this is nit-picky - I love pieces like this - but I'm in a profession where one picks nits over things like this. :)
Excellent nits. Very glad you clarified.
And taking that $750 EV bet might not maximize utility either. If someone can't afford to lose the $500 -- losing it would cost them their home or something -- then it would be irrational for them to take the bet.
This misunderstanding is common. See this blog post from economist Steven Landsburg for more:
Nice work Sam - look forward to your future pebbling.
Great read!
Guilt-free guacamole, very nice. The converse to Matt Moore would be Tim Lincecum, who consistently goes for the short-term payday from San Francisco. This high-risk approach already has generated high yields, but required Lincecum to be confident he'd stay healthy and productive long enough to cash in. $65 million later, he won't have to worry about guacamole ever again, and he's about 19 months away from potentially buying Mexico (and all its avacados) if he maintains his performance. Not an approach that works for everyone, but I suspect he has no regrets.
It occurs to me that there's a further imbalance in the risk equation for teams vs. players: Where a team can have some confidence that any mistakes will average out over time - if you sign five rookies to cheap long-term deals and one is a washout, the savings on the other four pay for what you waste on that guy - Matt Moore can't play the same game, because he only has one life to live. All the more reason to expect more of these deals in the future.

Anyway, great article, and has definitely given me lots to think about. (And reminded me that I need to read more behavioral economics.)
To state this in financial terms, the firm (and their owners) can diversify their risk, while their employees usually cannot since so much of their wealth is tied up in their human resource.

This issue comes up a lot in the corporate governance literature.
On behalf of the hockey fans out there, I might suggest that even considering a contract as long as 20 years is just nuts on the part of the team. The NY Islanders signed a then-24 year old goalie named Rick Dipietro to a 15-year deal for 67.5 million. In the 6 seasons since, he has averaged under 29 games per year and his performance has been subpar; he has won 14 games over the last 4 seasons combined. The Islanders are paying Dipietro for the next 9 years whether they like it or not.

Alex Ovechkin of the Washington Capitals has a $9.5 million per year cap hit for the next 9 years, and he has seen a fairly sizeable drop from his MVP level of play these past 2 seasons. That's looking like a terrible contract right now for the Caps.

Buyer beware, I guess.
This is really, really good. Starts off with theoretical economics, ends up humanizing players. That's a neat trick.

I'll never be able to look at another "team-friendly" deal without thinking of Brandon Wood ordering guac.