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This piece originally appeared on BP Wrigleyville, Baseball Prospectus' local site for all your Cubs needs. And be sure to visit BP Boston and BP Bronx for Red Sox and Yankees analysis as well.

We’re in the end of days now. The story of Kris Bryant and service time, which dominated the Cubs’ spring training, has entered its next stage—hopefully, the one wherein Bryant dominates the National League on his way to a Rookie of the Year award.

But maybe we didn’t have to wait. There is a school of thought that suggests, perhaps accurately, that if Bryant were to have accepted a multi-year extension covering at least one of his free agent years by Opening Day, he would have started the year on the major-league roster, and a number of baseballs intended for some opposing catcher’s mitt would instead have already soared through night air, destined to ricochet among the steel beams of the Wrigley bleachers. There are a number of reasons that didn’t happen, but the most basic reason is that Bryant is expected to be a very good, low-risk major-league baseball player, and that is exactly the type of player who is least likely to sign an extension. Here’s why.

Extensions serve a single purpose: They eliminate risk. For the player, they eliminate the risk that injury will sap or destroy entirely their earning power; for the team, they eliminate the risk that the player will leave during free agency, or earn an uncertain amount during arbitration. Both sides therefore purchase certainty: For the team, that purchase is in the value of the extension, minus their estimate of the player’s cost without an extension (times their estimated risk it’ll be higher). For the player, that purchase price is the amount they estimate they’d make without an extension (times their estimated risk it’ll be lower), minus the value of the extension. When those two numbers—the purchase price of certainty for the team, and the purchase price of certainty for the player—are equal to each other, you get an extension.

Let’s take a look at this in equation form. Here’s the equation for an extension value a player will accept:

(1 – PER) * PEC ≤ PEV

That’s the player's estimate of risk (PER) times the player’s estimate of their value (or cost, PEC) over the years covered by the extension. They’d accept an extension value (PEV) at that level or higher. Now let’s look at the team’s side of the equation.

(1 – TER) * TEC ≥ TEV

It’s basically the same thing—an estimate by the team of the cost of the player without an extension, times the risk they cost more than that. A team would accept an extension with that value or lower. Now, let’s write what has to be true for an extension to happen:

TEC * (1 – TER) = TEV = PEV = (1 – PER) * PEC

Basically, the estimated values have to be the same for both sides. When they do, you get an extension at that value. Let’s say, for example, that the Cubs think Bryant might cost $50 million for his arbitration years (four, because of his likely Super Two status—let’s say at $8, $11, $14, and $16 million, plus two pre-arb years) and $25 million for his first free agent year (without an extension) and that there is a 15 percent chance that he gets hurt to the point where he’s not worth that amount. The team side of the equation would therefore be equal to:

= $75 million * (1 – 0.15)

= $63.75 million

The Cubs might therefore be willing to sign an extension at or below $63.75 million, with perhaps a little wiggle room on the upside. But would Bryant? He’s a pretty confident guy. Let’s say he believes in himself to the point that he thinks he’ll make $60 million in his arbitration years (maybe at $10, $14, $16, and $18 million annually), and $30 million in his first free agent year. Moreover, he thinks there’s only a 5 percent chance he fails to produce to that level. That puts his side of the equation at:

= $90 million * (1 – 0.05)

= $85.5 million

That means he’d be willing to sign an extension, today, worth $85.5 million or higher, again perhaps with a little wiggle room. Our equation, therefore, looks something like this:

$63.75 million ≠ $85.5 million

There’s a pretty big gap there, and that’s assuming my estimates are accurate. Bryant might be even more confident in his ability to perform and earn a big bonus, and the Cubs might be even more confident that their negotiators can keep Bryant’s arbitration salary down. The Cubs might have done some digging and found, for example, that third basemen as big as Bryant tend to break down pretty early, and so might increase their risk evaluation, thus driving their extension value down. And—back to Bryant—the $6.7 million signing bonus he signed back in June 2013 means he can afford to go year-to-year in salary, thus taking on more risk; he’s already made more money than most Americans ever will.

The combination we seem to have in Bryant—of a player who believes he can make a great deal of money, and who believes the chances he won’t are low—means that it was very unlikely that an extension would get done, because the value of an extension he would be willing to accept is so high. And then there’s another reason: Scott Boras. Boras, Bryant’s agent, has a history of following the money, and the money is in free agency. Since 2008—as far back as the MLBTradeRumors Extension Tracker goes—just three Boras clients have signed extensions for five years or more while having less than the six years of service time necessary for free agency, never mind being pre-arb. They are:

1) Elvis Andrus, TEX ($120 million, 8 years) – 4.000 years service

2) Jered Weaver, LAA ($85 million, 5 years) – 5.100 years service

3) Carlos Gonzalez, COL ($80 million, 7 years) – 2.059 years service

And that’s it. The Andrus deal already looks like an albatross for Texas. The Weaver deal has been pretty good, and the Gonzalez deal looks like a steal. But Weaver was 28 when he signed his extension, meaning he’s not really a comparator. And Gonzalez—the only Boras client, since 2001, to sign a pre-arb extension with his team—was in a totally different financial position than Bryant is now. He’d signed as an amateur free agent in 2002, receiving thereby a signing bonus much, much smaller than the one Bryant already has in hand, thereby driving up his intolerance for risk. In short, none of the three Boras extensions signed in the last seven years provides a particularly good model for a possible Bryant extension, and only one—signed by Gonzalez—was even signed in the pre-arb stage Bryant is currently in. That means that, unless Bryant is surprisingly ineffective or injured, this show is headed for free agency.

A certain group of fans, and columnists, love to suggest that the front office is being cheap by not signing Bryant to an extension this year. But the way extensions work—and the dollar amount the front office has already committed to Bryant in the form of a signing bonus—means that an extension was always a longshot. The kid is ready to bet on himself.

Thank you for reading

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faztradamus
4/21
Thought Longoria would have been an obvious comp.
rianwatt
4/23
Talent-wise, and in terms of his potential impact on his franchise, it's a nice comp. The positional similarity doesn't hurt. But Longoria got $3.7 mm less in signing bonus, came up in a different time for the game economically (it moves SO fast) and, perhaps most critically, is represented by Paul Cohen rather than Scott Boras.
jfranco77
4/21
So let's say the Cubs are willing to go $8, $11, $14, and $16 million, then 25, and call him up on Opening Day if he signs. That gets us to the $63.75 million you listed above.

But Bryant's alternative isn't really $10, $14, $16, and $18 and then $30. It's really 10 (super 2), 14/16/18 (3 regular arb years) and then 20 (extra year of team control). That's 78mil, discounted 5% for a number of 74.1.

Because the Cubs aren't calling him up to make him a free agent in year 7 if he doesn't sign.

74.1 is a lot closer than 85.5. Of course, the flip side of that is that the Cubs can't explicitly put delaying his call-up on the table.
rianwatt
4/23
That's a fair point. There's still a gap, though, and that assumes the Cubs would have been direct with Bryant in saying they would not call him up unless he signed an extension, which history suggests this front office would never do. It would cause way too much behind-the-scenes bad blood, and broken trust with players. Bryant could guess that the choice he's facing is the one you describe, but he wouldn't be sure.
AlexTheGreat
4/21
I wonder if Boras can offer his clients insurance against performance loss, in order to convince them against signing an extension to avoid risk.
rianwatt
4/23
No incentive to do so. He makes his money on the big FA contracts. Why lower the chances of those payouts and take on risk himself? The diversity of his client base already provides him a hedge against any individual player failing - why take on their risk?