Behind the ScoreboardAugust 18, 2009
Strasburg, The Nats, and Game Theory
By Sky Andrecheck

Last night, the big news around the baseball world was the Nationals coming to an agreement with Stephen Strasburg, the most touted college pitcher in perhaps the history of the draft. For those still waking up, Strasburg signed a foul-year deal worth $15.1 million, making him the richest draftee ever, but falling far short of the $50 million figure agent Scott Boras tossed around at the time of the draft.

Last night's 11th hour dealings were an interesting study in game theory, with super-agent Scott Boras, matching wits with Nationals owner Ted Lerner, team president Stan Kasten, and GM Mike Rizzo. Oh yeah, and Stephen Strasburg himself also had a say in the process. The baseball world watched intently last night because while both parties had a lot to gain from making a deal, both had much more to lose by not signing. Strasburg had a powerful incentive to sign, because if he did not, he would have to sit a year, risking injury or regression, just to be back in the same situation a year later. The Nationals of course, had an incentive not to let a can't miss prospect that the franchise so desperately needs to slip through their fingertips.

In fact, both sides were likely miles apart on the value of the contract....but not in the way you might think. For the Nationals, the value of the wins Strasburg will produce may be $30-$40 million dollars, at least as valued by the WSJ and Biz of Baseball. If they pay more than that theoretical "break-even" dollar amount, that means they could get those wins more cheaply elsewhere. If they pay less, they'll be getting a bargain.

Strasburg also had a break-even point, except his was determined by the amount of money he could likely get the following year, if he decided to sit out the season. Of course this has to factor in any depreciation that might occur, due to injury and the decreased leverage he'll have the following year if he decides to sit. When factoring the uncertainty and the risk, plus the fact that the young man wants to play big league baseball, a guess for his break-even point would probably be somewhere around $11 million. Anything more than that would be gravy, while anything less and he would be hurting himself by signing rather than holding out and re-entering the draft next year.

Graphing the intersection of these two (admittedly hypothetical) value curves, we see that the both sides should have been willing to do a deal valued anywhere between $11-$35 million. While the lines intersect where each side gets an equal gain from the deal at about $23 million, any deal struck within that range should have be acceptable. So why did the negotiations come down to 11:59 last night? Well, each wanted to get the best deal of course. When the possible value acceptable deals ranges so widely, it's hard to come to an agreement - after all there is big difference between $11 million and $35 million, and while both sides would theoretically gain with a deal anywhere in that range, neither side wants to be seen as chumps.


Of course, using those break-even points, the final deal, at $15.1 million, was far more advantageous to the Nationals than Strasburg. Why? For one, I mentioned that the Nationals would be getting a bargain at anything less than a $35 million dollar deal. But, in the MLB draft, teams are accustomed to getting big bargains. That is why having high draft picks is a good thing - the draft is a place where you can sign valuable players for less than you could elsewhere. If teams paid market value according to their projected Wins Above Replacement, there would be no advantage to having high draft picks or even drafting many players at all.

Second, the deal does not occur in a vacuum. The Nationals are aware that their negotiations with Strasburg will affect how other players negotiate with them in the future. If the Nats broke down and gave Strasburg a $30 million deal, this might be worthwhile in the short-term, but they would also raise the expectations for every other high profile player they picked in the future (including a likely Bryce Harper selection next year, which will almost assuredly entail the same type of negotiations as this year's drama with Strasburg). When this is factored in, the true break-even point for the Nationals is lowered considerably.

Strasburg, on the other hand does not have this same kind of recurring scenario. At most, Strasburg will be back at the bargaining table with the Nats one or two more times, and those will be under completely different pretenses since he will by then be eligible for either arbitration or free agency. As a result, Strasburg's break-even point isn't changed much by the possibility of future deals (Boras, on the other hand does have an incentive to draw a hard-line and raise the break-even point since he will be back at the same bargaining table many times - however, as the player, Strasburg has the final say).

Third, the way the negotiations are structured gives the Nationals an advantage. With a firm deadline imposed by MLB, the parties must come to an agreement by a specific time. Since it is the team that offers the player the contract, and not the other way around, this gives teams the final leverage to push the value of the contract towards the player's break-even point. For instance, the team can tender a "final offer" to the player before the deadline and refuse to entertain other scenarios. With the clocking ticking and the offer on the table, it is Strasburg, not the Nationals, who must decide in the final moments whether or not the deal is satisfactory. And, if that deal is worth more than Strasburg's break-even point, he'll sign it. The Nationals, knowing this, can offer a deal worth slightly higher than his break-even point, and he should still sign.

Of course, if there is no deal on the table, and the team is still listening and cowing to Boras' demands at 11:55, the Nats lose a lot of their leverage. In fact, under the game-theory principle of eliminating options, it might have been a good idea for the Nats brass to take a mid-August jaunt to a remote, unreachable island in the Pacific, or an expedition to cellphone-towerless Antarctica. By giving Boras a contract, saying "take it or leave it, see you later" and truly being unreachable at the deadline, the Nationals would eliminate the possibility of extending a higher offer, thus putting the onus on Boras and Strasburg to accept the the Nats offer or go without.

As it turns out, the Nationals didn't have to go to the South Pole or the Moon to sign Strasburg to a very reasonable deal. Considering that virtually every scout projects him as a future #1 starter and someone who can immediately step into a major league rotation and produce, the Nationals came away with a bargain. If Strasburg's value was truly $35 million, the Nationals just saved $20 million over the price they would have had to pay for getting those wins elsewhere. Here in DC, having watched the Nationals bungle move after move, I was pleasantly surprised that Washington seemed to handle the negotiations very well, signing the new face of the franchise with 77 seconds to spare, and putting them in good position to sign Bryce Harper to a similar deal the following year.

Now that the anticipation of the deal is over, the anticipation of Strasburg's first major league start begins....


"it might have been a good idea for the Nats brass to take a mid-August jaunt to a remote, unreachable island in the Pacific, or an expedition to cellphone-towerless Antarctica. By giving Boras a contract, saying "take it or leave it, see you later" and truly being unreachable at the deadline, the Nationals would eliminate the possibility of extending a higher offer, thus putting the onus on Boras and Strasburg to accept the the Nats offer or go without."

I'm sure you're being a bit facetious here, but in that scenario I could see Strasburg walking away. One key element of negotiations like this is to maintain good relations so that both parties act in their economic interests instead of on emotions. If you piss off your potential future employee, he is much more likely to act contrary to his economic interest. If he sees the pain he can cause you, that may have more value than the money he can gain.

Play nice, and he'll look at the numbers. Play hardball, and he may walk to spite you.

You are right, Noseeum. The scenario you describe explains why theory and reality don't always agree.

To elaborate further, the Ultimatum Game, when carried out in practice, shows how people can act against economic interests out of spite....which indeed would be a major risk of using that strategy.

The above comment by noseeum succinctly points out the problems that arise when one actually tries to use game theory principals practically: reality often cannot be easily described using a payoff matrix. :-)

Congrats to both sides for getting a deal done. I think it is definitely a positive for Strasburg. As Rich would say, "the first $15 million is more important than the last $15 miliion." He is on his way to bigger and better things. Also great for the Nats, as they get a bonafide #1 starter guaranteed for the next few years. The only loser (or maybe a better phrase would be the least winner) is Boras, as he can't expect "Football Money" for his draft picks next year. HA! I don't know about everyone else, but Boras as the "loser" in this transaction doesn't really bother me that much...

Assuming Boras get 10% of the contract (I have no idea what his rate is, but let's assume), he's not exactly going to be hurting for change. I don't really think he's a "loser" in this scenario. He just won a little less than he wanted to.

Any "risk" on Strasburg's part is minimal. He is guaranteed $15.1 million minus Boras' fee no matter what happens. How many highly touted pitching prospects have been flops at the major league level?

Strasburg definitely projects as a top of the rotation starter, but a truckload of potential is less valuable than a pound of results. Here's hoping he succeeds in Washington.

Another factor may have contributed to the signing. In the current economic climate, who can say what will be offered in bonus money in the next few years?

Very interesting article, Sky.

Sounds like Strasburg got royally taken, in that he was forced to sign for half of what he is worth --- but then, as you point out, the owners set the rules, so why should the outcome be a surprise? In fact, I imagine that "Game Theory" would predict that Strasburg would settle for much less than he is worth.

Part of the point of the article is that Strasburg is going to settle for "less" than his potential worth now, for two big reasons:

1. He may never realize that potential, in which case the 'first $15 million' becomes the ONLY $15 million; thus making it more, not less, than he's worth.

2. He may realize that potential, in which case he is again likely to be paid more than he's worth, especially towards the end of his career.

In either case, he's got money in the bank now and the promise of more based on his production, which is an ideal result. At those future negotations he will have a body of Major League evidence to draw on to win a truly insane contract from somebody. That $15.1 million turns out to be a great investment for both player and team, and to bowdlerize the appropriate quote from A Beautiful Mind, "That way, everybody wins; that way, we all get paid."

Very nice article and analysis, BTW. I think the primary reason why the settlement seems to favor the Nats is that you generally have to pay a heavy discount to avoid risk (for certainty), which is what Strasburg did. That strategy is often proper because of the decreasing utility of money.

If I offer an average (not rich) person 10 million dollars or a 10% chance at 150 million (which is worth 15 mil) dollars, not only will they take the 10 mil for psychological reasons, but it is probably correct in a mathematical sense since the marginal dollars above and beyond the 10 mil has decreasing value. That is because you can do and buy just about everything you want within reason with 10 mil. In fact, many people with 150 mil only spend 10 mil or so and leave the rest to their heirs (which has value of course). The reason is that many people don't know what to do with all that money and/or don't really want or need it.

BTW, the fact that technically the team has to offer a contract to the player and vice versa I don't think gives the team any advantage in the negotiations. The player can just as well tell the team, "I'll take nothing less than 20 mil, take it or leave it." Either team is welcome to make any offer, turn down any offer, or refuse to listen to an offer.

Your suggestion that it might be a good strategy for a team to make a take it or leave it offer and then go hide until the deadline is also a little misguided. That is rarely an effective strategy in any negotiation (although it can be part of the negotiation toolbox) for obvious reasons (if that truly was not your final offer, you lose the chance to get the deal done if the other side will only settle for something greater OR if that truly was your final offer, you probably offered too much - and if you end up negotiating after offering a take it or leave it deal, you are left with no credibility).

Plus, the other side can do exactly the same thing. Strasburg can give the Nats a figure and then not entertain any other figs. He can even remain out of contact if he wants to as well. In fact, when someone does make me a take it or leave it offer, I often turn around and do the same thing to them. They say, I'll give you $1,000 take it or leave it," so I say, "That's nice, I'll take $1200 take or or leave it." And of course we settle at $1100!

Glad you enjoyed the article MGL - you make some good points, especially about the marginal value of money. From the aftermath, it sounds as if the Nats basically had a strategy of offering about $15 mil and letting Strasburg make the decision on whether to sign, even though Strasburg was probably worth much more than that to the team. It seems as though the strategy worked!