We have heard way too much about Josh Hamilton and hometown discounts since the Sports Illustrated article from a few weeks ago. However, conventional wisdom about hometown discounts is horribly wrong. (Sports media providing poor analysis, what a shock!) This post will clarify the issues, especially in regard to Hamilton.

Two misconceptions in particular run rampant: that we should take players at their word when make public declarations and that hometown discounts unequivocally make it more likely the player will sign with the team. Both of these ideas are wrong. We should not believe a word Hamilton (or his wife) said in the article. And if your sole goal is to see Hamilton in a Rangers uniform, then you might want to hope he will not give the Rangers a discount and that the Rangers know it.

Let’s start with the public declarations. The Hamiltons say that the Rangers will get no hometown discount. As expected, sports reporters treated his words as gospel; if the player says it is true, then it must be true! This is absolute nonsense. Anyone who has sat through a round of poker can see right through it. From a financial standpoint, Hamilton clearly benefits if the team offers him a contract without a hometown discount. Thus, if Hamilton would accept the largest hometown discount in the history of mankind (at the cost of his mysterious charitable plans), he has incentive to pretend like he would accept no hometown discount. There is simply no way to tell whether he is bluffing or not until he actually signs a contract.

The second misconception is that hometown discounts unequivocally make it more likely that the team will sign the player. In truth, reality is much more complicated than that. Hometown discounts can either help or hurt, depending on the nature of the discount.

I have a working paper and a video presentation that delve deeper into the issue, but an example is good enough to explain what’s going on. Suppose the Rangers value Hamilton worth $120 million but Hamilton is being offered (or will be offered) a $100 million contract from a rival. If no hometown discount exists, the Rangers should be able to sign the player without problem—a contract worth $101 million, for instance, leaves both the Rangers and Hamilton better off than if Hamilton signed with the rival.

Now suppose the Rangers only valued Hamilton worth $95 million. Without a hometown discount, the situation is hopeless; the most the Rangers would be willing to offer is $95 million, but the opposing contract is worth $5 million more. But if Hamilton is willing to offer the Rangers a $10 million discount, then they can reach an agreement. For example, the Rangers could offer a contract worth $93 million. The Rangers earn a profit of $2 million. Likewise, Hamilton prefers signing with the hometown team, since a $93 million contract with the Rangers is functionally worth $103 million after including the hometown benefit, which is more than the $100 million he would receive elsewhere.

This case reflects the traditional notion of the hometown discount—hometown teams can sign hometown players more easily, since the hometown player is willing to accept less money. However, this effect only holds up when the team actually knows how much of a hometown discount the player is willing to receive. This is a ridiculously strong assumption. How on earth do the Rangers know exactly how much Hamilton is willing to accept? They might have a ballpark idea (heh), but to know the exact amount would require actually being inside Hamilton’s head. Sorry, but that’s not happening.

Allowing for uncertainty makes the situation much harder to analyze, which takes up a bulk of the paper. But to summarize the results, if the outside contract offer is extremely competitive, the team gambles with its contract offer. Players willing to accept large hometown discounts accept, while the others accept the offer from the rival.

Why is this? Well, suppose the Rangers value Hamilton worth $100 million, and the outside offer is also worth $100 million. In addition, suppose the Rangers believe Hamilton is willing to offer somewhere between $0 and $10 million of a hometown discount, but it is not sure of the exact amount. The Rangers could match the $100 million offer and induce Hamilton to sign regardless of the true amount of his discount, but the Rangers make literally no profit on the contract; they value Hamilton worth $100 million, but pay him $100 million.

In contrast, the Rangers could offer $95 million to Hamilton. If Hamilton is willing to give a hometown discount of $5 million or more with 50% probability, then the Rangers profit by $5 million half of the time, for a net gain of $2.5 million. This is worth more than offering $100 million, yet it means that Hamilton signs with the rival half of the time!

On the other hand, when opposing offers are low, the Rangers have no reason to make this gamble. Suppose the outside offer is only worth $20 million but the Rangers still value Hamilton worth $100 million. At this point, matching the $20 million offer is optimal for the Rangers; their profit margin is $80 million, which is large enough to make the gamble not worth the risk.

So, in conclusion, the nature of the hometown discount determines whether the player is actually more likely to sign with the team. If everyone knows what is going on, then it can only help. But when the team is uncertain of the player’s hometown discount, things can go haywire, especially when the outside offers are competitive.

In relation to Hamilton, I think we all expect him to receive very competitive offers on the free agent market. So if you really want Hamilton to re-sign with the Rangers, you might actually prefer that he offer no discount at all.

Again, you can read the entire paper here. The paper is broader than the examples I gave here. I know that just making up numbers and showing what happens appears a little campy, but the paper actually shows that the conclusions I draw hold up in much more general conditions.

Lastly, you can watch a video on the paper down below. There is still a lot of math in it, but I work through most of it visually: