New Paper: The Hometown Discount Paradox

If you read the sports media much, you often hear about the concept of a “hometown discount”—when a player signs with his hometown team (or any team with a desirable location to the player) for less money than he could receive elsewhere. Unfortunately, misconceptions regarding the hometown discount run rampant. My latest working paper (more of a research note) dispels a couple of them.

First, we often hear players making public declarations that they will refuse to give a particular team a hometown discount. Sports reporters treat these 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, the player clearly benefits if the team offers him a contract without a hometown discount. Thus, even a player who would accept the largest hometown discount in the history of mankind has incentive to pretend like he would accept no hometown discount. There is simply no way to tell whether the player is bluffing or not.

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.

Although the paper delves much deeper into this issue (and includes a lot of easy to follow pictures!), I will present an example to explain what I mean. Suppose the hometown team values a player worth $120 million and the player is being offered a $100 million contract from a rival. If no hometown discount exists, the team should be able to sign the player without problem—a contract worth $101 million, for instance, leaves both the hometown team and the player better off than if the player signed with the rival.

Now suppose the team only valued the player worth $95 million. Without a hometown discount, the situation is hopeless; the most the team would be willing to offer is $95 million, but the opposing contract is worth $5 million more. But if the player is willing to offer the hometown team a $10 million discount, then they can reach an agreement. For example, the team could offer a contract worth $93 million. The team still profits for $2 million. Likewise, the player prefers signing with the hometown team, since a $93 million contract with them 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. The team should have a ballpark idea on how much of a discount the player should accept, but to know the exact amount would require actually being in the head of the player.

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 team values the player worth $100 million, and the outside offer is also worth $100 million. In addition, suppose the team believes the player is willing to offer somewhere between $0 and $10 million of a hometown discount, but is not sure of the exact amount. The team could match the $100 million offer and induce all of the players to sign, but the team makes literally no profit on the contract; it values the player worth $100 million, but pays $100 million to the player.

In contrast, the team could offer $95 million to the player. If exactly half of the players are willing to give a hometown discount of $5 million or more, then the team profits 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 the player signs with the rival half of the time!

On the other hand, when opposing offers are low, the team has no reason to make this gamble. Suppose the outside offer is only worth $20 million but the hometown team still values the player worth $100 million. At this point, matching the $20 million offer is optimal for the team; its 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.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s