Shaping the Harper Negotiations

There is a solution concept in game theory known as the Shapely Value. A few years ago I explored this as a way of determining which positions might be worth the most valuable, but the calculations for what I was trying to do were intractable.

Shapely values look at the players or items in a game, and the value they give to the game dependent on the order they are added. There is an example at the link above of a game in which there are three gloves, one left and two right. The game has a value of one when opposite gloves have been picked, zero otherwise. The left handed glove twice as valuable as the right-handed gloves, as it completes the set twice as often.

In terms of assembling a 25-man roster, I saw it as the first 17 players added had no value (measured in WAR), as it strikes me that 18 players is the minimum needed to field a team that could play every day. That 18 would require a certain set of players exist to fill in the various roles (skilled infielders, relief pitchers, etc.). That set may not be filled in until the 25th player.

In addition, I set an upper limit the value a team would get when adding a player. If the team was already at 50 WAR, an value after that would count as zero for the player. At 50 WAR, the team is going to make the playoffs, so anything after that adds nothing to the chance of the team getting to vie for the championship.

To sum up the rules:

• The first 17 players get zero value.
• The first player after the 17th player who completes the 18 man minimum requirements gets all the value up to that point.
• If players only get credit for WAR that brings the total to 50 or less. So if a team has 48 WAR, and a three-WAR player is added next, that player gets credit for two WAR.

In the case of Harper (or any big money free-agent), they are the last man in. The rest of the roster tends to be set, so they would get credit for whatever WAR they are bringing to the table. There are reports that the only two teams remaining in negotiation with Harper are the Phillies and the Nationals (although you should be skeptical of that claim). What does adding Harper last to those two teams do?

This Google Sheet shows the 2019 projected WAR for the top 24 players on currently on the Phillies and the Nationals. Adding Harper to the Phillies brings their to projected WAR total to 36.1. Adding him to the Nationals bring their projected WAR total to 50.1

Those two numbers are the problem. A total of 36.1 WAR would put the Phillies around 85 wins. That’s the place where a little good luck leads you back to the playoffs, but a little bad luck puts you under .500. The Nationals are at 45 WAR without Harper, more than good enough to make the playoffs. My Shapley rules would not allow 0.1 of Harper’s projected WAR, making him less valuable to Washington. So the Phillies need to decided if they want to pay for a player who doesn’t put them over the top, and hope they develop more talent. The Nationals need to decide if he’s worth the money to create an even better super team.

If I ran the Nationals, I’d offer Harper $50 million for one year, saying, “Let’s try one more time to win a World Series for the town.” Harper would still be a young free agent a year later, and a great year would raise his value. For the Phillies, I would go three years, $145 million with mutual options, so that if the team doesn’t develop, Harper’s contract won’t drag on a future rebuild.

The right place for Harper would be on a good, young team where a four to five WAR player would push them over the edge. Looking at total team projected WAR, it looks to me like the Twins, Rays, and Athletics would be perfect fits. Unfortunately, none of those teams tend to spend big money on free agents. The Rays are especially intriguing, since I suspect Harper’s power would work especially well in that park. It would certainly up the Rays attendance. Maybe it’s time for one of these teams to open up the purse strings and go for it.

from baseballmusings.com http://bit.ly/2U527mz