The Fate of Alex Rodriguez

The Toronto Blue Jays should sign Alex Rodriguez.

That’s my conclusion after a quick and dirty analysis based on Nate Silver’s work on Marginal Revenue. The numbers below show that if Alex Rodriguez had been a Blue Jay in 2007, the team would have:
1) generated $24.9 million in marginal revenue by going from 83 to 91 wins;
2) avoided paying Troy Glaus $10.8 million.

In simple terms, that means the Jays could have paid Rodriguez $35.7 million, come out even financially, and potentially made the playoffs.

By the same logic, the Mariners and Tigers could have afforded a salary in the neighbourhood of $30 million.

Coincidentally, that's just what Scott Boras is thinking. Candidly talking about Rodriguez exercising his right to opt out of his New York contract, which would pay $81 to 91 million over the next three years, Boras calls Rodriguez an “I.P.N. player” – one who delivers iconic, performance and network value – who could play to age 45. There are mutterings of $300 million ten year contracts.

If Boras can demonstrate that Rodriguez would have been worth $35 million to the Blue Jays in 2007, then he's got a shot at convincing an owner to pony up for a record-breaking long-term deal.

The owner will have to account for a future decline in production which will mean Rodriguez generates less revenue for his team. But that should be partially offset by inflation which will increase team revenues, and it's really a separate topic.

Today, I want to explain how Rodriguez could be worth so much already.

THE BACKGROUND
In 2006, Silver asked and answered the question “Is Alex Rodriguez Overpaid?” in Baseball Between the Numbers.

To come up with his answer, he developed a "marginal value" for each added win – the amount of revenue a team would generate for each additional win it recorded.

The key to his analysis was that depending on a team's win total, the revenue it could earn from one extra win was different. Going from 89 to 90 wins -- a move that greatly increases the chances of a playoff berth -- was worth close to $4.5 million. But going from win #81 to #82 was worth only $1 million.

So to identify the teams where Rodriguez could generate the most revenue, we need to start by looking in the wins column to find the teams that could gain the most valuable wins from his presence.

To answer that question, I pulled together three pieces of information in a table below:

Which teams were close to the playoffs but missed or nearly missed?
Thirteen teams had between 76 and 89 wins this year, ranging from Oakland to Philadelphia and San Diego. While there are teams above this win level with uncertainty about their future third base production (such as Boston with Mike Lowell), they almost certainly have cheaper ways to maintain or increase their win level and so I excluded them.

What did their existing third basemen contribute in 2007?
The chart below shows the players used in 2007, and in the “Lost WARP” column the wins above replacement that the team would be forgoing if Rodriguez was to replace the incumbent.

This is a proxy for what their future third base production might be, and with a couple of exceptions (Philly, Dodgers) I considered only the everyday players.

As a proxy it’s imperfect. Thirty-five year old Chipper Jones stands little or no chance of playing for ten more years, so Atlanta might consider that its future WARP from the position is less than the 8.7 Jones put up this year. On the other end, Minnesota might believe that anyone will be better than Nick Punto, who was barely above replacement level while eating up 8.7% of the Twins’ plate appearances.

At least one other number warrants explanation. Ryan Braun’s WARP is much lower than his batting production because of his atrocious defence.

Finally, I did not consider what synergies might be created by shifting players to other positions. This is a real consideration, as witnessed by New York’s earlier decision to move Rodriguez to third and keep Jeter as shortstop.

What would Rodriguez add?
The answer used below is the same for all teams – 11.1 wins above replacement level (his WARP1 in 2007). The column “A-Wins” shows how many wins the team would have had in 2007 had Rodriguez been the everyday first baseman. Obviously this does not address the question of his projected future production. Unless Scott Boras has some voodoo spells, Rodriguez will not be generating 11.1 wins above replacement for the next ten years.

What marginal revenue would be created by this substitution?
Possibly the most interesting result, this is the sum of the marginal revenues created by the team’s actual 2007 wins and its “A-Wins.” It’s different for each team based on where the sit on the curve.

And the winner is: Los Angeles, which could have created $26 million in marginal revenue this year if it had substituted Rodriguez’s production for the tag-team of Betemit, Abreu and Laroche. At 91 wins, they’d have been playoff bound.

The Blue Jays and Twins are not far behind, with the potential for $24.9 and $24.6 million in marginal revenues. The values have a great deal to do with the low production the teams got at the position this year – Glaus underwhelmed with his 3.1 WARP, and Punto was near replacement level – and their near perfect position on the curve at 83 and 79 wins. Five other teams could generate more than $20 million in marginal revenue.

One of the big market contenders – the Mets – would be burning money by signing Rodriguez. It’s because they have Wright, obviously. If the Mets found a way to keep both hitters (replacing Delgado at first base), the numbers would be quite different.

Team	07 Wins	Current 3B	Lost WARP	A-Wins	Marg Rev
LA Dodgers	82	Bet+Abr+Lar	(2.1)	91	$26.0
Toronto	83	Glaus	(3.1)	91	$24.9
Minnesota	79	Punto	(0.3)	90	$24.6
Philadelphia	89	Dobbs+Helms	(1.3)	99	$23.7
Detroit	88	Inge	(3.8)	95	$23.4
San Diego	89	Kouzmanoff	(1.7)	98	$22.8
Seattle	88	Beltre	(4.7)	94	$21.7
Milwaukee	83	Braun	(4.4)	90	$20.7
Oakland	76	Chavez	(1.9)	85	$9.3
Chicago Cubs	85	Ramirez	(7.7)	88	$8.9
St Louis	78	Rolen	(3.9)	85	$7.9
NY Mets	88	Wright	(11.2)	88	$4.1
Atlanta	84	Jones	(8.7)	86	$4.1

Eliminating the Incumbent
There is one last step: to eliminate the salary of the player that Rodriguez would substitute for. In theory, the maximum amount it would make sense to pay Rodriguez would be the sum of the marginal revenue he creates and the salary the team no longer has to pay its incumbent third baseman.

The same caveats apply: the 2007 salaries are an imperfect proxy for future salaries, and now we’re also assuming that teams could find other homes for their incumbent third baseman.

Given those assumptions, in 2007 the Blue Jays could have paid more than $35 million to Rodriguez and come out ahead financially. It’s a staggering sum – more than $10 million above his current average annual contract value. And again, it’s driven by the underproduction from Troy Glaus, who was paid $10.8 million this year. But mediocre production from high priced veterans is hardly a unique phenomenon.

Glaus might serve as a reminder to all General Managers considering the A-Rod sweepstakes that past production may not mirror future returns. Being on the hook for a four-year contract is one matter, but buying into a ten-year deal at a record-setting price is taking an extraordinary risk that the performance five or ten years out will justify the dollars. Still, if there’s any client of Boras’ who can get that deal, it’s Rodriguez.

Team	Marg Rev	Incumbent's Salary	MRev+IncSal
Toronto	$24.9	$10.8	$35.7
Seattle	$21.7	$11.5	$33.2
Detroit	$23.4	$4.9	$28.3
LA Dodgers	$26.0	$1.1	$27.1
Philadelphia	$23.7	$2.9	$26.6
Minnesota	$24.6	$1.8	$26.4
San Diego	$22.8	$0.4	$23.2
Milwaukee	$20.7	$0.4	$21.1
St Louis	$7.9	$12.0	$19.9
Oakland	$9.3	$9.0	$18.3
Chicago Cubs	$8.9	$8.0	$16.9
Atlanta	$4.1	$11.0	$15.1
NY Mets	$4.1	$1.0	$5.1