Diamond Dollars Reviewed

“I’d have to say for the money we had to work with and what we got, we’re probably doing as expected. I don’t think you’re going to win this division on $70 million. I don’t think you’re going to make the playoffs on $70 million.” – J.P. Ricciardi

To Ricciardi’s credit, he said this before Vince Gennaro wrote Diamond Dollars, the first comprehensive look into the economics of Major League Baseball. Otherwise, he would have known just how to build a winning team on a $70 million payroll from chapter eight, “A Strategic Approach to Assembling the Roster.”

In Diamond Dollars, Vince sets out to quantify the relationship between wins and revenues for every major league team, though much of the book is dedicated to discussing the implications of his results, rather than the statistical process itself. Using multiple regression analysis, Vince builds individual “win curves” for each team that show how much “baseline” revenue they stand to make (that is, money they will make no matter the team’s success) and how much additional marginal revenue (that is, revenue above that baseline) they will make at each level of wins.

Vince’s research into the relation between wins and revenues points to four factors that add to revenue: win dollars, postseason dollars, World Series dollars, and what he calls the “accretion” or “erosion” effect. According to Vince’s research, teams make money by winning in the regular season, which increases attendance; making it to the playoffs, which brings additional revenue streams; winning the World Series, which makes for huge additional future revenues; and finally, by winning or losing a lot for many consecutive years, which can move its revenue baseline up or down.

By quantifying the value of each those layers for every major league team, Vince can compute their win curves. What Vince finds is that, economically-speaking, replacement level for revenues is around 70 wins. That is, if a team wins 50 games or 70, it won’t have an impact on their revenue stream.

This potentially has important implications for baseball analysis, as replacement level is essentially an economic concept (it’s the value of a minimum-salaried player). Generally, replacement level has been assumed to be well below 70 wins, but if there is no difference between a team of .400 win percentage level players (that’s 65 over a full season), and .300 players (49 wins), why pay extra for the 65-win team? What this would mean is that we as analysts generally overvalue barely above-replacement level players, while undervaluing the true elite.

Vince spends a chapter explaining how the win curves work for individual teams—for example, he shows that the difference in revenue between winning 89 and 90 games is worth $4.3 million for the Yankees, but just $1.6 million for the Twins. If both teams are on the verge of making the playoffs, but need that final piece of the puzzle, who do you think is going to pay for it?

Vince then moves on to valuing individual players in a team context. He uses the Baseball Prospectus Wins Above Replacement (WARP) metric, which is an issue because WARP uses an extraordinarily low replacement level, which in turn results in overstated value estimates. Vince does acknowledge this issue, and he provides some alternative estimates using Win Shares Above Bench, but I was still not thrilled with his use of WARP.

Vince evaluates player value by asking how many wins his team would have had without him, and then looking at the difference in revenue that would have made. Vince actually used this method in a Hardball Times article last year. While this is the right idea, Vince makes two mistakes in his valuation:

While it may be true that the Yankees earned $33.7 million more with Derek Jeter (Jeter’s value according to Diamond Dollars) than they would have without him, that number would only have mattered if they were looking to sign him as a free agent. Once Jeter is on the Yankees, his value is equal to the proportion of wins above replacement he contributed to the team multiplied by the marginal revenue produced by the 2006 Yankees. Otherwise, if you were to add up the value of every Yankee player as determined by Vince, they would well exceed the marginal revenue they produced.

Vince’s marginal revenue curves are theoretical in nature. That is, a team gets credited with the revenue it would earn from making the playoffs multiplied by its probability of making of the playoffs, which in terms of measuring a player’s value in the future is fine. However, if we are looking at the past, and know whether or not the team made the playoffs, that’s all that matters. If it did, the team should be credited with the revenues that will bring; if it didn’t, it should not.

But Vince is not content with valuing players based just on his win curve analysis. He then attempts to account for marquee value, injury risks, and performance variation. While I applaud Vince for taking on these often-ignored issues, I am not sure he handles them correctly.

For example, Vince notes that marquee players like Roger Clemens are big fan draws. In 2004, the Astros drew 1,525 more fans when Clemens was on the mound than when he wasn’t. But how much of that was Clemens’ marquee value, and how much of that was the Astros’ higher probability of winning when he took the mound? After all, the key insight in Vince’s win curve system is that teams draw more fans when they win more games. In Clemens’ appearances in 2004, the Astros went 23-10, while without him on the mound, their record was just 69-60. Does the difference between a .697 and .535 winning percentage equal 1,525 fans? That seems pretty likely to me.

I also am not exactly sure how Vince came up with his formula for marquee value, which makes discussing its merits more difficult. But based on what Vince does say, it seems that a player’s marquee value is mostly a function of his team’s wins. I tend to agree with that idea—Derek Jeter would not be an American icon if the Yankees were winning 70 games a year—but if that’s the case, then why should we attribute marquee value to a player at all? Shouldn’t this already be accounted for in the win curve?

The marquee value question is one that perhaps could merit a whole book, and Vince just doesn’t have the space to address it properly. So while I am skeptical of his conclusions, I do appreciate that he brought up this very interesting question.

Vince then addresses the risk inherent in a player’s performance, and suggests that teams should pay less for riskier players. He draws an analogy to volatile stocks, but I’m not sure that works. Stock values are linear, while the value of a win, as Vince convincingly demonstrates is not. Here’s why that’s important.

Imagine an 85-win team. It can sign either Rich Harden or Tim Wakefield, both of whom around projected to be around two wins above replacement. If it signs Wakefield, it’s likely to win 87 games, but what good will that do? The team will probably miss the playoffs (unless it plays in the National League Central), and lose out on a huge playoff windfall. But if it signs Harden, it might win just 85 games, or it may win around 90. That shot at making the playoffs makes Harden significantly more valuable, not less!

As Vince points out so many times, baseball revenues are all about context. A 93-win team probably gains more from Wakefield than it does from Harden, but that 85-win team might not.

Diamond Dollars is at its best in chapter nine, where Vince discusses branding. His experience as a former Pepsi executive really shines through in this chapter, and while the whole book is, in my opinion, a must-read for team executives, the chapter on branding alone would make it worth the price.

The chapter also brings up an interesting question for me, which is whether or not Vince has correctly identified each team’s revenue baseline. Vince finds an “erosion” or “accretion” effect, showing that teams that win or lose perpetually will see their baseline revenue rise or fall, but I wonder if that effect is understated by a bias in the data. After all, you won’t see today’s Yankee juggernaut lose 90 games or more three years in a row, and unfortunately, you probably won’t see the Royals win 90-plus games three straight seasons either.

In that case, the erosion and accretion effects might not be great enough, which would add to the value of winning games.

A few assorted quibbles I had with the book:

- I remain unconvinced that 30 or less data points are enough to come up with a reasonable win curve for each team. The standard errors around the estimates must be huge. I do like that Vince shows the overall relationship between wins and revenue as well, but I would have preferred for him to start with the overall win curve and modify based on each team’s individual circumstances than to generate a win curve for each team separately.

- It’s not clear that Vince has adjusted for inflation; if not, his win curves are going to be understated, and the value of a marginal win less than it should be.

- Vince talks a little bit about the effect of a team’s valuation on the value of a marginal win, but not nearly enough. The fact is, baseball teams are a limited commodity, and a very prestigious one at that. People are willing to pay a lot of money for a successful baseball team, which greatly increases the value of a marginal win.

Diamond Dollars sets out with a very ambitious agenda, and it largely fulfills it. Vince demonstrates convincingly that we can identify the relationship between revenues and winning, that the relationship differs for each team, and that by identifying that relationship, we can understand how to better build a team on a budget.

The book raises as many questions as it answers, but I feel that’s a great thing, and perhaps the basis for some future books.

I highly recommend this book; any baseball fan or executive must have Diamond Dollars in their personal library if they wish to understand the way that baseball works today.

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