FanPost

Purchasing WAR in Bulk

In my post on Matt Holliday, some of you balked at the notion that it was wise to invest a large percentage of our payroll in a single offensive player. This led me to a question for which I did not have the answer: are Wins Above Replacement (WAR) more or less expensive if bought in a single player or via multiple players on the free agent market?

Obviously, the most advantageous way to purchase WAR is to obtain it below cost. That is the rationale behind high-risk, high-reward signings such as that of Rich Harden or potentially Erik Bedard. But that is also the rationale behind having a core of young, cost-controlled players - while they are earning the minimum or in their arbitration years, their salary is not tied to their production and should be far less than their value. Therefore, if a team has a lot of young players, they are already generating a lot of surplus value, and that team can afford to pay market cost for production at the remaining positions.

But how to do this most efficiently? Instinctively, many people feel that you should diversify your investments, thus spreading out your risk. Common sense also tells us that since there are more good players than there are great players, the great players should cost a premium and therefore provide less production per dollar spent.

What I decided to do was to look at the Wins Above Replacement of players who had reached free agency and were therefore being paid a market price for their services, and to calculate how much they were being paid for each win over replacement. I then divided the players into two categories, those who generated a WAR above 4.5 in the 2009 season, and those who generated a WAR between 2 and 4.4. This is not truly statistically rigorous, but I felt it was a quick way to get an answer to my question.

Fewer than 30 offensive players had a WAR above 4.5 in 2009, and few of those have reached the end of their arbitration years. The players who have are Derek Jeter, Carl Crawford, Miguel Cabrera, Derrek Lee, Mark Teixeira, Ichiro, and J.D. Drew. The numbers are WAR, 2009 salary, and salary/WAR.

Jeter - 7.4 $21.6 $2.92

Crawford - 5.5 $8.3 $1.51

Cabrera - 5.4 $14.4 $2.67

Lee - 5.3 $13.3 $2.51

Teixeira - 5.1 $20.6 $4.04

Ichiro - 5.1 $18.0 $3.53

Drew - 4.7 $14.0 $2.98

Average salary per WAR: $2.88 million

The sample of players who have reached the end of their arb years and earned 2 to 4.4 WAR is obviously larger. Let's take a look: Mike Cameron, Raul Ibanez, Casey Blake, Michael Young, Torii Hunter, Scott Rolen, Todd Helton, Juan Rivera, Brian Roberts, Lance Berkman, Placido Polanco, Johnny Damon, Orlando Hudson, Russell Branyan, Chipper Jones, Paul Konerko, Brandon Inge, AJ Pierzynski, Bobby Abreu, and Carlos Lee.

Cameron - 4.3 $10.0 $2.33

Ibanez - 4.2 $7.2 $1.71

Blake - 4.2 $5.0 $1.19

Young - 3.9 $13.1 $3.36

Hunter - 3.8 $18.0 $4.74

Rolen - 3.8 $11.6 $3.05

Helton - 3.6 $16.6 $4.61

Rivera - 3.4 $3.3 $0.97

Roberts - 3.4 $8.0 $2.35

Berkman - 3.1 $14.5 $4.68

Polanco - 3.1 $4.6 $1.48

Damon - 3.0 $13.0 $4.33

Hudson - 2.9 $3.4 $1.17

Branyan - 2.8 $1.4 $0.50

Jones - 2.8 $10.0 $3.57

Konerko - 2.6 $12.0 $4.61

Inge - 2.5 $6.3 $2.52

Pierzynski - 2.5 $6.4 $2.52

Abreu - 2.5 $5.0 $2.0

Lee - 2.5 $19.0 $7.6

Average cost per WAR: $2.96 million

(Note: I excluded Alex Rodriguez, who posted a WAR of 4.4 in an injury shortened season. To put him in skewed the results in my opinion, particularly as if he had played a full season he would have had above 4.5 WAR)

Rather than we might suspect, the production of free agent hitters who produce more than 4.5 WAR is slightly less expensive than the production of free agents who produce 2.5 WAR or more. This is obviously a very small sample of only one season. But in the free agent market, the elite players seem to come at a slight discount relative to their expected production. My hypothesis is that this will generally be true.

But what really stands out is how few players there are in both categories. Batters who are past their arbitration years who produce 2.5 WAR or more are few and far between; there are fewer than there are major league teams. The group grows even smaller if we eliminate players like Jeter, Ichiro, Helton, Roberts, and Berkman who have only played for the team that originally brought them to the majors, and smaller still if we eliminate players like Cabrera who were traded but signed an extension with their new club. In short, few players worth 2,5 Wins Above Replacement will ever be available on the free agent market, and hardly any worth more than 4.5.

We can also see that it costs between $2.5 and $3 million per Win above Replacement for players worth 2.5 or more WAR, which means that paying more than $2.5 million per WAR for a player worth less than 2.5 WAR is a mistake; you will get more value out of a more expensive option.

The Orioles are operating with the philosophy of growing the arms and buying the bats. What this data from last season seems to show is that buying the bats is harder than it sounds; there aren't enough bats worth buying out there. It also seems to show that paying one player for many wins above replacement is more cost effective than paying many players for fewer wins above replacement.

Finally, I'll point out free agent Matt Holliday's WAR in his most recent four seasons, his only full seasons in the major leagues: 4.4, 8.0, 6.3, 5.7. Holliday appears to be one of these rare specimens, a 4.5+ WAR player who is available as a free agent. This category of player provides an equal if not greater value per dollar as the equivalent performance of multiple other free agents. So long as you believe that Holliday is likely to remain a 4.5+ WAR player if healthy for the duration of his contract, signing him is a singular opportunity which rarely presents itself. Buying the bats is harder than it sounds.

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