Rich,

1. We don't want PAST WAR, but FUTURE WAR. That means regression, meaning a lower expected WAR in the future than what was observed in the past.

2. You must separate one year deals from multi-year deals.

We've done this analysis already for a few years now. You'll get somehting like 2.6 million future dollars for 1 future win for 1-yr deals, and 4.5MM future dollars for 1 future win for multi-year deals.

Great work as always Rich. On Holliday, I find it interesting that his contract reflects his value almost to a T, when comparing it to the league averages minus the RP's. For a contract that was widely panned last winter, it seems like in reality, it was really a very solid one. Fair to Holliday and to the Cards. My fear about it echos Tangotiger's comment about future WAR projections. Holliday will need to keep producing at a high level to justify the length of the contract. A 4 or 5 year deal would have made it easily to stomach.

Here's a thought for a future story: take the FA signings and their value in terms of $/WAR, and then rank the GM's. It would be interesting to see which GM's get the most value for their money.

Tango: The difference in our $/WAR has more to do with including or excluding relief pitchers than regression. By including relief pitchers, you artificially increase the average $/WAR for starting pitchers and position players. That was the point of my article.

Rich,
You always make me think and improve my baseball knowledge. This was great stuff but why is it that the relievers are so overvalued and overpaid especially when you subscribe to Bill James theory on relief pitching?

Rich, I think Tango's point still stands. Holliday was signed for his age 30-36 seasons.

No one can assume he's going to average the same WAR in those seasons as he did in his age 27-29 seasons.

You're crediting him with too much WAR over the life of the contract, which obviously will reduce the $/WAR.

Of course there's also the assumed inflation over the life of the contract. As Holliday's expected WAR declines each year, the market value of a win will also be assumed to be increasing.

A reliever's WAR (at least in the Fangraphs model) is dependent upon his LI, and several of the relievers in your chart moved from setup or shared closer roles to full closer roles (at least that was the plan, prior to injuries and poor performance and the like)--Gonzalez, Wagner, Saito, Dotel, and Soriano all moved to teams that intended to use them in higher leverage situations than did their previous team. Since leverage is largely influenced by usage, it follows that FA relievers would be paid according to their maximum WAR given the leverage bidding teams would plan to give them rather than according to the level their previous team chose.

Re relief pitchers, yes, I believe they are generally overpaid as a group. Based on the number of innings pitched, even when adjusted for leverage, it is hard to justify the salaries of most relievers. However, that was not the essence of my article. Instead, it is my contention that relievers, irrespective of their usage, are not paid on the same $/WAR scale as starting pitchers and position players. As a result, I believe it is a mistake to include their salaries and WAR in the aggregate mix when trying to place a value on free agents. Doing so serves to artificially increase the dollars per WAR for all free agents.

Players are paid for future performance, not past performance. If we put 2010 WAR values into the chart, we get the following numbers ('7-'09 values in parentheses):

Total WAR: 75 (104)
Non-pitcher WAR: 44 (60)
Starting pitcher WAR: 19 (34)
Relief pitcher WAR: 12 (11)

Total $$/WAR: $4.2M ($3.0M)
Non-pitcher $$/WAR: $3.4M
Starting pitcher $$/WAR: $5.5MM
Relief pitcher WAR: $5.1MM

I covered this for several years--in the THT Annual and on our site. I used Win Shares Above Bench *in that year* divided by dollars paid *in that year.* Anything else is a guesstimate. Took me 40-50 hours and some inside contacts to make sure I had the info correct.

Here are my figures for 2007:

http://www.hardballtimes.com/main/article/2007-net-win-shares-value/

Since it takes three win shares above bench to make one win above bench, teams paid $5.3 above the minimum salary per actual win delivered in 2007 from free agents.

Here is a post that shows that WSAB and salaries above minimum matched extremely well (see comments for exact info):

http://www.hardballtimes.com/main/blog_article/wins-and-salary/

Yes, there are difference between WAR and WSAB, but I don't believe they're significant enough to warrant a figure of half that $5.1 million.

I have felt that fangraphs' WAR is less effective in valuing relief pitchers. Leverage is given less emphasis than the Win Shares methodology (due to chaining). And FIP probably isn't the most accurate method of valuing relief pitcher performance. In any event, the results seem to indicate that teams place different values on leverage and perceptions of reliever performance than Fangraphs.

I think the economy had a negative impact on free agent salaries, beginning in the 2009 off-season and extending to last off-season. Players remained unsigned longer and many ended up signing for significantly less than expected. During the depth of the recession (prior to the 2009 season), many teams publicly stated that they were cutting their payrolls due to declining advertising.

Good work, Rich. Worth mentioning also is that WAR seems to be a more conservative estimate of marginal productivity than some alternatives, such as WARP; that'll inflate calculations about what the market is saying a win costs.

On Tango's point about contracts being forward-looking so we want future marginal product, that's true -- but it's not always true that regression to the mean implies lower forecast values. That will depend on recent observations (e.g., was last year's output a negative deviation from the mean, from which we might see a bounceback?), the age of the player, and the forecast horizon.

And noseeum's point should not be lost in the shuffle: long-deferred outlays (like Tulo's) could be reduced to present value in making these $/win calculations, and then combined with forecasts about output.

But your key finding -- that a team which assumes it ought to pay $4.5M per marginal win is likely to be disappointed in its return on investment -- seems eminently reasonable.

He's worth whatever he can get a GM to pay.