Sabernomics: Werth Deal is Aggressive, But Reasonable

That’s my own attempt to plot wins vs. revenue for 2005-2009. I pro-rated the total revenue for each season to equal 2007 total revenue.

Notice that the linear model looks pretty good, if you ignore 5 points above the $300M line. Those are all Yankees. In order to put them near the best-fit line, you need the third-degree polynomial. Changing the whole model because of an outlier like the Yankees? Yeesh.

A related point is that JC’s model assumes every team rides the same revenue curve. I think he did some studies that backed up this assumption, but I’m hard pressed to believe it, especially over a short time period. If the Yankees won 70 games, would their revenue drop to $150M? Doubt it. If the Pirates won 100 games, would their revenue jump to $250M? Doubt it.

Anyway, what I think is going on is that teams more or less spend in order to maximize their revenue on their own curve. Teams like the Yankees and Red Sox have a steeper curve, so they spend more in order to make more. Teams like the Pirates don’t see nearly as much as a return getting to 95 wins, so it’s not worth spending the money to get there. Over the 2005 through 2009 time period, each team generally won about the same number of games. The Yankees were 90+, the Pirates were 75-. Applying a best-fit curve to the whole shebang is misleading. I don’t know the technical term for this, but the points are bunched by team, not all spread out over the whole graph.

Here’s a mockup of that phenomenon:

Each color represents a different team. The lines are an example of a different revenue curve for each team. Teams would slide along their own line as they won and lost more games. But in order to connect all the point, you need the exponential curve.

The downside of JC’s cubic regression equation is that it’s much too flat in the 60-80 win range and too steep above that point.

I took the 2004 Marcels from Jeff Sackman’s site and compared them to the 2010 performances for the top 100 projected hitters by FG wOBA. 68 of those players were 32 or younger in 2004.

Weighting by 2010 plate appearances, Marcel projected a 2004 wOBA of .382, while they actually posted a .350 wOBA. That’s about 15 runs of lost production per 600 PAs. It’s all “aging” or decreases in talent caused by injuries over that time span.

However, playing time dropped dramatically. 30 of the players were no longer active in 2010, and ten more had fewer than 300 PAs. Marcel projected 503 PAs per player in 2004, while there were only 257 per player in 2010 — half as many.

If you only look at players who played in 2010, they were projected for 533 PAs in 2004, but had 460 in 2010.

Using a crude RAR/VORP model (wOBA – .310) * PA / 1.15, these 32 and younger players were projected for an average of 30 RAR in 2004, but posted an average of 9 RAR in 2010. Removing the players out of the league in 2010, RAR per player drops from 33 expected in 2004 to 16 in 2010.

One last one. I removed anyone who was projected for less than 450 PAs in 2004. 52 of them. Only 32, or about 60% were even in the league in 2010. On average, RAR dropped from 34 to 10, or to only 30% of the initial level. And even if you could guarantee the player would be around in 2010, RAR dropped over 50% of the initial level, from 36 to 16 RAR.

1. If you were Batman, my sometimes hyperbolic statements would be the criminals cowering in the darkness.

2. I’ll admit that this doesn’t “upset the balance” if you admit that Carl Crawford’s potential deal is drastically inflated because of it. And as Royals fans, that should really piss us off (not that we had a shot at him anyway).

Unless I’m misreading Justin, the final point seems slightly contradictory: “It doesn’t matter if they eventually get what they paid for (unless you’re a Nats fan), the problem is that they paid more than the market was willing to currently bear, and in so doing have somewhat upset the balance of the entire Winter Meetings and every contract after this. It may eventually look like a fair deal, but it’s a bad contract now.”

Actually, it DOES matter that they eventually get what they paid for. You could argue that the Nationals have mistaken priorities, but you can’t say that this is a bad deal if they accurately projected Werth’s value over the next seven years and paid him a salary commensurate to that value.