April 21, 2010 at 8:00 am by Capitol Avenue Club under Atlanta Braves
On February 8, 2010, I wrote the following:
So, keeping [Jason Heyward] down for two weeks nets the Braves $4 million in surplus value, and keeping him down for six more weeks nets them an additional $6.2 million.
It seems completely obvious to me that keeping him down for two weeks is the correct financial decision. The probability of Heyward being even a +1 win player in a two week span is so minuscule I don’t think you even blink about keeping him in the minors for two weeks. After all, over two weeks a player gets ~50 PA’s.
It’s been two weeks. If the Braves had promoted Jason Heyward two days ago, rather than on April 5, 2010, they would control him through 2016, rather than 2015 as they currently do.
So, now that we’ve played the games, let’s take a look and see if it was actually worth it.
Normally when I calculate win values, I use linear weights (or the rate-stat version, weighted on base average) as my offensive metric. However, when we’re talking about actual outcomes, you want to use something that models reality a bit better. The first place everyone jumps is WPA. The problem with WPA is it’s highly influenced by the leverage of a situation–how important the situations were. Jason Heyward had nothing to do with how important the situations he was in were, and it’s inappropriate to give him credit him for this. Tom Tango writes about WPA:
This is like you cash in your chips, and you end up being given 10x more than you deserve because there’s a new employee dishing out the change. Sure, you get to keep the money. But, you didn’t earn it. The only thing you deserve is your money, irrespective of things outside your control, but within the context in which you earned it.
With this in mind, Tango created WPA/LI, which removes the leverage aspect of WPA–changing WPA from strictly a story telling statistic to something closely resembling a win value metric. WPA/LI is what we want to use when we’re looking at just how valuable Heyward’s bat has been for the first twelve games.
The other challenge of calculating Heyward’s win value involves replacement level. Simply calculating his wins above theoretical replacement level doesn’t cut it. We need to know what the actual replacement level was, what would’ve actually happened had he been in AAA for the first 12 games.
In order to do this, we assume the playing time matrix would have included only Nate McLouth, Melky Cabrera, and Matt Diaz in Jason Heyward’s absence. Furthermore, we assume they would’ve performed the exact same over Heyward’s PA’s as they did over their own PA’s. Assuming this isn’t exactly correct, but I’m not about to get into any regression equations for a 12-game sample.
For fielding, I used Dewan’s +/-.
So, what we want to do is calculate the total wins above replacement of the outfield (as a whole) thus far, then calculate what it would’ve been had Jason Heyward been in AAA and the other three outfielders played every day. Subtract the latter from the former, and we’ve got Heyward’s win value. We use the same model as always to calculate the win values: Offense + Defense + Replacement + Positional Adjustment = WAR.
Here’s what the outfield has actually done:
In distributing Jason Heyward’s 52 PA’s, I gave 22 to Matt Diaz (bringing his total xPA to 50), 8 to Melky Cabrera (bringing his total xPA to 58), and 22 to Nate McLouth (bringing his total xPA to 58). In distributing Jason Heyward’s 109 defensive innings, I gave 64 to Matt Diaz (total xInn: 109), 11 to Melky Cabrera (total xInn: 109), and 22 to Nate McLouth (total xInn: 110). Then, I calculate their total xWPA/LI based on xPA and their total xDRS (defensive runs saved, based on Dewan’s +/-) based on xInn, plug the parameters into our model (Offense + Defense + Replacement + Positional Adjustment = WAR), and voila, we have our answer.
Here’s what the outfield would be expected to do without Jason Heyward:
So, the outfield has produced 0.65 wins above replacement, and without Heyward we’d expect them to produce -0.48 wins above replacement. In essence, Jason Heyward’s presence on the roster for 12 games net the Braves 1.13 wins. I was tempted to multiply this by the marginal value of a win and compare it to the surplus value lost and be done with the exercise, but this would’ve been a mistake for two reasons. Reason number one involves the Braves’ position on the win curve (right at the playoff bubble region), making marginal wins more valuable. Reason number two? The 1.13 wins aren’t marginal wins, they’re net wins. Let me explain.
When I originally calculated the surplus value of the three contract scenarios in February, I gave Jason Heyward credit for 0.2 wins over the season’s first twelve games. We’ve got to subtract the 0.2 wins we assumed Heyward would provide from the 1.13 wins he actually provided–0.93 wins. Simple enough.
Teams paid ~4 million per win on the free agent market this past off season. However, like I said, the Braves’ position on the win curve makes the marginal wins more valuable, they’re worth about $4.5 million to the Braves. 0.93 marginal wins times $4.5 million per marginal wins = $4.18 million. Since the Braves only lost $4 million in surplus value off of Heyward’s contract by calling him up 12 games early, they come out ever so slightly ahead in this game.
On the other hand, Jason Heyward made significant impact in multiple close games, and you could argue Heyward has been even more valuable than 0.93 wins. You’re sort of getting into WPA versus WPA/LI at that point, but some valid arguments could be made.
Like any results based analysis, just because it worked out doesn’t mean it was a good decision. My findings don’t vindicate the front office, only show that it has worked out. Bad decisions (like perhaps this one, I don’t know) work out all the time, and they’re still bad decisions.
This says much more about just how good Jason Heyward has been than it does about the front office. By the way, Jason Heyward is currently 1st in WPA and 7th in WPA/LI. The scary part? This doesn’t even include last night’s game.