A Matter of Scale
February 14, 2004
A look at the difference between RSAA and Win Shares, inspired by Rob Neyer’s latest column.
In a recent column comparing the careers of Dennis Eckersley and John Smoltz, Rob Neyer compared the Win Shares and Runs Scored Above Average (RSAA) of the two. Isolating their years as starters, Rob found that Smoltz had reached 181 Win Shares and 191 RSAA, while Eck’s numbers were 169 and 119.
In other words, Smoltz had about 60% more RSAA, but only 7% more Win Shares. As Rob said, “I’m not sure why Smoltz has a huge advantage in RSAA and a small one in Win Shares, but either way he comes out ahead…”
I was intrigued by the Win Share angle, and I quickly looked at a couple of the usual culprits, such as differences in their team’s “won/loss differentials” and the fact that Smoltz might be disadvantaged by having to bat. But those weren’t the issues at all.
The reason Smoltz has a huge advantage in RSAA is because it uses a different scale than Win Shares does. This is something Bill James discussed in the Win Shares chapter called “The Baseball Player as an Iceberg” and it’s an important thing to remember.
First, RSAA is a stat that has been popularized by Lee Sinins’ outstanding Sabermetric Encyclopedia. It’s a measure of how many runs a pitcher allowed above or below the league average, times the number of innings he pitched. Corrected for ballpark, of course. It is a very simple, efficient number to evaluate the impact of a pitcher.
Win Shares, on the other hand, is a comparison to a theoretical baseline of zero. We know that there is a pseudo-replacement level built into Win Shares, but it is much lower than average. And this makes it a very different animal.
Consider the iceberg, floating on the water. Most of that iceberg actually lies below the water, but we tend to judge icebergs by what we see. So one iceberg may look much bigger than another to us, let’s say twice as big. But when you add back in all the ice beneath the water, we might find that it is actually only 20% bigger. Or something like that.
RSAA is equivalent to the ice above the waterline. Win Shares are the entire iceberg. And that’s it for that analogy. The main point is that you can’t compare the two, because they use completely different scales.
The good news is that we have a way to put the stats on an equivalent scale. Based on the Win Shares baseline, we know that starting pitchers in 2003 averaged 0.057 Win Shares per innings pitched. So I multiplied Eckersley’s and Smoltz’s innings pitched as starters by 0.057 to establish an average Win Shares baseline.
Next, I subtracted their average Win Shares baseline from their total Win Shares and came up with Win Shares Above Average for each pitcher. And that made all the difference.
Smoltz reached 44 Win Shares Above Average in his starting career, and Eckersley reached 27. In other words, Smoltz achieved about 60% more WSAA than Eckersley—same percentage difference he achieved in RSAA.
You can rest assured that Win Shares is consistent with RSAA and most other pitching stats you’re liable to run into. Just be sure that you use the right scale.
I also thought you might be interested in a graph of Smoltz’s and Eckersley’s Win Shares Above Average by year.
Eckersley had the better start, but Smoltz caught up in his later years. The interesting thing is that the total difference between these two guys came in their tenth years, when Smoltz had his best year as a starter, and Eck had his worst.
Coda: Here’s one more graph, per the request of David Burden. It’s kind of confusing, but it shows that Eck and Smoltz compare very well at this stage of their careers, and that the next three years will be critical for Smoltz to keep up the pace.
Care to extend that graph through the end of Eck’s career, so that we might see what Smoltz has to achieve goign forward?
Also, if it’s not hard with your graphing software, it’d be nice to see the running total as a superimposed line graph.
In any case, thanks for the analysis - I was a little surprised Rob brushed over that point so quickly. Turns out it was pretty striaghtforward.
One begins to wonder - should WS really be the stat promoted, or WSAA? (Or perhaps one of the two after making all the adjustments experimented with this winter.) In fact, you’re getting far enough away from the base WS that you just might have the right to name a new stat.
Cheers!
Posted by .(JavaScript must be enabled to view this email address) on 02/15 at 01:55 PM
Hi David. I wondered if you were still coming around.
I actually do think that WSAR should be promoted ahead of WS. In fact, I think James would agree. Even if we did nothing with WS except that, it would be a big improvement. Pete and I are planning on posting both next year.
I’ll work on the graph. Thanks for the suggestion.
Posted by
studes on 02/15 at 02:36 PM
Thanks in advance. I’ve been around, but I didn’t have much to add on the Fielding vs. Pitching discussions. In the defenseive realm, I think our ability to analyze statistics has gotten ahead of our ability to measure and track the stats themselves. We almost need data for every batted ball on where each player positioned himself, what the pitch was, and where it was hit. I think some folks are keeping tabs on that last fact - where the ball was hit - in order to calculate range factors, but the picture still seems incomplete.
That said, I think your analysis of the question showed that a fielder’s contributions aren’t ever going to have the same impact as his bat; it mainly seems we need this sort of information to tease out the pitcher’s ability from the competance of the fielders behind him. (Although I’m still amazed how many WS Neifi ends up with.)
Do you have a spreadsheet available that has both the salary info and WS inputs? (Presumably a left-over from the Money For Nothing series). I’m curious how many WS I could put together from seven free agents if I just ignored defensive ability. Picture this: Jeter at short, A-Rod at third, and Bonds at second. Sure, the defense would suck, but would it matter?
Posted by .(JavaScript must be enabled to view this email address) on 02/15 at 03:11 PM
Here’s the graph, computed on Win Shares Above Replacement instead of Average. Better way to go.
Now that we’re getting our arms around the replacement level of Win Shares, I’ve been meaning to get back to the economics. I’ll try and put a spreadsheet together and send it to you. Shouldn’t be too much work.
Posted by
studes on 02/15 at 03:34 PM
(Working on the team of fielding butchers)
It looks like, from the second graph, Smoltz would need four more seasons like his last to claim himself as Eck’s equal, in terms of WSAR at least. That’s be quite an accomplishment.
Posted by .(JavaScript must be enabled to view this email address) on 02/15 at 03:35 PM
Here are the top free agents from this winter, in terms of Hitting Win Shares fom last year, with their fielding WS in parenthesis. I’m only counting guys that switched teams, so that we can assume there were no home-town discounts . . . although a guy like Sheffield obviously had a preference for New York.
Gary Sheffield, 31.55 (2.95 OF)
Javy Lopez, 24.38 (5.35 C)
Ivan Rodriguez, 19.21 (4.24 C)
Miguel Tejada, 18.45 (6.89 SS)
Rafael Palmeiro, 18.34 (0.86 1B)
Carl Everett, 18.10 (2.68 OF)
Jose Guillen, 18.05 (1.72 OF)
Reggie Sanders, 15.28 (2.31 OF)
Signing these eight guys would cost you around (13 + 7.5 + 10 + 12 + 4 + 3.75 + 3 + 3) $53.25M in 2004; I’ll ignore future dollars here, just as I’ve ignored the fact that a lot of high WS guys have been acquired via trade rather than free agency this winter. (Thanks to Dugout Dollars for those figures.) Fill out the 25 man roster with stiffs at $300k, and you’ve got a payroll of a bit under $60M.
To maximize that lot of guys, we’ll leave Lopez, Tejada, Palmeiro, Sheffield, Everett, and Sanders at their positions, and let I-Rod and Jose Guillen butcher it up at 3rd and 2nd. Giving them 0 fielding win shares, we’ve accumulated 184.4 WS, or about 61 wins. Not much of a team, but if they were willing to spend even another ten million on pitchers, they’d probably get respectable in a hurry.
The more interesting point here is that, unless we’re willing to pony up negative win shares for fielding, you’d be a *lot* better off paying $12M to hire Palmeiro, Sanders, and Guillen, and letting one of them butcher SS, than to hire Tejada at all. Assuming also that last year’s WS has any bearing on the future.
If someone’s feeling ambitious, perhaps you could put together an all-free agent team, maximizing WSAR against some aribtrary budget. I’m kind of doubting Tejada would be on the list.
Posted by .(JavaScript must be enabled to view this email address) on 02/15 at 04:01 PM
One thing at which you might want to look is the quality of defense behind each pitcher. That could well explain the difference in measures.
Posted by .(JavaScript must be enabled to view this email address) on 02/16 at 01:32 PM
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