If that's one of my worst mistakes -- to sign somebody who has 20 home runs and 97 RBIs -- I'll take it.

-Royals' General Manager Dayton Moore, on Jose Guillen's 2008 performance.

Everyone knows that RBI are, if not worthless, way down the list of ways to judge a players offensive performance, right? There's tons of stuff written on it, but here is a really good, non-technical piece written by America's Greatest Living Sportswriter, Joe Posnanski.

Nonetheless, it is hard not to be impressed by RBI numbers, to see a player as an "RBI man" who produces runs. To get that man runs across the plate, he has to have some skills, right? Sure, he's getting more opportunities because he's in the middle of the order, but a truly terrible hitter wouldn't have driven in all those runs, right? Let's take a look-see.

In Baseball Prospectus' Baseball Between the Numbers, Jonah Keri takes an illuminating angle on this issue. He takes all the individual 100 RBI seasons since 1972 (I'm not sure why -- perhaps the introduction of the designated hitter rule?) and divides the RBI by the player's VORP (BP's Value Over Replacement Player stat) for that season. The higher a number of RBI/VORP a player has, the more overrated his value is by his RBI. The results are predictable -- famous "clutch hitter" Joe Carter having the highest number of most overrated 100 RBI seasons since 1972. It's a good piece and approach to the "RBI issue."

However, there are significant problems with VORP, both in its approach to positional adjustments and its incorrect weighting of walks, home runs, and doubles. Keri's approach is straightforward and illuminating, but can be improved by using a better measure of offensive value.

What would that measure be? Readers of this space arely likely anticipating wOBA as my answer, while while it's on the right track, we're looking for a counting stat -- runs created above some baseline. Fortuneatley, just like there's a relationship between batting average and total hits using at-bats, there's a relationship between wOBA and runs created above average (wOBA is basically  linear weights expressed as a rate stat). At FanGraphs, they call this "wRAA, here," I call it BRAA since I'm not sure if my results are exactly the same, and I use different park adjustments. The "1.15" is there because it is what forces wOBA onto an OBP scale, and to convert to runs above average, that needes to be undone (the custom lineare weights script used here and at FanGraphs uses a customized "wOBAScale" for each season).

Thanks to previous work by Tom Tango, Colin Wyers, and terpsfans' park factors , I was able to calculate BRAA for all seasons back to 1955 (Thanks, guys!).

To get my lists of "most overrated" and "most underrated" seasons by RBI, I simply followed Keri's lead and divided the players RBI by his BRAA (Keri used VORP, of course). The more RBI per BRAA a player has, the more his RBI overstate his offensive contribution. This is a "junk stat," of course, but while there might be more  sophisticated ways of doing it, I like it for its straightforward simplicity. The problem, of course, is that many players on the list are below average, which means I'll end up with a negative number for some bad players with lots of RBIs -- we want a positive number for them. So I had to add something proportionally do each player so that they would all end up "positive." I could have picked any number to add, but I decided instead to go with pseudo-"replacement level" (pseudo because there are no replacement level hitters or fielders, only replacement level players) by adding in 22.5 runs for every 700 PAs each player had that season. This also parallels Keri's piece, which works not from average, but from replacement level (defined differently, of course, and with positional adjustments with which I disagree). Still, there was one particularly "great" season that came up negative -- Keri ran into this problem with RBI/VORP as well, so I adopted his solution -- to simply add 10 to the number I got. So, the final version of the junk stat is RBI/(BRAA+(PA*(22.5/700))+10) = RBI per BRAR (Batting Runs Above "Replacement").

Here are the results. There are separate sheets for the Most Overrated RBI Guys 1973-, Most Underrated, and 2008's 90+ RBI Guys sorted by Overrated to Underrated. The columns are mostly obvious: wOBA is each players' unadjusted wOBA for that season using the custom weights, BRAA is his park-adjusted linear weights runs created above what a league-average hitter would have created in the same number of plate apperaances, and RBIperBRAR is RBIs per BRAA scaled as discussed in the previous paragraph. Again, the higher the RBIperBRAR number is, the more a players RBI numbers (generally) overstate his offensive ability.

There is much to "admire" here, particularly some wonderful performances from the Most Overrated list. Let's extract a few for discussion:

The first few are simply the "top"seasons, then I picked some that looked interesting. Starting at the bottom: I probably don't hate Paul O'Neill enough to be a real non-Yankees fan, but man, do he and Tino's ever illustrate  how much batting order effects RBI numbers: both were clearly below average, but O'Neill hit right behind Derek Jeter (.416 OBP in 2000) and Martinez behind Bernie Williams (.391 OBP).

I included Sammy Sosa on this chart not because I want to pick on him or anything, but I just found it interesting that he had two seasons this high up on the Overrated chart, and they pretty well bookend his incredible run from 1998-. Jeff Francoeur probably doesn't care about being on the list, since, unlike RBI (and OBP),  they don't put RBI per BRAR or wOBA on the scoreboard. Still, it's sort of sad (in a "ha-ha" way) to think that Frenchy's got a long way to go to even return to his .308 wOBA of 2006.

Vinny Castilla, well, there's a shocker. There's no need to point out that Pedro Feliz is a bad hitter. In fact, he's about an average player once you factor in his excellent defense. I just thought it was curious that so many third basemen were at the top of this list.

Finally, we come to one classic example and my persoinal favorite.

The "classic" overrated RBI guy is Joe Carter. Bill James tackled how overrated Carter was due to his reptuation for "clutch-ness" in the New Historical Baseball Abstract, and his take on it is in many ways unsurpassed. Still, even James may have overrated Carter as a player, as he doesn't even make Rally's Top 300 Position Players since 1955 by WAR list. Not that he didn't have some good seasons... but we aren't dealing with those. Here's a guy who drove in 102 runs hitting in the middle for the order for Toronto in 1997 with a .297 wOBA. You don't like wOBA? You think a .284 OBP might be okay? How about this -- he drove in 102 runs in 1997 and 115 in 1990 in  while not even slugging .400 either season.

But Batista's 2004 greatness was nothing compared to what he had already achieved for the Orioles in 2003. This is the season for which I did the +10 modification, and the reason I lowered the bar from 100 to 90 RBI: 99 RBI in 670 PA,  .283 wOBA for -22.6 bRAA and a .235/.270/.393 line. Let's put that .283 wOBA in perspective: Adam Everett has a career wOBA of .290. If that isn't enough to ween a person of RBIs as a measure of offensive value, I don't know what is. Or maybe the Tigers should be hitting Everett cleanup this season...

Perhaps you still think that some players just have a "knack" for situational hitting, i.e., with runners in base or in scoring position, such that a high RBI/bRAA ration speaks in favor of their hitting abilities. I guess you'll have serious issues with the guys on the mmost underrated by RBI list, then. Look who appears 6 times in the top 10. 'Nuff said.

In conclusion, let's look at 2008's players with more than 90 RBI. Look at the bottom, first. Grady Sizemore, Lance Berkman... Albert Pujols. OK, obviously, Sizemore hits leadoff, and Berkman and Pujols had good years even for them, so they might be expected to "out-wOBA" their  RBI numbers. Still, any ranking that has them at the bottom has to make you think that being at the bottom is a good thing, right?

And who is that the top? The worst mistake Dayton Moore will take: Jose Guillen.

Still not convinced? I'll revisit this next week using a more contextual approach to situational hitting to see if there's anything there.

Thanks to Sky Kalkman for his stylistic and methodological suggestions on this piece, and to terpsfan for his park factors and instructions on how to implement them. Neither of them, of course, is responsible for my screw-ups.

Update, 5/18/2009, 11:40 p.m. EST: At the Book Blog, Tom Tango suggests that it would be better to just use RBI per absolute runs created rather than above average/replacement. I had considered doing so when working on this piece originally, but decided not to for various reasons.

However, Tango’s point is a good one, so I’ve quickly caculated Batting Runs Created. It’s the same formula as above average, but adds in the league average R/PA for each plate appearance:

(((wOBA-lgWOBA)/wOBAScale)/PA)+(lgR/PAPA)

The spreadsheet has been modified accordingly. The old ones are still there and are useful, I think, in that they reflect a similar methdology to that of the Jonah Keri piece that inspired this post. Those that are sorted by RBI/BRC are labeled with "BRC." I didn’t bother to park adjust those numbers, which causes some anomalies, but what I’m going for are the basic groups of players who are "better" or "worse" than their RBI numbers indicate. The players are basically the same. Batista's 2003 is the most RBI-riffic season on both lists. Joe Carter holds the #2 spot in BRC version, but this time its his 1990 season. For 2008, Jose Guillen has "dropped" to the fourth spot and is replaced by... wait for it... Mike Jacobs.

Thanks to Tom Tango and terpsfan for their suggestions, and there will be more on this topic next week (and hopefully in the comments this week!).