The following is an analysis of why Guillen's 97 RBIs in 2008 were overrated.  I myself used to side with the RBI crowd, but have come around to a different vision of thinking, as have most on this site.  But for the few holdouts, I present you this. 

This is slightly modified from a comment I made in another thread.

This equation is a rough estimate of the RBI potential of a player:

RBIs = Runners On x BA + HR.

Guillen last year had a .242 average, 40 RBIs, and 9 homers. Plug those numbers in and solving for Runners On he had roughly 128 last year, and delivered 31 of them. Turns out he actually had 124 runners on when he came to the plate.

<sarcasm>What an excellent RBI man!!</sarcasm>

2008 Guillen – 20 HR, 97 RBI, .264 BA. solving for Runners On = 292, actual = 303. So taking out his RBIs for driving himself in (homers), that means he delivered 77 of those 303!

<sarcasm>Again, what an excellent RBI man!!</sarcasm>

So here’s the big question:

How do you increase RBI production?

Well, let’s look at the equation. RBIz = Runners On x BA + HR, so there are 3 factors.

1. Increase homers.
2. Increase batting average
3. Increase runners on

Considering Guillen is below his career average for batting average lately, that probably won’t happen. His homers are trending downward over the last 5 years, so probably can’t increase RBIs through that. How about getting more runners on in front of him? DING DING DING! The one thing out of his control is pretty much what will determine his RBI total. Stick Mark Teahen/DDJ/Callaspo/Olivo/Buck/Gordon in Guillen’s spot in the lineup and all of them would do the same or outproduce him given the same circumstances, let’s take a look at 2008 (Guillen’s “good” season):

Teahen: .255, 15 homers, with Guillen’s 303 runners on = 92 RBIz
DDJ: .307, 12 HR, Guillen’s 303 runners on = 105 RBIz
Callaspo: .305, 0 HR, Guillen’s 303 runners on = 92 RBIz
Olivo: .255, 12 HR, with 303 runners on = 89 RBIz
Buck: .224, 9 HR, with 303 runners on  = 77 RBIz
Gordon: .260, 16 HR, with 303 runners on  = 95 RBIz

So very similar totals to Guillen from everyone but Buck, whose BA was terrible.  Let's look at what changing a few of Gullen's 2008 variables will do to his RBI total. 

1 If we increase his BA to .300 (a 13.6% increase) his RBI total becomes 111, so a 14 RBI increase.  For every percent the BA went up, he gained an RBI.

2 If we increase his home runs, the formula only projects an increase of 1 RBI per homer, but assuming the extra homers came from flyball outs, his BA would raise as well which would knock in a few more RBIs.  So let's say homers increase by 13.6%, that gives him 23 homers (and 3 more hits added to his BA to make it .269), which gives him a new formula total of 105.  So that's definitely less bang for the buck than #1.

3. Let's up Guillen's baserunners by 13.6%.  Now he has 344.  Plug that into the formula and the RBI total is 111, so again a 14 RBI increase (not a coincidence as this essentially boils down to doing #1 again, 1.136 x BA x Runners On gives you the same number no matter the order you multiply in).  So what's more likely?  That Guillen can raise his BA to .300 from .265, or that he gets 41 more runners on base in front of him in a given year?  You can't change Guillen, but you could put guys with higher OBP on in front of Guillen to get him more runners.

Clearly, the overriding factor here is how many baserunners you have on. Second place looks like it should go to BA, but a given MLB player isn't likely to raise his average significantly.  As a career .270 hitter probably doesn't have too many .300 seasons in him, and if he did, it's probably due to BABIP which is out of his control.  So is it more likely a player raises his average 36 points in a year (assuming no really low outlier years) or that a player hits an extra 6-10 homers in a given year (which would roughly equal the RBIs gained from the BA increase)?  Increasing home run power is possible for younger players, though in Guillen's case, he's clearly declining (I'd put Guillen's odds of having a 20+ homer season in 2010 at 5%, and that might be high).  So I would say that at first glance BA appears to have the greater effect, but HRs are more prone to have outlier years than BA.  So the formula says BA is more valuable for RBIs, but in reality, I think increasing home run power may have the greater realistic chance of happening, and thus account for a greater effect.  

But the main argument here is about the high importance of baserunners.  Remember that DDJ had only 210 baserunners on for him in 2008 and drove in 73 (my formula estimates 76 RBIs), but with Guillen’s baserunners, DDJ is an RBI All-Star!

Clearly the Royals do not “need” Guillen. What they need are people that can get on base. The RBIz will follow.