Home Run Productivity

Introduction

I was browsing over at Bill James Online the other day, and saw that Josh Hamilton has 46 RBIs on his 31 home runs.  My first thought was, "That's a lot of solo home runs."  This leads to an interesting question in my opinion:  who hits the most "productive" home runs?

Definition of RBIs/HR:

We can measure this by taking the number of RBIs a player has as a result of home runs, and dividing it by the number of home runs (which gives us an RBIs on HRs per HR, or RBIs/HR for short).  

The first set of data I looked at was for Rangers players with at least 10 home runs (to limit random variation due to a small sample size of HRs) , sorted HRs:

Rangers RBIs/HR (minimum 10 HRs): 

From this small sample, it seems that a reasonable average is approximately 1.6 RBIs/HR.  The next obvious step is to examine more data.  However, since this data isn't in a place where I can find it sorted very neatly,  I'm going to select my sample by choosing hitters for which there is not a small sample size (in other words, the top 22 home run leaders in MLB), sorted by HRs:

Top 22 HR Hitters in MLB RBIs/HR

And the winners are:

The most productive home run hitters on this list are (1) Vladimir Guerrero (1.84 RBIs/HR), and (2) Jose Bautista (1.74 RBIs/HR).  Instead of suggesting that someone like Vlad is more "clutch" with his home runs, a more likely explanation is probably that the best hitter in the league, Josh Hamilton, hits directly in front of him and has gotten on base at a rate of over 40%.  In general, a player's RBIs/HR seem to be directly correlated with the ability to get on base of the hitters directly ahead of them in the lineup (but that's another fanpost for another time).  Bautista seems to be a quick exception to this, however, as a quick scan of Toronto's lineups (or their roster in general) reveal a consistence absence of high-OBP guys in their lineup.

The least productive home run hitters on this list both play for the same team: they are (1) Prince Fielder (1.18 RBIs/HR), and (2) Rickie Weeks (1.32 RBIs/HR).  Rickie Weeks, of course, hits leadoff, so he is preceded by the pitcher and the #8 hitter, so his low  RBIs/HR comes as no surprise.  Prince Fielder's is fairly surprising, however, given that he is preceded by Ryan Braun (.303/.361/.484).  Braun reaches base at a respectable rate;  a possible reason may lie in the number of times Braun has cleared the bases ahead of Fielder:  he has 17 HRs and 15 GIDPs, meaning that Braun has voided would-be RBI opportunities for Fielder 32 times.