Confusing Correlation and Causation, or Why We Don’t Use RBI

February 9, 2013 at 6:01 pm by Franklin Rabon under Atlanta Braves

One major project that we’re going to undertake this year at CAC is to have a sort of ‘educational’ series, to explain some of the concepts behind the way we analyze baseball. If you’ve done a lot of the ‘required reading’ in the links above, a lot of this will be redundant, however we are also going to go into some more detail in actual blog postings as well. For some of our more regular readers, you may find some parts of this series to be addressing issues you already understand, but hopefully even the most ardent readers may at least find a new way of thinking about topics you’re already familiar with.

Today we analyze that old chestnut of the traditional baseball writer/announcer, the RBI. Perhaps no single stat, outside of maybe pitcher wins, is more divisive between so called ‘sabermetricians’ and ‘traditional baseball media’ guys and gals. The RBI has long been a staple of backs of baseball cards, the line that pops up below a hitter when they come to the plate in a television broadcast and it’s one of the Triple Crown stats that Miguel Cabrera so famously lead the American League in last year.

Traditional media will expound upon the fact that knocking in runs is the whole point of offense (which is undeniably true) and thus the RBI should be king. In some ways that’s a simply compelling argument, so we better come strong if we’re going to challenge the throne of the RBI. Further, if you take any given list of the best hitters in the league, they’re inevitably amongst the higher RBI guys. Sure, there may be an exception here and there, but mostly they’re highly intertwined. Between 1919 and 1928, Babe Ruth was undeniably the best hitter in the game, in those 10 years, he lead the league in RBI 6 times, with two of the years he didn’t being years where he was injured. Further, one of the two non-injured years, he had 164 RBI, but finished second to teammate Lou Gherig’s 175. Surely, where there is smoke, there is fire. RBIs have to be important, right? They’re soooo highly linked with great hitters, and obviously the whole purpose that a batter comes to the plate is to cause his team to score runs, right?

Let’s take a detour for a second from baseball, and consider something that baseball players have a fondness for, red sportscars. Having worked in insurance before, I’m aware that statistically, red sportscars are substantially more likely to be involved in an accident than grey sportscars. The simple act of having red paint on your car can often cause your insurance premiums to rise in some states. So, let’s consider my hypothetical friend Bob. Bob has a red sportscar, but Bob, like many of us, doesn’t exactly want to be in a wreck, so Bob trades in his red sportscar for the same model black version. Now, most of us have enough sense to call Bob an idiot. However, Bob would object to you that STATISTICS PROVE that black sportscars get into fewer wrecks than red sportscars.

What we all sort of intuitively understand, but perhaps can’t explain is that our friend Bob has confused correlation (a statistical fact) with causation. Specifically in Bob’s case he’s confused the fact that more ‘flashy’ drivers tend to buy flashy red sportscars, and are more likely to drive ‘flashy’ and pass somebody in the suicide lane during rush hour to skirt through a changing light, and get into a wreck. The red paint and more accidents are both effects of the same root cause (wanting to be flashy while on the road), but Bob has assumed that the paint’s ability to absorb high frequency light waves is causing more accidents somehow.

Now, lets add one further analogy, and apply it to the sports world. Rushing yards and team victories. One common statistic that you’ll often hear NFL announcers spew out nearly every game is something along the lines of “Team X’s record when they rush for over 150 yards is (insert very good record), so obviously they need to make it a mission to get (running back’s name) his yards, no matter what!” Seems to make sense, when the team rushes for a lot of yards, they almost always win, so they should try to rush the ball a lot. How can you even argue that point? Well, what do teams do when they have sizable leads in the fourth quarter? They run the ball in order to drain the clock. What do teams do when they’re trailing in the fourth quarter? They pass the ball in order to score while taking as little time off the clock as possible. Thus, it’s often the case that winning is causing rushing yards, and losing is causing a lack of rushing yards, instead of the other way around. The team is running because they’re winning, not winning because they’re running.

Now, how does this apply to RBI? Well, let’s consider what it takes to get an RBI: Men on base and a solid hit, a homerun, or a walk with the bases loaded (obviously that’s simplified, but okay for our purposes here). In all cases, RBI are drastically increased if a batter has lots of men on base in front of him. In our first paragraph, we mentioned the astounding fact that Babe Ruth and Lou Gherig had 164 and 175 RBI respectively. How in the heck did that happen? Well, because the 1927 Yankees had a MIND BOGGLING SIX guys in the regular lineup with on base percentages over .380. Virtually every time Babe or Lou stepped to the plate they were hitting with 1-2 guys on base in front of them. Sure, they were fantastic hitters, but having the rest of your team get on base at nearly a .400 clip as a team makes you look much better in the RBI department.

Next, let’s consider how lineups are formed by managers. What do you want your first two guys to do? Get on base as ‘table setters’ and even perhaps use speed to get into scoring position for your 3-4-5 hitters. You want your #3 hitter to get on base a lot as well, in an ideal world. What do you want from your number 3,4,5 hitters? More than anything else you want them to just be flat out great hitters, so they can best take advantage of your 1,2,3 hitters being on base a lot. It’s the spot in the lineup and quality of the lineup in front of the hitter that’s causing the RBI mostly. He also happens to be a great hitter, but he’d be a great hitter regardless of what team or what spot in the batting order he hit in. Babe Ruth would have still been a great hitter if he was (obviously idiotically) forced to bat ninth. What we see is that being a great hitter is causing the batter to hit 3rd, 4th or 5th, but batting in those positions are actually what are causing the RBI more than anything else. It’s already a convoluted chain at that point, and the convolution is further compounded by the fact that the quality of the 1,2,3 hitters (which the batter getting the RBI has no control over whatsoever) drastically impacts RBI totals.

Well, so what? RBI are still often fairly well correlated with how good of a hitter a player is, who cares if the causal chain is murky at best? The reason is that RBI aren’t so much an inherently poor stat as much as a comparatively bad stat. That is, in a world where we only had RBI totals to judge hitter quality, things wouldn’t be hopeless. But we don’t just have RBI.

What was it that made Chipper Jones a great hitter? Was it that he had a lot of runs or RBI, or that he walked a lot, hit a lot of doubles and a lot of homeruns? Obviously the latter. We wouldn’t call Chipper Jones a poor hitter if he hit ninth and got much fewer runs and RBI, we’d call the manager an idiot who was mismanaging his talent. It’s walks, extra base hits and homeruns that matter, not runs and RBI. And luckily for us, we have those statistics. We can easily look them up. We can, with a little calculation even figure out the rates at which those outcomes occur.

Essentially, using RBI to judge hitter quality is like trying to read a book through a stained glass window from 10 feet away, when you could simply walk over, pick the book up and read it normally with minimal effort. Sure, you could maybe sorta make out the words of the book through the stained glass window, but why would you even try? Why not just walk over and pick up the book and read it normally? Looking at a hitters walks per plate appearance (BB/PA), singles per plate appearance (1B/PA), doubles and triples per plate appearance (XBH/PA) and homeruns per plate appearance (HR/PA) give you a razor sharp view of how well the player performed (though, due to ball in play luck, may not tell you exactly what his skill level is, but that topic is for another day, remember, results and skill aren’t exactly the same thing). Knowing that information, the only other thing RBI would tell you is whether or not the guys who hit in front of him were good at their jobs. Why would we judge a hitter’s quality based on the quality of other people who just happen to be on his team and just happen to bat in front of him. Only in a few very small cases is the hitter the manager, and never has he been the GM, so it seems quizzical at best to judge him on those merits. Thus, we see that RBI, while not totally awful, only serve to obscure a judgement that can otherwise be crystal clear. Using RBI is like trying to listen to your favorite song over a static-y radio station when you have the CD with the song on your CD player.

Finally, let’s talk briefly about weighted on base average (wOBA) and true average (TAv), two similar statistics pioneered by Tom Tango and the Baseball Prospectus staff, respectively. We just talked about what I often call the component stats of a hitter, in a very simplified form, what these stats do is that they take those component stats, and then weight them based on how historically important the various components are (ie how much more important is a double than a single, a triple than a double, a homerun than a triple, etc), then re-scale them to give a number that roughly corresponds with our notions of what a good OBP is (wOBA) or a good batting average is (TAv). True average also takes into account a few other aspects, like bunting, and hitting into double plays as well, but (for “saberists”, unsurprisingly) that seems to not have a huge impact, and the biggest difference is simply scaling to batting average v. scaling to OBP. If you really have to have a single number, these are great, as is the league and park adjusted version of wOBA, wRC+. (we go into more detail on these three statistics, and more in the sabermetric primer series of the podcast that will be released late tomorrow/early monday).

In conclusion, the problem with RBI is that it’s essentially a distorted reflection of a hitter being a good hitter, while we have ready access to stats that are much more informative, and less distorted by teammate quality and spot in the batting order. RBI is more of an effect of an effect (batting order position) of a cause (being a good hitter) plus teammate quality, it’s not the reason why a hitter is a good hitter. There simply isn’t a good reason why we should care about RBI, other than empty tradition. Tradition isn’t necessarily bad… if it makes sense, but in the case of RBI there just isn’t any sense in using it. When you use RBI as a measure of hitter worth, you’re confusing correlation with causation. How a hitter hits is the causation. It just happens that how many people are on base in front of him is sort of roughly correlated. You shouldn’t use ‘sort of roughly correlated’ stats when you have simpler stats representing the clear causation.