Runs and RBI: What Significance Do These Statistics Have?

A year or two ago, I had an argument with a friend of mine about two statistics - runs scored and runs batted in. As we know, they are both statistics that are heavily dependent on circumstance, though they are widely used to measure the skill of individual players in baseball. My friend proposed that runs are more indicative of a player's offensive skill than RBI, while I argued that the two statistics are equally unreliable when evaluating a player's skill. At the time, though, neither of us had the proof to back up our statements. Today, I will attempt to prove my assertion.

How is this possible, you ask? As you may know, wOBA (weighted on base average) is an accurate measure of a player's offensive production. For those of you unfamiliar with the stat, a full description can be found here. By plotting the wOBA of all qualified Major League hitters against their respective R and RBI totals, we can calculate the correlations, and determine if there is any difference between R and RBI in terms of significance. We can also determine how significant the stats really are, to some extent, in the big picture.

I gathered the statistics of all qualified hitters from the past three seasons and constructed two graphs for each year: Runs vs. wOBA and RBI vs. wOBA. The two graphs appear very similar in most respects. Here is a look at the two relationships in the 2009 season (as of 9/12/09.)



Again, there is not a significant difference between these two graphs in terms of correlation. The R squared values for the two relations are nearly equivalent (Runs: 0.426; RBI: 0.378.) A difference of 0.048 in this case is not significant; the two values are virtually the same. Looking at the R squared values from the past 3 seasons (shown below), we see that nothing much has changed in recent years.


The R squared value for both relations settles very close to 0.4. Given that there is a difference of only 0.03 between the three year averages of the two statistics' R squared values, we can safely say that neither is more indicative of true offensive production any more than the other. This also means that the runs scored and runs batted in statistics accurately demonstrate a player's true offensive output only 40% of the time, which is not high at all. To give some perspective on this matter, the relationship between OBP and wOBA in 2009 is shown below. Note that the R squared value is 0.748 - much higher than that of runs or RBI.


My hypothesis was correct: neither statistic - runs scored or RBI - is more indicative of a player's individual offensive production and skill. Furthermore, the unreliability of these statistics in player evaluation has been clearly proven.

Once again, thanks for reading. Any feedback is much appreciated!