Why Is There No Version of wRC+ Including Baserunning?

Would someone be so good as to please implement this for me? This statistic can and should definitely exist and would be easily derivable from the stats FanGraphs already has. Yes, there is the offensive runs above average figure, but this is not a rate stat, and is not scaled to 100. What the people want is a wRC+ rate stat for offense that includes baserunning — for why should baserunning be excluded if what we want to know is who are the best offensive players on our team, which certainly includes their contributions on the bases or the lack thereof? (I’m looking at you Wilmer Flores; I saw you thrown out three times on the bases in a single game last week.)

I think the argument is clear for adding a baserunning-included linear weights rate stat, and one which is park- and league-adjusted, and one on the intuitive, familiar, and non arbitrary 100 point scale. (I prefer wRC+ because the scale of wOBA seems entirely arbitrary and unintuitive in meaning.) I don’t think the user should need to try to cobble together figures on their own and perform division to determine various players’ offensive contribution per plate appearance, if they have a simple question, such as “Who are the best 8 or 10 or 12 or 14 offensive players on our team, in their careers, or this season?” Despite all the stats given to us, I don’t really see one that answers this without my performing calculations.

That’s right; I have figured out how to calculate this myself, but it would be nice to have it automatically calculated. Here’s how you do it. (There is probably an easier way than this, but this is the way I figured from the materials available.)

Take the Players (Park/League Adjusted) Batting Runs above Average (listed at the bottom of the page under Value, or subtract baserunning runs from offense runs) and divide by wRC+ the percentage above average, converting wRC+ to a percentage and subtracting 100 (i.e. for a wRC+ of 104, divide by .04). This will give you the League Average Batting Runs in the player’s plate appearances. Now that you have this figure, simply add back in the Offensive runs above average (or the Batting Runs above average + Baserunning runs above average) to get the total park- and league-adjusted linear weights runs for the player including baserunning and hitting. And of course, to get our wRC+ baserunning-included statistic, we simply now divide by the league-average runs (which we already calculated, and which has the park and league adjustments built into it because of how it was calculated) and we arrive at the desired baserunning adjusted wRC+. Voila.

As an illustration, take Curtis Granderson, who I have down, as of September 15 having a career 117 wRC+, and a sum total of 192.9 Offense Runs, and 50.9 Baserunning Runs. By the way, we should immediately see that his career wRC+ is going to be seriously under-rating his overall offensive contribution since roughly 1/4 of his career offensive runs above average derive from his good works on the bases.

1) We start by subtracting the Baserunning runs from the Offense runs to get the Batting Runs above average (You can skip this step if you look down under value, where this stat is listed, though you can probably calculate it faster than you can scroll if you’re like me):

192.9 – 50.9 = 142

2) Next, since a wRC+ simply means his batting was 17 percent above league average for his career (park-adjusted), we divide the batting runs only by .17 to get the league-average batting runs, park-adjusted:

142 / .17 = 835.29

3)  Next, we add back the player’s total offensive runs above average, to the league-average figure over that span, park-adjusted for where the player played already, to get the player’s total park- and league-adjusted runs, including baserunning.

835.29 + 192.9 = 1028.19

4) Last, but not least, simply divide by the figure we arrived at in step 2 (the park-adjusted league-average runs a player would have produced in however many plate appearances) to arrive at your magnificently complete new baserunning-included wRC+:

1028.19 / 835.29 = 1.2307, or 123 on the 100 point wRC+ scale.

Thus, in the case of Granderson, his ostensible wRC+ of 117 is significantly under-playing how much better than average he’s been over his career on offense, relative to his opportunities, since his “true” wRC+, including baserunning, is actually 123, not 117.

I can’t see what the argument for baserunning not being included would even be; I understand why one would also want the batting-only figure, but the batting + baserunning figure is surely also important to know, and if I had to only have one, to my mind, I’d unequivocally take the figure that gives total offensive contribution relative to opportunities and adjusted by context, rather than a partial figure that tells me only about batting. Luckily, there’s no real reason to choose; we can and should have both.

You might now be thinking, wait, what about below-average players? (I momentarily had this trivial thought, but the negative runs above average, and the percentage wRC+ below 100 will cancel out, of course.)

A demonstration, using the aforementioned lead-footed Wilmer Flores as our exemplar. Flores, has -7.0 batting runs above average for career, -2.8 Baserunning above average, -9.8 offense above average, and a 95 career wRC+. Here I’ve skip step 1 by just finding Batting Runs on the bottom of the page.

  1. -7/.05=140 (which represents league average runs in Flores’s career plate appearances, including adjustments)
  2. 140-9.8=130.2 (the number of offensive runs Flores actually contributed, including his base-running miscues.)
  3. 130.2/140=.93 or a wRC+ of 93, once we appropriately dock Flores for his base-running.


Now, while this isn’t that complicated for me to calculate, I propose this, or something like it be implemented for a total wRC+ that includes baserunning. Obviously it could be calculated for season stats too just as easily. If you have baserunning runs, Offensive total runs, and wRC+, the figure I’m looking for can easily be implemented. Thanks for reading.

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7 years ago

If I understand you correctly, the league runs you derive by dividing batting runs by the fraction above average contained in wRC+ in effect is adjusted for park and league. So to take the Granderson example, with his 835 league runs, if there were another player on another team who played the exact same time period as Granderson, his league runs would not be the same. There would be an unadjusted value for league runs that would be the same for every player during this period, but the value changes for each player because of different home parks, and it’s this changed value I think you are calculating.

However, baserunning runs are not adjusted for park nor I think league. So shouldn’t the effect they have on wRC+ be determined by dividing them by the unadjusted league runs? To determine these, you multiply PA by the run/PA value found in the FG guts page. However, the latter changes every year, so you must multiply each season’s total PA by the R/PA value for that year. You can’t just take an average R/PA value over Grandrson’s career, because some seasons he will have had more PA than others. You must determine league runs for that number of PA for each season, then sum them. I haven’t bothered to do this, but I see that Granderson has about 7000 career PA, and that the R/PA value during his career has fluctuated mostly between .110 and .120. So I’d guess the unadjusted league runs during this period is very roughly 800 runs, certainly in the neighborhood of the adjusted figure of 835, but not exactly the same.

Let’s just assume it’s 800. Then one divides the 51.3 baserunning runs (as I write this) by 800, to get 6.4%. You add this to his batting wRC+ of 117, and get 123, the same as you got. IOW, it didn’t make any difference, in this case. But it might in some cases, such as when analyzing Rockies players, and their huge park advantage for hitting. Using the adjusted value of league runs as you calculate it would have the effect of reducing the baserunning value below what it should be, because it’s assuming that baserunning runs are inflated just as batting runs are in Coors, when in fact this is not the case.

7 years ago

The reason this type of stat is not in circulation is that it only effects players who have extreme baserunning numbers comparatively to the league. Your examples shown above only change the players outcome a few points north or south.

Essentially, baserunning is a negligible part of a players total offensive production. There are countless studies showing that Stolen Bases for example don’t have much effect on a players or teams production overall.

If you want to argue that such a stat would be more refined and thus superior, then maybe you have an argument. But the jury is still out on the accuracy of baserunning stats in a similar way as defensive ones.

7 years ago

“the jury is still out on the accuracy of baserunning stats in a similar way as defensive ones.”

It depends on which component of baserunning. SB/CS values should be just as accurate as values for batting events, because like the latter, they’re based solely on the change in run expectancy, which is known very accurately. Same with wGDP. UBR is not as accurate as the other two, because like defense, it depends on assuming somewhat arbitrary buckets, and determining the run value of balls hit to these buckets. Still, the degree of uncertainty is less than for defense, because there are fewer outcomes to deal with. A baserunner either goes from first to second or first to third, or from second to third or second to home, e.g., whereas with defense a fielder may or may not catch the ball, may or may not cut the ball off, may or may not throw the ball to the in field in time. In other words, much of the uncertainty on a batted ball is assigned to the defense, leaving less for the baserunner.

I agree with you, though, that baserunning does not change the wRC+ values too much for most players, and you can just look at a player’s baserunning values to get a rough but probably adequate idea of how much, and in which direction, they complement his hitting.

Shirtless George Brett
7 years ago

Fangraphs mostly already has this with the OFF stat. Its just not on the scale you prefer.

Shirtless George Brett
7 years ago
Reply to  kingshowman


The point is that Fangraphs already displays the information you are looking for just in a different format. If you know that 0 = average and every 15 runs above or below is a tier then OFF is going to tell you the same basic thing that a wRC+ that includes BsR would.

Which is generally not much because as someone else pointed out, BsR is usually a pretty small factor. The difference between wRC+ with BsR and without is a couple % points, as your examples show.

Lee Trocinskimember
7 years ago

It’s funny, because SB/CS actually used to be included in wOBA, then was taken out a few years ago. I was one of the many people who suggested separating the bat from the baserunning.