-The K Zone-

March 7th, 2018

Dissecting wRC+, by Ian Joffe

This Year’s Sequel to Dissecting WAR

Today, weighted runs created plus, or wRC+, is the widely the considered the most comprehensive and most widely respected offensive statistic in the game. Last year, because I was tired of feeling obligated to provide context for WAR every time I mentioned it, I put wins above replacement on the dissection table, and just linked that article every time I mentioned WAR. Now, I plan to do the same for wRC+. Weighted runs created plus did not become the gold standard overnight. It took years of sabermetric theory to lead to the inception of wRC+, building up statistical knowledge from a foundation in Bill James and Moneyball and story by story with various different statistical techniques. Each letter in wRC+ represents its own floor in this allegorical skyscraper, and each of those floors needed several others to stand below it. Let’s at the very beginning, with Branch Rickey in 1954.

Ricky developed slugging percentage seven years after signing Jackie Robinson, part of his hall-of-fame string of career achievements. SLG was revolutionary for its time, granting real values to each part of the offensive game. However, as statistics advanced, people began to realize that the values which SLG assigned (1 point for a single, 2 points for a double, 3 points for a triple, and 4 for a home run) are actually rather arbitrary. A double is not worth exactly twice a single, and a home run is not four times a single but only 4/3 times as valuable as a homer. More recently, OPS (on-base plus slugging) tried to more accurately weight each batted ball event, but was still off by a little – it turns out that on-base percentage is about 1.8 times more valuable than isolated power. To figure out the exact values of each of these statistics, sabermatricians created a vital tool to modern stats: the run expectancy matrix. The run expectancy matrix, based on annual data, tells the odds of scoring a run in an inning given a certain outs-count and base runner situation. It also predicts the number of runs scored based on those factors. For example, with runners on the corners and one out, one can expect 1.130 runs to be scored, and there is a .634 chance that at least one run is scored. Here’s the full table from top SABR mind Tom Tango’s website.

It is from the run expectancy matrix that Tango figured out how to derive a value for each type of on-base event. Each hit or walk creates a change in the run expectancy of the innings. The relative changes in run expectancy are the true differences between the types of hits. Those relative differences are made into what we call linear weights, the more accurate equivalents of the 1, 2, 3 and 4 of slugging percentage. They change annually along with the run expectancy matrix, but currently are:

  • 0.690 for unintentional walks
  • 0.888 for singles (worth more than walks because of the potential to drive in unforced runners)
  • 1.271 for doubles
  • 1.616 for triples
  • 2.101 for home runs

The numbers are put into an equation that looks similar to slugging percentage, but with the new weights, that sum is then multiplied by a constant to make results that appear on a scale that looks similar to on base percentage. The product is OBA, on base average.

The next step is to make RC+, runs created plus. Like any SABR statistic that ends in a plus sign, RC+ is weight so that league average is 100 and each 1 statistical point above 100 is 1 percentage point above the MLB average. A player with 105 RC+ has an OBA 5% above average. A player with 95 RC+ has an OBA 5% below league average.

The final step in making wRC+ has to do with the w, “weighted.” To add the w, one must take into account park and league (American vs. National) factors. After adjusting wRC for those numbers, you have the final product WRC+, which is the best offensive statistic that can be used to compare players from any team during any era.

A 100 wRC+ is, by definition, average. Offensive all-stars tend to have wRC+’s above 125. Keeping in mind that wRC+ only measures offense, MVP candidates need a wRC+ North of 140. Since 1900, Babe Ruth and Ted Williams have the highest career wRC+, at 197 and 188. Mike Trout is #7 on the list, with 169, and Joey Votto is 11th with 158.

In times long past, if you wanted to take a quick look to see how good a player was offensively, you checked their batting average, and maybe their home run total. If you considered yourself data savvy, you might use SLG. In 2018, if you want to quickly check how good a player is offensively, looking at their wRC+ is a smarter move. There is, of course, not single tell-all offensively statistic, but today, wRC+ is the closest you will get.



Baseball Reference


Tango Tiger


Images attributed to:

Getty Images