wRC and wRC+ Definitions
It’s easy to make the game more complicated than it needs to be, but when a batter steps to the plate, he really has one overall goal to accomplish: to create runs. Actions which help create runs include getting hits, drawing walks, and more. On the other side, actions which harm a team’s opportunity to score runs include ground outs, fly outs, and of course, strikeouts.
It’s against this backdrop that we introduce two statistics: wRC and wRC+. The abbreviation “wRC” stands for Weighted Runs Created. These stats are based on an earlier stat simply called Runs Created, which was developed by Bill James. The Runs Created version was typically used to assess how many runs a team would be expected to score, but it was also used occasionally to evaluate players. wRC and wRC+ improve on this earlier version by adding weights to specific outcomes in order to more fairly value performance. For instance, a double with worth more than a single, but by how much? The weights used by these stats make sure each type of offensive performance receives proper credit.
Let’s discuss the idea of ‘creating runs’ and why it is so important. Obviously, wins and losses are decided by runs, so scoring as many as possible is the goal. However, assigning credit for those runs is difficult, because multiple players typically combine their efforts to produce a run. Both wRC and wRC+ get around this problem by offering the appropriate weights to events that can lead to the production of runs.
So, why the need for two stats? There are a couple of important differences between the two. For one thing, wRC is considered a “counting” stat because it accumulates as a season goes along. On the other hand, wRC+ is a “rate” stat, which moves up and down throughout the season based on a player’s performance. A good way to understand this difference is to think about hits and batting average. Hits is simply the total number of hits a player has accumulated, while batting average is the rate at which he records hits. wRC and wRC+ are similar. wRC adds up the Weighted Runs Created by a player for a given time period, while wRC+ establishes a rate that factors in important elements like league and park factors.
The Concept of wRC and wRC+
As modern statistics have analyzed the game more carefully, it has become clear that more advanced statistical metrics can give fans and teams a better perspective on the abilities of each individual hitter.
At the heart of wRC and wRC+ is a statistic known as weighted on-base average, or wOBA. The basic idea behind wOBA is that each hit should be given its fair value. In a batting average, all hits are valued equally, which is obviously not the case in the real world. For instance, a home run is far more valuable than a single, but batting average sees them as equals. Something like slugging percentage attempts to get around this issue, but it still doesn’t capture the full picture accurately. With wOBA, we’re able to assign fair values to various types of hits, giving an improved picture of batter performance.
As you will see when we get to the calculation for wRC, it relies heavily on wOBA for these benefits.
Why are wRC and wRC+ Important?
These two statistics are important because they are an excellent way to sum up a player’s offensive contribution in a single number. With so many stats available in baseball today, it can be hard to know where to focus your attention when evaluating hitters, and these two stats offer a nice solution to that problem. By assigning appropriate credit for the runs a hitter creates, wRC and wRC+ have become important metrics in hitter evaluation.
Specifically, it is really wRC+ that takes so much of what matters and rolls it up into a single number. Since it is scaled to have league average performance always equal 100, it takes just a glance to see whether a player is an above- or below-average hitter. A wRC+ over 100 is an above average performance, while anything under 100 is below league average. Some baseball fans who are put off by the complexity of many modern statistics would find that they can easily understand what wRC+ represents, once they are introduced. This is one of the stats that does have the potential to reach a much wider audience.
How are wRC and wRC+ Calculated?
Although these stats share plenty in common, including a name, the calculations are actually quite different.
Let’s start by looking at how wRC is calculated:
wRC = (((wOBA – League wOBA/wOBA Scale) + (League R/PA)) * PA
Some important points:
- “wOBA” is a player’s Weighted On Base Average
- “League wOBA” is the total Weighted On Base Average for the season
- “wOBA Scale” is a constant calculated for each season
- “League R/PA” is the average runs scored per plate appearance on the season
- “PA” is a player’s total number of plate appearances
For wRC+, the math gets a bit more complicated:
wRC+ = (((wRAA/PA + League R/PA) + (League R/PA – Park Factor * League R/PA))/(AL or NL wRC/PA excluding pitchers))*100
- “wRAA” is a player’s Weighted Runs Above Average
- “League R/PA” is League Runs per Plate Appearance
- “Park Factor” adjusts the stat for locations of games
- “AL or NL wRC/PA” excluding pitchers adjusts the stat for league conditions
If you want to calculate a player’s wRC or wRC+, you’ll need to look up a variety of statistics to fill in the equations above. Fortunately, all of these numbers are readily accessible, on sites such as Baseball-Reference.com and FanGraphs.com.
What are Good wRC and wRC+ Numbers?
As we mentioned in the introduction, wRC is a counting stat and wRC+ is a rate stat. That means players will accumulate more wRC as they go through the course of the year, while wRC+ will go up and down based on performance (with 100 always being league average).
To give you some frame of reference for these two metrics, we have presented two tables below:
All-Time wRC Leaders (1900-2018)
| Player | Season | wRC |
| Babe Ruth | 1921 | 214 |
| Babe Ruth | 1923 | 211 |
| Barry Bonds | 2001 | 200 |
| Lou Gehrig | 1927 | 199 |
| Babe Ruth | 1927 | 195 |
| Jimmie Foxx | 1932 | 193 |
| Lou Gehrig | 1930 | 193 |
| Babe Ruth | 1924 | 193 |
| Babe Ruth | 1930 | 192 |
| Lou Gehrig | 1936 | 192 |
All-Time wRC+ Leaders (1900-2018)
| Player | Season | wRC+ |
| Barry Bonds | 2002 | 244 |
| Babe Ruth | 1920 | 239 |
| Barry Bonds | 2001 | 235 |
| Barry Bonds | 2004 | 233 |
| Babe Ruth | 1923 | 231 |
| Babe Ruth | 1921 | 224 |
| Ted Williams | 1957 | 223 |
| Rogers Hornsby | 1924 | 221 |
| Ted Williams | 1941 | 221 |
| Mickey Mantle | 1957 | 217 |
There won’t always be these kinds of legendary performances taking place each season, so it may be helpful to understand what a standout wRC+ performance looks like during a single season.
2018 wRC+ Leaders
| Player | wRC+ |
| Mike Trout | 191 |
| Mookie Betts | 185 |
| J.D. Martinez | 170 |
| Christian Yelich | 166 |
| Alex Bregman | 157 |
| Brandon Nimmo | 149 |
| Jose Ramirez | 146 |
| Paul Goldschmidt | 145 |
| Manny Machado | 141 |
| Anthony Rendon | 140 |
What are the Problems with wRC and wRC+?
The list of complaints for these two stats is a short one, as they are well-respected in the statistics community for their ability to identify the best hitters in the game. Both stats, particularly wRC+, are highly useful but there are a couple of shortcomings you should be aware of.
First, wRC is not adjusted for the league of the batter or the parks he plays in. This does limit the effectiveness of wRC somewhat, but is corrected in wRC+, where both factors are included.
Also, neither of these stats take the position of the player into consideration. A good hitting shortstop would typically be considered more valuable than a first baseman offering the same production, since the shortstop fills a more demanding defensive position. This doesn’t limit the effectiveness of the stat in analyzing a hitters production, but it is something to keep in mind.