wRC+ Explained: The Number That Compares Hitters Across Parks and Years
wRC+ turns a hitter's run creation into a scale where 100 is league average, adjusted for park and season. Learn the formula, a worked example, how to read it and what it leaves out.
wRC+ is the statistic most analysts reach for when they want to answer one question: how good was this hitter at creating runs, compared with an average hitter in the same league, in the same year, playing in the same park conditions? The answer comes as a single number on a scale where 100 is exactly average. A 130 means the hitter created 30 percent more runs per plate appearance than an average hitter, and a 70 means 30 percent fewer. Because the number is adjusted for the ballpark and measured against its own season, it lets you set a hitter from a 1968 pitchers' park beside a hitter from a 2000 hitters' park and ask a fair question.
The name stands for weighted runs created plus. The "weighted" part comes from wOBA, the rate statistic that credits each way of reaching base in proportion to the runs it is worth. The "runs created" part says the value is expressed in runs. The "plus" part is the same convention used by OPS+ and ERA+: a scale of 100 that adjusts for context. If those three ideas are clear, the formula is easy to follow, and this article walks through all of them with a worked example.
It also covers what wRC+ cannot tell you. It measures hitting only, and a number that sounds like a final verdict on a player is nothing of the kind. Used well, it is the best single batting number in common use. Used carelessly, it produces confident mistakes.
The three ideas inside the name
Start with wOBA, which is explained fully in the wOBA article. Batting average treats a single and a home run alike, and on-base percentage treats a walk and a home run alike. wOBA, weighted on-base average, gives each outcome a weight reflecting the runs it tends to produce. A walk is worth less than a single, a single less than a double, a double less than a triple, and a triple less than a home run. The weights come from studying how many runs actually scored after each type of event, so the statistic is built from baseball results instead of from an opinion.
Next comes the step from rate to runs. A hitter with a wOBA above the league average is creating more runs than an average hitter would in the same number of plate appearances, and the distance between them can be converted into runs. The conversion uses a constant, called the wOBA scale, which is usually somewhere near 1.2. Dividing the difference in wOBA by that scale and multiplying by plate appearances gives weighted runs above average, or wRAA.
The last step is the "plus." Weighted runs created, wRC, is wRAA plus the number of runs an average hitter would create in the same plate appearances. To compare hitters who had different numbers of opportunities, wRC+ divides the hitter's run creation per plate appearance by the league's, after a park adjustment, and multiplies by 100.
The formula in plain terms
For those who want the algebra, the standard definition is as follows.
- wRAA = ((player wOBA - league wOBA) / wOBA scale) x plate appearances
- wRC = wRAA + (league runs per plate appearance x plate appearances)
- wRC+ = (((wRAA per PA + league runs per PA) + (league runs per PA - park factor x league runs per PA)) / (league wRC per PA, excluding pitchers)) x 100
The structure is more important than the symbols. The numerator is the hitter's run creation per plate appearance with a correction for the park. The denominator is what the league's non-pitcher hitters created per plate appearance. The ratio is multiplied by 100. A hitter who matches the league has a ratio of 1.00 and a wRC+ of 100. The constants (the wOBA weights, the scale and the league run rate) are recalculated each season, which is why the number is comparable across years.
Park factors are the part of the formula people most often misunderstand. A park factor measures how much a ballpark changes run scoring compared with a neutral park, usually based on several seasons of data so that a single odd year does not distort it. If a park raises scoring by 10 percent, the hitters who play half their games there are given a downward adjustment. Published versions of the statistic apply the adjustment in slightly different ways, so check the definition on whichever site you use.
A worked example you can follow with a calculator
The numbers below are illustrative, not real players. Suppose the league wOBA is .315, the wOBA scale is 1.20, and the league scores 0.115 runs per plate appearance. A hitter named A comes to the plate 600 times with a wOBA of .380.
- The gap to the league is .380 minus .315, which is .065.
- Divide by the scale: .065 / 1.20 is about .0542 runs per plate appearance.
- Multiply by 600 plate appearances: wRAA is about 32.5 runs.
- Add the league baseline, 0.115 x 600 = 69 runs, to get wRC of about 101.5.
- Divide the per-PA figure (.1692) by the league figure (.115) and multiply by 100: about 147.
So Hitter A, with no park adjustment, created about 47 percent more runs per plate appearance than the league. Now suppose A plays half his games in a park that raises run scoring by 10 percent. The park correction subtracts about 0.0115 runs per plate appearance, which makes the numerator .1577 and the result about 137. The same wOBA in a friendlier park is worth ten fewer points. That is a simplified version, since it applies the full park effect, and published versions usually apply a smaller one, but it shows the sort of difference the adjustment is meant to capture.
A handy rule of thumb follows from this example. In this league, a difference of .010 in wOBA works out to roughly 7 points of wRC+. The exact rate depends on the season's constants, but if you know a hitter's wOBA is .020 above the league's, you can say his wRC+ is probably in the neighborhood of 115.
How to read the scale
| wRC+ | Rough reading |
|---|---|
| 160 or more | Elite, the kind of season that wins an MVP vote |
| 140 | A star hitter |
| 120 | Clearly above average |
| 100 | League average |
| 80 | Below average, acceptable only with value elsewhere |
| 60 or less | A serious liability at the plate |
These bands are my own rough guide, not an official table, and the useful part is the shape, not the labels. The scale is linear in runs per plate appearance, so a 140 hitter is twice as far above average as a 120 hitter. A fair share of regulars sit between 85 and 115, and the best hitters in a season pull away from that group.
One caution is about what the percentage means. A wRC+ of 130 says the hitter created 30 percent more runs per plate appearance than the league's average hitter. It does not say the hitter was 30 percent better at baseball, and it does not say he will produce 30 percent more runs over a season, because that depends on how many plate appearances he gets.
Why it travels across parks and eras
The usefulness of the statistic rests on two normalizations. The first is by season: because the weights and the league average are recalculated each year, a hitter is always measured against the run environment of his own time. That matters because scoring has swung widely. The Deadball Era was a time of low scoring in which a .280 average was a strong season. After 1920, as the live-ball era shows, the average hitter's line looked very different.
The second normalization is by park. A hitter in a small park with a short fence and thin air gets help that a hitter in a large park does not. By pulling the home park's effect out, wRC+ measures the hitter more nearly than the box score does. When a player changes teams, his wRC+ can change simply because he moved to a different park, and the adjustment is meant to reduce that.
Neither normalization makes players from different eras equal. A 140 in 1968 and a 140 in 2000 both mean 40 percent better than their own leagues, but the two leagues had different talent pools, pitchers, equipment and strategy. wRC+ answers how dominant a hitter was relative to his contemporaries, not how he would fare against pitchers of another era. That is still a useful question, and it is more honest than comparing raw averages.
wRC+ next to OPS+, wOBA and other batting numbers
The most common alternative is OPS+, covered in the OPS and OPS+ article. OPS+ also sets 100 at league average and adjusts for park, but it starts from on-base percentage plus slugging percentage. That sum treats a point of on-base percentage and a point of slugging as equal even though a point of on-base percentage is worth more runs. In practice the two statistics usually agree within a few points, and they diverge for hitters whose value is concentrated in walks or in power.
wOBA is the raw rate that wRC+ is built from. It is expressed on the scale of on-base percentage, so a wOBA of .320 sounds familiar, but it has no park adjustment and no league adjustment. If you are comparing two hitters in the same season and the same park, wOBA is enough. If the parks or years differ, use wRC+.
Other pieces of the profile add context. Isolated power shows how much of the production comes from extra bases. Strikeout and walk rates show the approach. And BABIP shows how much of a hot or cold season rested on balls in play that fell for hits. Because wRC+ takes hits at face value, a high BABIP inflates it and a low BABIP depresses it, so the pair together is a better guide to what will persist.
What wRC+ leaves out
A number that appears to summarize a hitter can mislead if you forget what it covers. First, wRC+ measures hitting and nothing else. A shortstop with a 95 wRC+ may be a valuable regular because of his defense, and a first baseman with a 125 may be less valuable than the number suggests because first base is the easiest position to fill. Value statistics such as WAR add defense, baserunning and position on top of hitting, but wRC+ stops at the plate.
Second, it does not include baserunning, so a hitter's speed on the bases is not captured. Third, it is blind to context such as the quality of the pitchers faced, the platoon advantage a manager gave the hitter, and the leverage of the situations. A player who hits only against right-handed pitching will carry a different wRC+ than one who faces everyone.
Fourth, it depends on sample size. Over a few dozen plate appearances a wRC+ can swing wildly, and even over a half season, some of what you see is luck. Several hundred plate appearances are needed before the number starts to settle, and several seasons before it becomes a reliable portrait of a hitter's true level. Finally, the park factors and league constants come from the data of particular years, and different providers compute them differently, so numbers from different sites may differ slightly for the same player.
How to use it: trades, fantasy and arguments
The best uses of wRC+ are practical. For fantasy baseball, it is a quick filter for hitters who are creating runs well, and combined with BABIP and strikeout rate it helps separate a breakout from a lucky month. A player whose wRC+ is far above his career level on a high BABIP is a regression candidate. A player whose wRC+ is below his career level on a very low BABIP may be a buy. The fantasy pages are the natural place to apply that reading.
For arguments about who was better, use it in two steps. Check that the hitters have enough plate appearances in the seasons being compared. Then compare the wRC+ values, and ask what each leaves out, such as defense, position or baserunning. The answer will rarely be a single number, and that is a feature, not a flaw.
For the arithmetic behind the inputs, the site's stat calculator handles averages and on-base percentages, and the leaders pages show the standard batting leaders so you can see where the traditional measures and the weighted ones part ways.
Common questions
Is a wRC+ of 100 bad? No. It means league average, and an average hitter is a useful player in the lineup, especially at a position where defense counts for a lot.
Why do pitchers not count in the league average? The league denominator excludes pitchers' plate appearances, since they are weak hitters and including them would pull the average down and flatter everyone else.
Can wRC+ be negative? Over a tiny sample, yes; a pitcher who bats a handful of times can produce one. For a regular over a full season it does not come close, and a figure under 50 is rare.
Is wRC+ the same as wRC? No. wRC is a count of runs created and favors players with more plate appearances. wRC+ is a rate that is scaled to the league, so it compares hitters with different amounts of playing time.
Do all sites use the same wRC+? The idea is the same, but constants, park factors and some details differ, so figures may not match exactly. Use one source when comparing players.
Where to go next
Read the wOBA article if the weights are still hazy, then the OPS and OPS+ article to see the older cousin of the statistic. The BABIP article completes the picture by showing how luck enters. The topic page at /searchset/stats-and-analytics/ collects more articles on the numbers behind the game.