Sabermetrics 101: wOBA, wRAA and wRC+

This is the third installment of a series on sabermetrics by Josh Strohman, an MLB contributor for The Walk On Blog.

Alrighty folks, get your thinking caps on because today will be the most involved installation of this five-part sabermetric series. At points in today’s discussion, you may get a little overwhelmed with some of the derivations; however, I want to implore you to continue furthering your knowledge of advanced statistics.

Today, I will attempt to help you understand the actual calculations of some of the most important advanced hitting metrics, and we will also learn some important sabermetric concepts along the way.

No need to continue wasting time with an introduction, so let’s jump in.

Weighted On-Base Average (wOBA)

wOBA is probably the single most important advanced batting statistic developed to date. It can be found on FanGraphs (as can the rest of today’s statistics), and serves as the foundation that many advanced metrics stand on.

wOBA counteracts the failures of statistics like OPS+ by correctly weighing the possible outcomes of an at bat. By doing this, it gives us a more accurate representation of how a player is contributing to a team’s run production.

How wOBA is determined

Last week I mentioned that there are two major problems with OPS and OPS+. First, it incorrectly weighs OBP and SLG as equals in run production. Second, SLG incorrectly weighs the value of 1B, 2B, 3B and HR’s in terms of run value.

wOBA compensates for these failures by using linear weights derived from RE24. Now I know that was a loaded sentence, but I am going to break down RE24 and linear weights, so we have a better understanding of wOBA and sabermetrics in general.

RE24 stands for Run Expectancy based on 24 base out-states. Again, I know that it doesn’t make sense, but trust me, it’s actually really simple.

When a batter comes to the plate, there are several different situations in terms of the number of players on base and the number of outs. For example, a hitter could come to the plate with 0 outs, and a runner on 3rd base. Another situation is 2 outs and nobody on base.

These are the base-out states. There are 24 different base-out states and each one has its own run expectancy. The run expectancy of each base-out state is RE24. You can read more about RE24 here.

Using the data from RE24 we can figure out what the expected run value of each of the six batting outcomes (BB, HBP, 1B, 2B, 3B and HR). These are linear weights. You can read more about linear weights here.

It is important to mention wOBA uses scaled linear weights to match yearly OBP averages. Because of this, the exact weights will change on a yearly basis. You can find yearly weights from 1871-present on the FanGraphs Seasonal Constants page.

Now that we got some of the statistical background out of the way, let’s get back into wOBA. Here is the equation for wOBA, keep in mind the scaled linear weights reflect the 2019 season.

uBB stands for unintentional base on balls, aka your standard walk. uBB are used because wOBA aims to measure how a player’s ability helps produce runs. Since intentional base on balls are outside of the hitter’s, they are omitted from wOBA.

wOBA: Things to keep in mind

wOBA is extremely easy to use because the linear weights are scaled to the league average OBP. So, if a good understanding of OBP values, you know wOBA values.

Because wOBA is a rate statistic that correctly weighs the value of each type of batting outcome, it is a good replacement for other rate statistics like batting average, OBP and SLG (although the classic triple slash-line has its uses).

The one shortcoming of wOBA is that it isn’t park and league adjusted, so just keep in mind that players in hitter friendly park may have an advanced and vice versa. wRC+ will make up for this shortcoming.

wOBA is probably the single most important statistics to understand because it pushes us to start thinking with a sabermetric mindset. It forces us to consider the relative run value of every action.

Tiers of wOBA values

As mentioned, wOBA is scaled to yearly OBP averages, so if you know OBP, you know wOBA. However, if you are unfamiliar with the context of OBP values, I’ve got you covered. Here are some general tiers of wOBA values.

Weighted Runs Above Average (wRAA)

Now that we have an accurate way of determining a player’s production with wOBA, we need to turn the level of production into an actual run value. That is where wRAA steps in. wRAA measures how many runs a player helped contribute to their team compared to the league average.

How wRAA is determined

wRAA is really easy to find if you have the player’s wOBA. Here is the equation for wRAA:

League wOBA is simply the league average wOBA for the season and the wOBA scale is a constant that sets the league average to 0. The seasonal values for both the league average wOBA and wOBA scale can be found on FanGraphs Seasonal Constants page (link above).

Since the league average is set to 0, every tick above (or below) 0, is worth a run. For example, in 2019, Cody Bellinger had a wRAA of 54.2, this means Bellinger was worth 54.2 runs above the league average at the plate.

wRAA: Things to keep in mind

wRAA is a really handy statistic helps us observe the offensive value of a player in terms of runs. Because of this, wRAA is used as the batting component of FanGraphs WAR. However, keep in mind that wRAA compares a hitter’s run production to the league average; whereas, WAR compares player’s overall ability to a replacement level player.

You should note that wRAA is strictly a batting statistic and should not be used for overall player value. However, we can convert a player’s wRAA into wins using a simple calculation.

It is a good rule of thumb to know that 10 runs of value, equal one win. Therefore, if we divide a player’s wRAA by 10, we can find how many wins a player’s ability at the plate is worth.

Because wRAA is a counting statistic that measures how many runs a player is contributing at the plate, it serves as a good replacement for other run production counting statistics like RBI’s and Runs.

wRAA is league adjusted, so you can compare players between different leagues and different years.

Tiers of wRAA values

wRAA puts a player’s production into a specific run value. Because of this, it serves as more accurate representation of offensive run production than RBI’s and runs. Here is a table that should give some context to wRAA values.

Weighted Runs Created Plus (wRC+)

We have finally reached the climax of our sabermetric journey. wRC+ is the single best and most complete hitting statistic. wRC+ is based off of the wOBA (through wRAA), and then takes everything a step further by adjusting for league and park.

How wRC+ is determined

We have a lot to unpack here so let’s just dive right in with the equation.

Well that looks like a jumbled mess, so let’s break it down. The first term we see is wRAA/PA, this is simply the player of interest’s season wRAA divided by their number of plate appearances for that season.

The next term we see is the most prevalent in the equation, LgR/PA. LgR/PA is simply the number of runs scored in the MLB season divided by the total number of plate appearances for the season and can be found on the FanGraphs Seasonal Constants page (link above).

The Park Factor is another constant that can be found on the FanGraphs Park Factor page. Note that Park Factors will be expressed in values near 100.

For example, in 2018 Dodger Stadium and Fenway Park had Park Factors of 96 and 105, respectively. Note that if you were to do the wRC+ calculation yourself, Park Factors need to be divided by 100 before being plugged into the equation. So, with our example above, Dodger Stadium’s constant would be plugged in as 0.96 and Fenway Park’s as 1.05.

The last term in the equation is Lg wRC/PA excluding pitchers. wRC is very similar to wRAA; however, the league average is not scaled to 0 in wRC. Like LgR/PA, Lg wRC/PA excluding pitchers is just the league’s (this time AL or NL) wRC divided by the total league plate appearances.

Lg wRC/PA excluding pitchers is pretty difficult to find, but it can be calculated using the FanGraphs seasonal leaderboards. So, if you wanted to calculate wRC+ yourself, you would need to do some research to find this value.

Now that we have the math out of the way, let’s talk a little bit about wRC+. Like OPS+, wRC+ is a normalized statistic. Last week I talked a little more in depth about normalized statistics, so if you want a more in depth break down, you can take a look at that.

However, I will briefly summarize normalized statistics, so we can have a basic understanding of wRC+. Normalized statistics set the league average to a value of 100 and every tick above (or below) 100 is a percentage better (or worse) than the league average.

Along with being park adjusted, the normalization of wRC+ makes it the single best metric to compare players from different teams, leagues and years. If you want to read more on this topic, FanGraphs has an excellent article on how wRC+ is the best metric to use when comparing players from different eras.

wRC+: Things to keep in mind

wRC+ is the single most comprehensive hitting statistic that has been developed. It correctly weighs the run value of each type of hitting outcome, while also being league and park adjusted.

Because of this, if you need a single hitting metric to determine the productivity of a player at the plate, wRC+ is the metric you should use.

Like other hitting statistics, be mindful that wRC+ does not adjust for position and only measures offensive value so it should not be used to measure overall player value.

Tiers of wRC+ values

wRC+ may be the best hitting metric that we have; however, it doesn’t mean anything if we don’t know how to use it. As always, allow me to provide some context.

Conclusion

Normally at this point I would simply tell you what we would be discussing in next week’s installment of the series; however, since this was an involved piece, I am going to break it down into a few simple points to walk away with.

1. wOBA accounts for all aspects of hitting (walks, singles, doubles, etc.), and correctly weighs them in terms of run value using linear weights derived from RE24.

2. wOBA is scaled so the average wOBA is equal to the average OBP.

3. wRAA takes information gathered from wOBA and converts it into a run value.

4. The league average wRAA is set to 0.

5. wRC+ is the most accurate hitting metric as it is based on wOBA, league adjusted, and park adjusted.

6. wRC+ is normalized with the league average set to 100. Every step above (or below) 100 is a percentage point above (or below) the league average.

Alright, back to next week, we will leaving hitting statistics and moving on to pitching metrics. This means we will be covering FIP and xFIP. Both are crucial to understand as they are probably the two most important advanced pitching statistics.