# A Guide to Baseball's Expected Statistics

Statistics that prefix with the letter “x” have made their way into baseball broadcasts across the country over the last couple years, and it’s *refreshing*. We’ve seen broadcasts finally showcase something other than batting average as the all-encompassing metric to define a hitter’s production. Some scoreboards in major league stadiums are showing OPS next to each hitter in the lineup before the game begins. In many ways, sabermetrics have taken over. That’s why you’re here, reading this article, right? As always, here at Simple Sabermetrics we are going to keep things *simple*. That means this will be a high level overview of expected statistics.

One of Jake’s __recent videos__ explored the luckiest and unluckiest hitters in MLB this season in terms of their *actual* performance to their *expected* performance. This particular slide was showcased, and it’s a great starting point to wrap your head around what we’re going to talk about.

As the video mentions, there are three factors that can be pinpointed to determine bad luck in baseball.

*Hard Hit Outs*

A well-struck baseball at 110 MPH exit velocity can be turned into an out as quickly as a 60 MPH __worm burner__. That’s part of the beauty of the game, and yet another reason why analytics have become so important in player evaluation (and just about every facet of the game). It’s no secret that players that consistently hit the ball hard are going to produce better results than players who do not. Some just will experience different levels of fate than others, and that’s where the “luck” is involved.

*Park Factors*

We won’t spend much time covering park factors within this piece. Jake’s example, while extreme, is a great testimony to the vast differences of ballpark dimensions across the league. Some types of batters thrive at certain ballparks, such as left-handed hitters at Yankee Stadium for its short porch in right field. Beyond outfield fence distances or heights, atmospheric conditions can also affect a batted ball’s outcome. Coors Field’s atmospheric conditions are why the ball travels further than every other stadium, as we saw in this year’s home run derby. The luck involved here is hitting a ball where the park factors will either benefit or limit the outcome.

If you’re looking to learn more on this topic, check out Jake’s __video__ on this from last week.

*Expected vs. Actual*

This is the main focus of this article. The best method to capture the variance in production for a hitter or single batted ball event is investigating the differences between actual and expected outcomes. The most popular expected statistics in this technologically-savvy baseball era include expected batting average (xBA), expected slugging percentage (xSLG), and expected weighted on-base average (xwOBA). Each of these are developed by MLB’s Statcast team and are publicly available on __Baseball Savant__. Let’s dig into detail on each of these.

**Expected Batting Average**

The __expected batting average__ of a single batted ball is the probability of that event becoming a hit. Simply, that is referred to as “hit probability”, which Statcast used to call this metric. The main difference is the former metric was represented as a percentage, whereas xBA is presented on the same scale as batting average. So, a line drive to left field with a .620 xBA equates to a 62% hit probability.

Statcast calculates xBA using the two main drivers of the likelihood of a hit after a ball has left the bat: exit velocity and launch angle. Sprint speed was introduced in 2019 as a variable for __“topped” and “weakly hit”__ batted balls. This helped to account for players more likely to beat out infield singles.

Other factors can include the spray angle, ballpark, atmospheric conditions, or defensive positioning, but these are excluded to focus solely on what’s most in the player’s control. Various hit probability models out there may have spray angle included to better describe an individual batted ball event, which is further removed from Statcast’s __main goal__ - describing the production of the player.

As we begin to collect a sample of a hitter’s batted ball events, the player’s overall expected production starts to take shape. With a healthy sample size, the average of a batter’s xBA events form his *expected batting average on contact*, otherwise called xBACON. Strikeouts are then factored in to arrive at the final expected batting average.

Let’s see how MLB hitters in 2021 are hitting compared to their expected batting average.

On the x-axis is the actual metric and on the y-axis is the expected metric. Players that sit below the red line are “over performing” where there may be luck or other factors that contribute to a higher than expected production. On the flip side, players above the line may have had the opposite fortune and are labeled as “under performing”. The plot labels the three players on each side that outperform or underperform their actual batting average the most. Randy Arozarena, Akil Baddoo, and Yuli Gurriel have experienced the most good luck out of all hitters with at least 150 plate appearances so far this season.

Similar to batting average, xBA still lacks the power to measure a player’s ability to hit more extra bases. That’s where expected slugging percentage is introduced.

**Expected Slugging Percentage**

Slugging percentage accounts for extra-base hits, which takes our measurement a bit further because of the glaringly obvious fact that extra-base hits are far more valuable. So, similar to xBA, __expected slugging percentage__ factors in the same two batter skills - exit velocity and launch angle - to measure quality of contact.

The means to arrive at the end product are a bit different from the first metric we explored. Since there are four different types of base hits, the probabilities for each of them are plugged into the formula for slugging percentage.

xSLG = (P(1B) + P(2B) * 2 + P(3B) * 3 + P(HR) *4) / At-Bats

A more complex method than xBA, but still simple enough to comprehend the concept that each type of base hit is weighed differently. The probability of an out still exists in this scenario, but is excluded because it is not needed in the formula. It is indirectly included as the sum of the four probabilities will add up to less than 100% with the remainder then being the out probability.

To recap xBA and xSLG, let’s consider a ball with an exit velocity of 95 MPH and a 15 degree launch angle. For this example we will use actual outcomes instead of expected, but the concept remains the same for what we are about to uncover.

*Image from Baseball Savant’s *__Field Visualizer__

Batted balls with this pair of metrics resulted in a hit 75.6% of the time, but of those hits, it went for a single base hit over half of the time. This is great, but extra-base hits are more valuable. xSLG detects the power production of the batted ball instead of just the binary outcome. This eliminates further variance caused by the randomness of factors outside the player’s control.

Therefore, xSLG is more indicative of a batter’s offensive production than xBA because it measures that quality instead of the ability to find green grass and reach base. But, there’s still one downfall of these two metrics. They do not account for *all* of a batter’s plate appearance. So far, these two have only included quality of contact and strikeout percentage.

**Expected Weighted On-Base Average**

If you aren’t familiar with wOBA, be sure to check out __this__ Simple Sabermetrics video. wOBA measures the offensive production of a hitter similarly to on-base percentage, except that it weighs each outcome differently and accordingly. So, let’s add one last layer of complexity to our final expected statistic.

The __expected weighted on-base average__ formula takes the base of xSLG’s formula and adds two details that take its value to the next level: linear weights and all plate appearance outcomes.

xwOBA = (uBB * wuBB + HBP * wHBP+ P(1B) * w1B + P(2B) * w2B + P(3B) * w3B + P(HR) * wHR) / (AB +BB + SF + HBP)

That’s a lot to digest, so I bolded the pieces there that were not included from the xSLG formula, except for the “w” that prefixes each event. The “w” stands for weighted value. More on that can be found __here__.

Unlike xBA and xSLG, xwOBA accounts for all plate appearances events, so it is able to measure the quality of contact *and* a batter’s other abilities to reach base or frequency to strike out. This crowns xwOBA as the most powerful measure of the three statistics, and is one of the reasons we chose to utilize the difference in wOBA and xwOBA as the luck factor in his recent video and why it is most prevalent on Savant’s leaderboards.

We spent the majority of this article from the hitter’s point of view, but these three expected statistics can be calculated for pitchers too. Finding their xwOBA against, for example, can more accurately describe the quality of contact (and non-batted ball success) that is being allowed over other basic metrics that are so volatile to variability and factors out of their control (defense, park, weather, etc.). So, let’s flip the coin and see which pitchers have had the most deviance from their expected performance.

The styling is identical to the previous visualization; the x-axis is the actual performance and the y-axis is the expected. Because we’ve flipped to the other side of the ball, we have to adjust the lens in which we view these performances. A pitcher that allows a higher wOBA than xwOBA is suffering from poor luck and can be labeled as “underperforming.” Those with better luck - higher xwOBA than wOBA - are getting away with better outcomes than expected so are “over performing.” The former live below the red line and the latter above it, which is opposite from the hitters batting average graph. The likes of Jack Flaherty, Keegan Thompson, and Brett Anderson are out performing their expected weighted on-base average peripherals.

For those interested in learning more about the intricate details of Statcast’s xwOBA model, I highly recommend __this article__ written by a member of their research team, Sam Sharpe.

**Regressing to the Mean**

Because expected outcome statistics are a measure of player talent, a method to understand the usefulness of these metrics comes from __this article__ from Baseball Prospectus writer, Jonathan Judge. Here’s a sentence from the article that is an important principle to understanding this concept.

“Principle 5: A player’s expected contribution cannot be directly measured; thus, it must be inferred from contribution measures evaluating descriptiveness, reliability, and predictiveness.”

A common misconception regarding expected statistics, like the ones we covered here, is that these measures are meant to be *predictive* of a player’s performance. We cannot say with confidence that a player will regress back to his expected performance just because his xBA is higher than his BA. It wouldn’t be a terrible guess, but there could be other factors contributing to the difference that is more stable over a season.

Instead, these metrics are meant to be *descriptive*, meaning that we’d expect the player’s expected statistics to correspond somewhat with the actual outcomes. That holds true among the three we explored. We were unable to scrape xSLG values from Savant, but we found that BA and xBA have a 0.799 R^2 value and wOBA and xwOBA have a 0.843 R^2, both very strong correlations.

A helpful anecdote to return to frequently is a batter going 0-4 during a game with four hard-hit outs who has a teammate that went 4-4 with three bloop singles and an infield hit. We also must be cautious of small sample sizes, but in this instance the player who went hitless displayed better skill without anything to show for it. This ties back to the luck factor of baseball. By using our expected metrics we gain a better idea for which of the two batters was more skillful during this game. This luck, or variability/randomness, will even out over the course of the season to a certain degree; the remaining difference between the expected and actual outcomes is what can be further explored by the excluded features: park factors, defensive positioning, weather conditions, and more.

Sharpe covers the reliability and predictability of xwOBA/xwOBACON in his article. He concludes that while these two metrics have relatively strong predictive power year-to-year (and first-half to second-half within a season), the marginal increase in correlation compared to their raw counterparts, wOBA/wOBACON, is not enough to use these metrics for predictions. Furthermore, barrel percentage has a higher correlation to the next year’s wOBACON, which proves additional support to this argument.

Expected outcome statistics were not designed to be predictive, as Sharpe and __Tom Tango__ point out. These statistics were designed to describe batter skill by focusing on what the batter can control: exit velocity and launch angle (and sometimes sprint speed). Without the likes of defensive positioning, park factors, or weather conditions, these are context-neutral statistics. By excluding these and ignoring context, we are able to measure the described player’s talent and compare players and events on even playing fields.

**Other Expected Metrics**

The sabermetric community may find a few other “expected” metrics familiar, such as xERA or xFIP. There’s also similarly named likelihood metrics like called strike probability or swinging strike probability. While these are calculated with vastly different formulas, the methodology of building a model trained on the truth ties the forever-known logical baseball ideas with statistical modeling to uncover new principles in baseball analytics.

These new principles have guided us since their introduction just a few years ago. The power of Statcast and other homemade sabermetrics continue to move the needle forward in our game. Using these expected statistics has given the baseball community another tool to identify under the radar players (or the opposite). xBA, xSLG, and xwOBA have made their home in the minds of eager baseball fans that have the same desire to understand why baseball acts the way it does sometimes. I wouldn’t be surprised to see these metrics eventually make their way onto the back of baseball cards. For now, let’s all rejoice at the scoreboards and TV broadcasts that showcase the expected batting average of a batted ball.