*This is the first lesson in the series TwinkieTown Analytics Fundamentals. For more information on this series, what I hope to achieve by doing it, and the topics that will be covered please take a look at the series **Introduction**. If you have topics you’d like to be explored in this series, please leave a comment and let me know!*

In 2002, the Twins won the AL Central by 13.5 games and won a divisional playoff series against the heavily favored *“Moneyball”* Oakland Athletics before succumbing in the AL Championship Series to an Anaheim Angels club that would go on to win the World Series. For many Twins fans of a certain age range, the 2002 club holds a special place in our hearts and fandom. After a long drought from success in the mid to late 1990s, that club persevered through the threat of contraction, put together a winning season in 2001, and became the core of what would become a decade long run atop the AL Central. All of this, including that they vanquished the Moneyball A’s in the playoffs, make the 2002 Twins the perfect place to start our first baseball analytics lesson.

**The Flaws of Batting Average**

Perhaps the most fundamental building block of baseball analytics (or sabermetrics, if you prefer that term) is understanding what batting average – one of the game’s most recognized and long-standing metrics for describing offensive production – is and is not telling us. The 2002 Twins were led in batting average by two players who hit exactly .300 for the season: Catcher A.J. Pierzynski and outfielder Jacque Jones. Since their batting averages were the same and team-leading, we might simply conclude that the two had equally good seasons and were equally valuable to their team in terms of offensive production. After all, isn’t that how we’ve used batting average statistics throughout baseball history? It’s a convenient, tidy, single number that lets us compare players. That simplicity is what led to the nearly universal adoption of it as the preferred metric for offensive production. Is that really what it tells us, though?

Batting average is calculated by dividing a player’s hits by his number of at-bats. For Jones and Pierzynski in 2002, that meant:

- Jones: Hits = 173, At Bats = 577 | 173/577 = .300
- Pierzynski: Hits = 132, At Bats = 440 | 132/440 = .300

Right away from these numbers we can see something that merits more investigation. The players had the same batting average (.300), but Jones collected 41 more hits in 137 more at-bats than Pierzynski. Now this disparity makes sense given A.J. was a catcher and received more days off throughout the season for rest and recovery. But it should raise some questions for us about using batting average to describe total offensive production the way we often do. How can we say the value of the two players contributions were the same when one came to bat so many more times than the other and collected more hits?

Beyond that, because it’s a simple division of hits over at-bats, we’re led to believe batting average should tell us how often a player gets a hit when he comes to the plate. That’s all well and good, except that at-bats is not the measure of how many times a player comes to the plate. An official at-bat comes when a batter reaches base via a fielder’s choice, hit or an error (not including catcher’s interference) or when a batter is put out on a non-sacrifice. That seems somewhat complicated. The takeaway is that at-bats don’t count a host of things that might happen in a turn batting – like walks, hit by pitches, sacrifices, and catcher’s interference. When you compile those outcomes together over the course of a season, you could easily end up with 50, or 100, or even more times batting that are *not counted* in the batting average calculation. Those outcomes do count as plate appearances – which counts every turn at the plate. In 2002 that meant 29 times at the plate weren’t counted for Pierzynski, and 49 times for Jones. Why does batting average ignore them? Don’t those opportunities and outcomes have potential value too?

The numerator (hits) of this equation also should not escape our interrogation. Another thing we should observe is that batting average gives all hits equal value. For its purposes, a hit is a hit regardless of what kind of hit it was. A single is a hit. A homerun is a hit. And batting average says they are worth the same. But is that the best way to look at it? Aren’t hits for more bases more valuable? Going back to our example, here is the breakdown of hits for our two 2002 Twins:

In addition to having more total hits than Pierzynski, Jacque Jones also hit 6 more doubles, and 21 more homeruns. If we relied solely on batting average as our measure of offensive production, we would have no idea of this disparity.

The upshot of this is that batting average doesn’t tell us what we’ve been led to believe it does. In truth, all batting average really tells us is how often a player gets any kind of hit across less than all his times at the plate. Its biggest flaws are that it ignores potentially valuable plate appearances by relying on at-bats and it treats all hits as equal weight. These weaknesses make batting average not very informative for assessing the value of contributions of players. Jones and Pierzynski both had .300 batting averages in 2002 – but did they really have the equally productive seasons? If batting average can’t help us answer this question, which other metrics might?

**More Complete Measures: OBP and SLG**

Fundamentally, a plate appearance for a batter can end two ways – he can make an out or not make an out. In a standard, nine-inning game a team gets 27 outs to score more runs than their opponent. As outs are then a finite resource, not making an out – in any of the myriad of ways that a plate appearance can end without making an out (hit, walk, hit by pitch, and more) – is arguably the most important thing for a batter to do. On-Base Percentage (OBP) is the metric to use to measure this. When compared to batting average, OBP is a much more complete measure because it factors in events like walks and hit by pitches to the numerator and includes those two plus sacrifice hits in the denominator. This corrects for the first flaw of batting average – not including all outcomes of a player’s time at bat – that we covered above. More simply put, OBP measures the number of times a player got on base divided by the number of times he came to the plate. It can be read and spoken like batting average as well, maintaining that simplicity of a single number for comparisons. In 2002, Jones’ OBP was .341 compared to Pierzynski’s .334.

But, like before, we’re still weighting the outcomes the same with OBP. A single and homer are treated as equal value with this measure. And that is where Total Bases (TB) and Slugging Percentage (SLG) come in. These are simple calculations that help us to account for the fact that all hits are not weighted equally. To calculate total bases, you simply multiply the type of hit by the number of bases it yields. So, a single is 1 base, a double is worth 2, and so on. Revisiting the table and stats for Jones and Pierzynski, we can really start to see the differences between their performance:

Largely on account of his 21 additional homeruns, Jones accumulated 102 more bases from his hits in 2002 than Pierzynski. But talking about raw counts of bases is clunky when the language of the game tends to be more centered around rate statistics. We can take total bases and turn it into a comparable figure to batting average and OBP called slugging percentage by dividing by a player’s at-bats. In this case, using at-bats as the denominator is OK because the only source of total bases are hits, which can only be gotten in an at-bat. We aren’t leaving anything out by using at-bats here.

Collectively, batting average, on-base percentage, and slugging percentage are referred to as a player’s “triple-slash” line and they are frequently presented together (BA/OBP/SLG), often without labels. In 2002, the triple slash lines for our two examples were:

- Jones: .300 / .341 / .511
- Pierzynski: .300 / .334 / .439

These figures give us a more complete understanding of a player’s production than batting average alone. We can quickly see that Jones got on base slightly more frequently and slugged at a significantly higher rate.

But how do we know that OBP and SLG are better measures of offensive production? Again, when you get down to the very foundation of the game, an offensive player’s job is to avoid making outs in order to create opportunities to score runs. To determine which measure is best for contributing to scoring runs for the team, we can use correlation analysis.

I pulled data for the past twenty Twins’ seasons (2000-2019) from fangraphs.com and ran correlation analyses of BA, OBP, and SLG against the team’s runs scored per game. The closer to 1.00 a correlation figure is, the more closely the data are related. As the table below shows, it’s clear that on-base percentage and slugging are simply better predictors of scoring runs than batting average.

After this, you might be thinking “great, now I have to use three numbers all the time, instead of just one? It was easier when we just had one number.” Not to worry reader, the sabermetrics world understands that pain and has one final measure that takes the improvements offered by OBP and SLG and rolls them up into one clean metric.

** **

**Weighted On Base Average (wOBA)**

You might be thinking if OBP and SLG both improve on batting average’s flaws – and we want one number instead of two – maybe we can just add OBP and SLG together to get our single number. And, you wouldn’t be alone. That Frankenstein stat actually exists in the form of On Base plus Slugging (OPS) and you may have seen it in baseball writing in the past decade or so. Unfortunately, there are several reasons this approach is wrong, not the least of which is that it is mathematically incorrect (adding two fractions with different denominators). However, the bigger flaw of this would be that it assumes that a point of OBP and a point of SLG are equally valuable relative to scoring runs. And to cut to the chase and spare you the math – many analyses using historical outcomes have concluded that just isn’t true in the data. In terms of run production, a double is not twice as valuable as a single. It’s more like 1.6 times more valuable than a single. And a point of OBP is around 1.8 times more valuable than a point of SLG.

This all leads us to our final measure – and the one that you should look to use when comparing players – Weighted On Base Average (wOBA). This is a rate statistic (like BA, OBP, and SLG) that attempts to credit a hitter for the actual value of each outcome (single, double, walk, etc.). Like slugging, wOBA is based on the idea that all hits are not created equal. But it advances on the deficiencies of slugging by accurately weighting the values of the hit types and walks. Because of this, it eliminates the weaknesses that exist in batting average, on base percentage, and slugging percentage. wOBA is shown on the same scale as OBP and ultimately is the best measure we have today for measuring offensive value. wOBA is the catch-all statistic of offensive performance that gives us a handy single number to compare players on a scale we’re familiar with.

Returning to our 2002 example let’s finally and definitively answer the question – which player had the better offensive season, Jones or Pierzynski?

While their batting averages were the same, wOBA clearly shows us that Jacque Jones had the more productive season in 2002, largely on the back of his higher OBP and stronger power numbers.

** **

**Lesson Takeaways**

- Batting Average has two major flaws that prevent it from giving us the information we often think it does.
- It uses at-bats as it’s denominator, instead of plate appearances. This ignores a host of potential outcomes that may be valuable to the team (like walks and hit by pitches).
- Batting average weights all hits equally, regardless of the number of bases they achieve.
- Outs are a finite resource in baseball. Therefore, one of the most important things a batter can do is not make an out (i.e. reach base). Reaching base gives you opportunities to score runs.
- On Base Percentage and Slugging Percentage are measures that correct for the flaws of batting average by including all plate appearances and weighting the value of different hit types.
- In terms of creating runs, On Base Percentage and Slugging Percentage are better predictors of team runs scored than Batting Average.
- Weighted On Base Average (wOBA) accurately weights the value of offensive outcomes, using historical data, making it the most comprehensive statistic we have today for valuing and comparing offensive production.

**Test Your Knowledge: Five Quiz Questions**

Test your knowledge by analyzing the below blind player comparisons.

The data shown is BA / OBP / SLG / TB

In each comparison, determine which player had the better offensive season. The answers are below:

#1:

A: 2004 Twin: .246 / .340 / .363 / 103

B: 2004 Twin: .251 / .342 / .495 / 209

#2:

C: 2002 Twin: .267 / .368 / .447 / 219

D: 2002 Twin: .269 / .325 / .433 / 166

#3:

E: 2006 Twin: .278 / .336 / .490 / 273

F: 2006 Twin: .284 / .362 / .504 / 281

#4:

G: 2008 Twin: .281 / .333 / .374 / 144

H: 2008 Twin: .272 / .335 / .471 / 218

#5:

I: 2019 Twin: .253 / .311 / .469 / 215

J: 2019 Twin: .247 / .346 / .576 / 219

Answer Key **(Answer in Bold)**

#1: A = 2004 Doug Mientkiewicz (wOBA: .314), **B = 2004 ****Corey Koskie**** (wOBA: .351)**

#2: **C = 2002 Corey Koskie (wOBA: .356)**, D = 2002 Dustan Mohr (wOBA: .329)

#3: E = 2006 Torii Hunter (wOBA: .352), **F = 2006 ****Michael Cuddyer**** (wOBA: .368)**

#4: G = 2008 Alexi Casilla (wOBA: .315), **H = 2008 ****Jason Kubel**** (wOBA: .347)**

#5: I = 2019 C.J. Cron (wOBA: .325), **J = 2019 ****Miguel Sano**** (wOBA: .378)**

**References:**

The data and sources are cited or linked throughout this post. Like others who have tried to write and explain these subjects before, I relied significantly on the following resources:

- Book:
*Smart Baseball*by Keith Law - Book:
*The Book – Playing the Percentages in Baseball*by Tom Tango, Mitchel Lichtman, and Andrew Dolphin - Book:
*The Hidden Game of Baseball: A Revolutionary Approach to Baseball and Its Statistics*by David Reuther, John Thorn and Pete Palmer - Fangraphs’ indispensable library: library.fangaphs.com
- MLB’s glossary: mlb.com/glossary

*John is a contributor to Twinkie Town with an emphasis on analytics. He is a lifelong Twins fan and former college pitcher. You can follow him on Twitter @JohnFoley_21.*

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