To the casual baseball fan the proliferation of sabermetric data and statistics in the sport may seem overwhelming and difficult to grasp; particularly with so many of these metrics getting bizarre notations like BABIP, wRAA, wRC+, and so on. These metrics deviate from the metrics most of us used growing up with the game, things like HR, BB, AVG, and RBI, both in terms of what they measure as well as their tangible-ness to the average fan watching the game. When Andrew McCutchen hits a single, most people understand that that means his Batting Average will increase by some amount. But as to what that hit meant in terms of his wRC+ or his WAR? Even if that formula was known to the average fan, you’d nearly have to be a doctoral candidate in statistics to be capable of doing that type of math in your head.

However, not all sabermetrics are quite so complex, enter On Base Percentage (OBP), Slugging Percentage (SLG), and On Base Plus Slugging (OPS). The formulas for these are much more intuitive to the average baseball fan, and go as follows;

OBP = (Walks+Hit By Pitch+Hits)/Plate Appearances

SLG = (1*1B+2*2B+3*3B+4*HR)/At Bats

OPS = OBP+SLG

OBP is similar to Batting Average (AVG) as it measures how often a player reaches base safely, however, it differs by also including walks, and dividing by plate appearances not at bats. Rather than assessing simply the ability of a player to get on base with a hit, OBP represents how often a player gets on base every time they step to the plate, as any player who gets on base is obviously more likely to score than one that does not, and is thus more valuable asset to the baseball club. In other words, if there were two players with the same AVG, but one had a OBP of .370 and the other had one of .300, the player with a .370 OBP would help their team win more games, by virtue of them getting out less frequently and helping score more runs.

SLG, is similar to batting average in that it only assess At Bats (AB), or times when the player either puts the ball in play, or strikes out but ignores walks and HBPs. Where SLG differs from AVG is that it weighs the type of hit the batter gets based on the number of bases they achieve; so a single is weighed as worth 1, a double is worth 2, triple worth 3, and home run worth 4. SLG assess a batter’s value based on the quantity of bases they collect with each At Bat, because the more bases taken in one swing of the bat, the more likely that person is to score. A runner who has just hit a triple and is standing at third base is more likely to be driven in by later batters than someone who hits a single.

OPS attempts to combine the advantages of these two statistics into one by simply adding the two together; therefore, not leaving out the value of extra base hits, like in OBP, and not leaving out the value of walks like in SLG. Despite its obvious advantages, there is a clear mathematical problem with OPS and that is that you cannot add two things without a common denominator. ½ +⅓ does not equal ⅖ but rather ⅚. Despite this logical flaw, OPS can give us a good indication of any given batter’s contribution to the team in an easily quantifiable way. Because OPS is not mathematically valid, other sabermetrics have been developed to address this issue.

The primary “rival” statistic to OPS is a stat known as Weighted On Base Average or wOBA. wOBA is calculated by weighing each outcome of a Plate Appearance in terms of their respective Run Value, which can loosely be interpreted as the likelihood of that type of hit or walk resulting in a run. To make this idea more clear here is the wOBA formula for the 2016 season;

wOBA = (0.691*uBB+0.721*HBP+.878*1B+1.242*2B+1.569*3B+2.015*HR)/Plate Appearances

In essence, the Run Value of a home run in 2016 meant that an average of 2.015 runs scored for every home run hit, and so on for singles, doubles, triples, unintentional walks, and hit by pitches.

In theory, wOBA does a better job of encompassing the entirety of a player’s offensive value to the team than OPS does, because of how it weighs each batting event; a single is more valuable than a walk in terms of possibility of runs scoring, because a player on second base can score on a single, but never can on a walk. Alternatively, OPS basically weighs walks and hits as being the exact same, each worth 1. Because of wOBA’s results-based weighing of the value of each batting event, and its avoidance of the mathematical errors, it is the preferred statistic among many online sabermetricians.

Perhaps it is simply my contrarian nature or perhaps my distaste for the easiest answer, but I decided to take a more rigorous look into this assumption that wOBA is the “better” of the two statistics. Before delving into the statistical analyses to be presented I would first like to cover a few important notes and definitions;

- The data set used was the individual season stats for each of the 30 baseball teams between 2010 and 2016, resulting in 210 unique observations and 30 groups
- I will be using various methods of statistical regressions, a method of finding the most accurate “trendline” possible through a set of data.
- The “R” I will be referring to is the “correlation coefficient” which measures how accurately the trendline in the data actually matches each real data point. R is a measure between -1 and 1, where -1 means there is a perfect negative correlation, 1 means a perfect positive correlation, and 0 means no correlation at all. “R-squared” simply means the square of R so by taking the square root of R-squared we will get the correlation coefficient, R.
- I will be testing the predictive power of AVG, OBP, OPS, SLG, and wOBA on both Runs and Wins for clubs over this 7 year time period.

**AVG**

This regression analysis shows us that AVG correlates to runs at R=SQRT(.5273)=.7262, in other words 72.62% of runs scored are explained by batting average. This isn’t bad, but we could do better.

**OBP**

For OBP we get a correlation coefficient of R=SQRT(.6976)=.8352. OBP correlates much more strongly to runs scored than AVG did, by more than 10%.

**SLG**

Here we find that slugging correlates to runs at R=SQRT(.8025)=.8958. This means that slugging correlates to runs scored better than AVG and OBP, at nearly 90% correlation and is approaching the upper limit of correlation of an even 1.

OPS

The correlation coefficient for OPS is R=SQRT(.8820)=.9391, an even stronger correlation than SLG.

**wOBA**

For wOBA we find a correlation coefficient of just R=SQRT(.8639)=.9294. So in fact, the more “advanced” metric is slightly less accurate at predicting offensive production of major league baseball teams than OPS, by about 1%.

Now what about the more important win prediction? This type of analysis is slightly more advanced, mathematically speaking, as we must find a way to control for the fact that defenses do not change that much year over year, if not we could have some event like a team that happens to have a stellar defense every year and wins most of their games because of it, and that would skew our analysis, independent of their offense. One method of doing this is to make use of something known as a fixed effects regression, which essentially controls for each specific team. What this means is that we can be more confident that the relatively consistent skill levels of defense will not have an effect on the year over year results of the regression. Due to the nature of these regressions a single graph is not possible and thus will not be included. The correlation coefficients will also be less than the correlations in relation to runs because while we have controlled for some of the aspects of defense we have not controlled for the fact that defense plays a part of wins, so it is likely there will not be a correlation much greater than 60-70%. Once again AVG, OBP, OPS, SLG, and wOBA will be the statistics analysed.

**AVG**

R=SQRT(.1283)=.3582

**OBP**

R=SQRT(.2751)=.5245

**SLG**

R=SQRT(.2670)=.5167

**OPS**

R=SQRT(.3174)=.5634

**wOBA**

R=SQRT(.3495)=.5912

What does this tell us? Well most obviously that wOBA is a better predictor of wins than OPS in this data set. Secondly, it tells us that trying to use purely offensive based statistics to predict wins is a fool’s errand. OPS correlates more strongly to the offensive output of baseball teams, which is the only impact that an offense can have on the outcome of a baseball game. It could be that there is a correlation between teams that have a good wOBA and good Defense or bad wOBA and bad defense, or perhaps it is merely random variation in the data that wOBA is a better prediction of wins. Either way, what is important is that the purpose of these statistics, OPS and wOBA, is to predict the value of a given player to their team’s offense, which is only half the game, so using something like wOBA or OPS to predict wins, which is in some part made up of the ability to play defense, is not logical. Judging these offensive statistics on anything other than the ultimate goal of an offense, getting runs, does not make sense.

What conclusions should baseball fans then take away from all this information? First and foremost wOBA and OPS are both great metrics for assessing a player’s and a team’s offensive production, each correlating to runs in the 90+% range. It is also important to note that OPS being a better predictor of runs than wOBA is a finding that is reproducible over larger, smaller, and different time periods. Therefore, those who discredit OPS because they do not approve of how it is generated fail to assess it on its statistical merits. Also this is evidence that just because a metric is more complex, it is not necessarily more accurate. Perhaps the best takeaway of all from this article, is for fans of sabermetrics; while the statistics of baseball are part of what we love about the game, there is no reason to overstate their importance, so as to make the game inaccessible to a fan who is not as fascinated by them, particularly when sabermetricians can’t even be sure that those statistics are worth the effort that went into them. OPS is an easy statistic to teach people, and perhaps more importantly, is a better predictor of offensive output than wOBA and some other advanced metrics.

Let’s Go Bucs.

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