On-base plus slugging percentage (OPS) has become a popular metric for evaluating baseball players. OPS has the virtue of being relatively easy to calculate and providing a good general indicator of a player’s offensive production. But OPS also has some methodological flaws that limit its effectiveness. Some simple adjustments to OPS can correct for these flaws while also making it easier to incorporate other offensive statistics, like stolen bases, into the metric.
OPS dates from the 1980s and now is routinely cited in evaluations of offensive production. OPS simply adds two separate, but important hitting metrics. On-base average (OBA) looks at how often a player reaches base (through hits, bases on balls (BBs or walks), or getting hit by a pitch) as a percentage of total plate appearances. Slugging percentage (SP) assigns weights by type of hit, with singles, doubles, triples, and home runs worth 1, 2, 3, and 4 points, respectively. That amount (total bases (TBs)) is then divided by total at bats. OPS simply adds OBA and slugging percentage together. The idea is that it captures both a player’s ability to reach base and his power.
This video provides an excellent introduction to OPS. It points out both the advantages and limitations of OPS. But the video misses what may be the most obvious limitation of OPS: double counting. In the financial analysis world, double counting is a definite no-no, as shown here and here. While OBA and SP are supposed to capture different aspects of a player’s offensive contribution, hits get counted twice. Hitting a single is worth more than a walk, but is it worth twice as much, as the OPS calculation implies? The weighting appears arbitrary, with singles weighted more relative to walks than they are under other metrics like wins above replacement (WAR) and wOBA (1.25X). Adjusting this metric for when and where someone played (OPS+) can compound this problem.
An alternative approach
Eliminating the double counting problem is quite easy. A new metric, called total batting average (TBA) would be calculated as follows:
(TBs + BBs + HBP)/ (ABs + BBs +HBP)
For simplicity purposes, I didn’t count sacrifices. While a bit more complex than OPS, the TBA calculation is still quite simple. You could calculate it with a basic spreadsheet, or even pencil and paper. It’s much simpler and more intuitive than, say, wOBA or WAR.
One limitation with this approach is that it treats walks the same as singles, just like OBA. But are the alternatives any better? Did the designers of OPS intend for singles to be worth twice as much as walks?
More complex approaches to weighting types of hits, like wOBA and WAR, have their weaknesses in this respect as well. These approaches have an empirical basis; but they also imply a degree of precision that doesn’t exist in the real world. The weights assigned to each offensive event vary depending on the designer (FanGraphs vs. Baseball Reference) and can change each year as you add new data. It can also lead to some anomalous results. For example, wOBA assigns a higher weight to HBP than to BBs, even though the two results have the same impact on getting on base and advancing runners. One rationale for the higher weight for HBP is that it could indicate a more rattled pitcher, while BBs could reflect pitching around dangerous hitters. But that explanation seems to confuse correlation with cause.
Rank orders between OPS and TBA are quite similar, as shown below. They do tend to disadvantage players with high batting averages that drew relatively few walks. As a result, Mickey Mantle, who walked a lot, jumps ahead of Rogers Hornsby and Joe DiMaggio in terms of TBA.
Incorporating Stolen Bases
One advantage of TBA is that you can easily make further adjustments to get a more complete picture of offensive performance. Stolen bases (SBs) don’t figure into the OBA, SP, or wOBA components. WAR has a baserunning component, but it’s complex, context-specific, and just not very transparent. But you can easily incorporate stolen bases into TBA. Just add SBs (an extra base) to the numerator and caught stealing (an extra out) to the denominator. Some prolific base stealers have been called “walking doubles” and that’s what this revised statistic can capture.
Lou Brock had over 3,000 hits and over 900 stolen bases through the course of his career. But he doesn’t get a lot of love when it comes to most advanced baseball statistics. That’s true for WAR, which in part penalizes Brock for mediocre defensive play. But Brock also doesn’t score very high on purely offensive statistics, like OPS and wOBA, at least relative to other star players. Including his steals (and adjusting for his relatively high caught stealing totals), Brock comes out a lot stronger, as shown below.
Compare Brock to Chet Lemon. Lemon was an underrated player who comes out quite well in more advanced baseball metrics. Lemon’s OPS was 43 points higher and his TBA 54 points higher. But Lemon was also a poor baserunner with just 58 steals in 134 attempts. When we throw base stealing into the mix, Brock’s adjusted TBA is higher, .523 to .509.
Brock also rates ahead of some all-time greats in this metric. Roberto Clemente had a .317 lifetime batting average but didn’t get a lot of BBs. He also didn’t hit a lot of homers though he hit lots of doubles and triples. He ran well but didn’t steal many bases. While Clemente’s OPS was 81 points higher than Brocks, his adjusted TBA was 8 points lower.
Rickey Henderson is another player whose relative ranking improves significantly from OPS to aTBA. Although he hit for power and received a lot of walks, Henderson’s OPS of .820 ranks only 81st in OPS among left fielders. (He ranks third in WAR.) In contrast, Lefty O’Doul ranked sixth at .945. But aTBA tells a different story. Henderson jumps ahead of O’Doul, .610 to .581. Now O’Doul had a short career and is not well known outside of baseball aficionados. However, Henderson’s aTBA ranks just below the all-time leaders and alongside such greats as Henry Aaron (.609), Mike Schmidt (.610), and Willie Mays (.620).
Concluding Thoughts
Do we really need another performance metric for baseball players? The British statistician George Box once said that “all models are wrong, but some are useful.” The same goes for baseball statistics. They all have their limitations, but many can provide useful information on important dimensions of a player’s performance. There are often trade-offs between precision on the one hand and simplicity and transparency on the other. But searching for a measure that comprehensively and precisely measures performance while also being simple and transparent is like searching for the holy grail.
TBA is nearly as simple a measure as OPS but corrects the double counting problem. It’s less clear whether and to what extent that it provides a more accurate measure of offensive performance. OPS probably underrates walks relative to hits while TBA probably overrates them. But aTBA (still a simple and transparent calculation) does offer a more significant step forward by incorporating stolen bases in a clear, consistent, and easy to understand way.
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