# Separating Power Hitters with Three True Outcomes

(Evan Boyd is a senior studying statistics at the University of Wisconsin-Madison. As a writer and a data analyst, Evan is looking into sports analytics for a career. Evan also is the Station Manager at WSUM 91.7 FM Madison student radio. Feel free to reach out to him at enboyd@wisc.edu for any questions or for a resume, and follow him on Twitter @eboyd42)

Suppose batter A has 40 home runs, and batter B has 40 home runs. Let’s call batter A Miguel Cabrera and batter B Adam Dunn. Clearly, if you had to choose between the two to be on your team, you would pick Cabrera. We all know the Adam Dunn scenario – a guy who can hit lots of home runs but strike out four or five times as much.

For batters, there are three statistics that take defensive players out of the equation: home runs, walks, and strikeouts. These are called the “Three True Outcomes” and if you put it as a ratio over plate appearances, you get a pretty high ratio for power hitters. In fact, the career leaders are Adam Dunn, Ryan Howard, and Jack Cust. It also includes Barry Bonds, Mark McGwire, and Jim Thome, players with much larger skill sets.

Let’s take a look at the 30 leaders in home runs in the MLB, with various offensive numbers. I plotted wRC+ by their TTO ratio. Using `ggplot2, ` I took the data from Fangraphs and translated it into a numeric list.

```qplot(as.numeric(as.character(leaders\$wRC)), as.numeric(as.character(leaders\$TTO)),  geom="point",
scale_colour_gradient(limits=c(50, 200), low="blue", high="red") + geom_text(check_overlap = TRUE) +
#geom_point(aes(size = 2),show.legend = FALSE) +
labs(list(title = "TTO, Leaders in Home Runs", x = "wRC+",
y = "TTO Ratio",colour="Strikeouts"))
```

Three areas of players stand out to me. First are the three outliers with a huge ratio: Chris Davis, Chris Carter, and Mike Napoli. Here we have our Adam Dunn levels: low wRC+, high strikeout rates. Chris Davis either strikes out, walks, or hits a home run in more than half of his plate appearances. Carter and Davis have averages below .230, which are the worst among these players after Todd Frazier, who just so happens to have the worst wRC+ on the list.

The other area that stood out are the guys with a high wRC+ but a low TTO ratio and thus a low number of strikeouts. Mookie Betts and Robinson Cano, for example, have power but can also hit for average. Mike Trout was his own area because he stands out from the pack. Not only does he have the highest wRC+, but he has a high TTO ratio. Kris Bryant and Freddie Freeman are right up there with him.

The relationship between wRC+ and TTO Ratio does not appear to be linear. In fact, it seems completely scattered. The higher ratios appear to have a higher number of strikeouts, as noted by Davis, Carter, and Napoli. It appears that the number of strikeouts has too much of an influence on a ratio that is meant to measure positive player performance.  The correlation between the two variables is -.259… why would having a high ratio of non-defensive outcomes have a negative relationship with generating runs?

Instead of plotting TTO Ratio and wRC+, let’s plot a number with a positive correlation. Using linear weights, we can treat strikeouts as if it is going against a higher TTO ratio, thus relying on walks and home runs. We get a surprise difference:

This makes more sense: the higher of a ratio you have regarding the three true outcomes, the higher wRC+. Now, our players with very high strikeouts fit well with their wRC+ and we can separate the “Chris Davis” hitters from the “Kris Bryant” hitters. While Mark Trumbo is the leader in home runs, he is in the middle of the pack – this is because he has such a low walk rate, but does not strike out as much as Chris Davis or Chris Carter. In his historic last year, David Ortiz takes the highest ratio, which makes sense when he has just as man walks as he does strikeouts. Bryant and Trout did not move much, and while both are high strikeout players, they walk a ton as well. According to FanGraphs, Bryant and Trout have the highest WAR among these hitters.

It is time to distinguish between good hitters and homer-or-busts. Sure, Mark Trumbo can have 7 hits and 7 home runs, but when it is in 40 at-bats and it comes with a handful of strikeouts, then he is not worth as much value as someone who cannot hit any home runs. When trying to find the best hitters against pitchers, it is best to look at the ones with the best adjusted TTO ratio.