# Strikeout Rates, BaseRuns, and the Orioles

As an Orioles fan, BaseRuns is never far from my thoughts. Since 2010, the team has outperformed its BaseRuns record every year — most notably in 2012, on the way to its first playoff appearance in over a decade. This year’s Orioles are no different, sitting last week at +5 wins versus what BaseRuns models. Fans say it’s Orioles Magic. The algorithm says such performances are expected. Jeff Sullivan doesn’t know precisely what to say.

After the team signed Pedro Alvarez, I paid attention when Dave asked if they would strike out too much, where by “too much” he meant “to such an extent that they’d win fewer games than their BaseRuns record suggests.” With another season in the books, I’ve picked up here where Cameron left off, exploring the relationship between a team’s strikeout rate and its BaseRuns in a few more ways.

I gathered BaseRuns data 2002-2016 (through last Thursday) and broke it down into its batting and pitching components. When analyzing strikeouts by batters, looking at wins or run differential doesn’t make sense to me. Wins and run differential include performances by the pitching staff, but it’s not Chris Tillman’s fault that Chris Davis strikes out so often.

Linear regression shows a small but visible relationship between a team’s relative strikeout rate (K+) and its batting BaseRuns overperformance:

The plot’s arrangement and the downward slope of its regression line show that, as relative strikeout rate *increases*, batting BaseRuns overperformance *decreases*. The R^2 of this line is .069, meaning K+ explains about 7% of the variance in batting BaseRuns overperformance. This variance is 481 runs, so K+ explains about 33 runs of batting overperformance. That’s a little over three wins’ worth.

Three wins! That’s enough to raise some eyebrows. The Orioles could’ve used three wins this year. The Astros, Blue Jays, Cardinals, Giants, Mariners, Marlins, Mets, Tigers, and Yankees all could have, as well. These teams fought down to the wire for a playoff spot.

The regression equation is: Batting BaseRuns Overperformance = 58.88 – 0.59 * K+. For every one point increase in K+, a team can expect to overperform its Batting BaseRuns by 0.59 fewer runs.

At the extreme end, that’s a swing of about 3.5 wins. There’s a 59-point K+ difference between the lowest strikeout team in this data set (75, which naturally belongs to the 2015 Kansas City Royals) and the highest strikeout team (134, which belongs to the 2010 Arizona Diamondbacks).

But that’s the extreme end. As the 0.59 coefficient shows, the effect of team-wide K+ is small. I suspect that, even if it were large, it’s impossible to gain such an advantage quickly. A strikeout is the result of many physical and mental processes, only some of which a batter controls; you can’t simply tell players to hit the ball more and expect them to improve overnight. And you can’t change just one batter, because we’re talking about *teamwide* K+. The effort may not be worth the results.

Bayes’ Rule provides more evidence of a relationship between K+ and batting BaseRuns overperformance. The rule gives the probability (P) of a belief (B) given some evidence (E). Its form is:

P(belief given evidence) = (P(belief) * P(evidence given belief)) / P(evidence).

or

P(B|E) = P(B) * P(E|B) / P(E)

Bayes’ Rule is great because it accounts for the possibility that a belief is caused by something besides the evidence we have. In this case, our belief B is that a team will underperform its batting BaseRuns. Our evidence E is only that a team’s K+ is higher than average.

The Bayesian variables are as follows:

- P(B) is the probability that any team will underperform its batting BaseRuns. In this sample of 450 teams, 219 did so. This makes P(B) equal to .487.
- P(E|B) is the probability that, given a team underperforms its batting BaseRuns, it was a high-strikeout team. Of the 219 teams to underperform, 121 were high-strikeout teams. This makes P(E|B) equal to 0.552.
- P(E) is the probability that any team is a high-strikeout team. Of the 450 teams in this sample, 217 had a K+ greater than 100. This makes P(E) equal to 0.482.
- P(B|E) is then equal to (.487 * .552) / .482, or .5577.

Final answer: given a high-strikeout team, there’s a 56% chance that it will underperform its batting BaseRuns. The inverse provides support: given a low-strikeout team, there’s a 58% chance that team will overperform its batting BaseRuns. These six- and eight-point percentages may help convince a GM that pursuing a low-strikeout player is worth foregoing a high-strikeout player. But they’re not so large that a team should expect immediate or drastic improvement.

A box plot helps us understand further. I grouped teams into buckets according to their K+ to see how much each type overperformed their BaseRuns:

The thick vertical line in the middle of each box is the median batting BaseRuns overperformance for each group. Notice how this line is more to the right for low-strikeout teams than it is for high-strikeout teams. This placement indicates low-strikeout teams overperform by more runs than high-strikeout teams do.

Specifically:

- Low-strikeout teams have a higher floor of overperformance. This floor is about -47 runs (2006 Blue Jays) whereas, for the high-strikeout teams, it’s -60 runs (2005 Arizona Diamondbacks). That’s about a one-win difference.
- Low-strikeout teams have a higher ceiling of overperformance. This ceiling is about 52 runs (2005 Cardinals) whereas, for the high-strikeout teams, it’s 48 runs (2015 Minnesota Twins). That’s only a few runs. But look at the outlier points. Low-strikeout teams have a tiny chance to outperform their batting BaseRuns by 80 runs (2008 Twins) or even 98 runs (2013 Cardinals). According to this plot, high-strikeout teams have no such chance.

So, strikeout rate does affect batting BaseRuns overperformance. But the groups of teams are affected unequally, as the following plots show:

The regression lines are similar but not the same:

Group | R^2 | Regression Equation | No. of Overperformance Wins Explained by K+ |

High-Strikeout Teams | .050 | Batting BaseRuns Overperformance = 90 – 0.51 * K+ | 1.2 |

Low-Strikeout Teams | .026 | Batting BaseRuns Overperformance = 56.2 – 0.56 * K+ | 2.3 |

The graph and table show that K+ matters more to low-strikeout teams than it does to high-strikeout ones:

- For high-strikeout teams, K+ explains 1.2 wins of overperformance; for low-strikeout teams, it explains 2.3 wins of overperformance.
- For high-strikeout teams, an additional point of K+ costs them 0.51 runs; for low-strikeout teams, an additional point of K+ costs them 0.56 runs.

Based on the data above, I’m convinced a team’s strikeout rate does affect its ability to score runs relative to what BaseRuns expects. I’m also convinced the costs of implementing a low-strikeout approach teamwide outweigh the benefits, at least in the short term. If a team’s going to make meaningful decisions based on this data, they’ll have to plan for it over time. Meanwhile, Orioles fans shouldn’t worry too much if the team signs or retains high-strikeout sluggers. Fans of low-strikeout teams, though, should cast a skeptical eye at such moves or if the team’s strikeout rate suddenly spikes.

Speaking of the Orioles, aren’t they a high-strikeout team? Yes, they are. Haven’t they overperformed their BaseRuns wins for many years now? Yes, they have. But they’re overperforming at run prevention, not run scoring. That’s a discussion I’ll leave for another time.

Ryan enjoys characterizing that elusive line between luck and skill in baseball. For more, subscribe to his articles and follow him on Twitter.

Does BaseRuns account for exponential effects in the way wOBA affects runs produced? That is, runs as a function of wOBA isn’t linear, even though we usually approximate it as so.

If BaseRuns doesn’t account for the exponentiality, then that would be all you’re seeing — high strikeout teams merely tend to have a lower wOBA, which decreases runs scored more than just by the linear reduced amount of wOBA. And vice versa of course.

BaseRuns is a nonlinear formula. I’m not immediately finding a picture of the shape of the residual to see if it catches all the nonlinearity.