During my junior year of high school, I took AP Economics. I found the class to be pretty interesting, and I look forward to continue studying the subject further. But this is a baseball website, and you probably don’t want to be hearing about the classes I took while in high school. However, there was an important concept I learned in AP Economics that applies to a baseball situation I recently discovered. That is, the idea of the trade-off. The trade-off is one of the most basic economic principles, something so basic that it’s subconsciously part of all of our decision-making processes, whether we decide to acknowledge it or not.

One person cannot do everything, and every decision made is at the expense of the other options. There is opportunity cost, and when calculating important decisions, one must weigh the benefits of their choice versus the costs associated with giving other choices up. That’s exactly what Yu Darvish has done this season.

Darvish had a wild start to 2019, walking hitters at an incredibly high rate. Through his first 13 starts, Darvish walked nearly 15% of batters he faced, easily the highest rate in baseball. But since then, Darvish has walked the exact same number of batters — seven — that he walked in his first start this season alone. His 2.7% walk rate during this period is now the third-lowest. Talk about regression to the mean; Darvish’s 9.2% walk rate in 2019 is now nearly identical to his career-average (9.1%).

When a pitcher starts walking fewer batters, especially when the change is drastic, it’s important to consider the process behind the results. Where are the pitches now going? Since June 10, Darvish’s zone rate has increased by five points when compared to his prior starts. His first-strike percentage has increased by nine. That seems about right, but it also creates the opportunity for more danger. Darvish could be throwing more pitches in the heart of the zone. That would certainly be reducing the number of walks he allows, but it also might be resulting in more home runs.

Spoiler alert: that is exactly what is happening:

Yu Darvish’s 2019 in Two Parts Time GS IP BF ERA FIP xFIP K% BB% HR% Before June 10 13 66.1 296 4.88 5.19 4.50 26.4% 14.9% 3.7% Since 11 65.2 257 3.97 4.29 3.20 31.1% 2.7% 5.8%

Now let’s check out what has happened to Darvish’s Heart%:

Pitch% by Statcast Attack Zone Zone Pre-June 10 June 10-Present Heart 24.0% 29.7% Shadow 42.6% 43.3% Chase 23.3% 20.2% Waste 10.1% 6.8%

During this recent stretch, Darvish has thrown nearly 30% of all pitches in the heart of the strike zone. Among pitchers with at least 500 pitches since June 10, that represents the 10th-highest rate, putting Darvish in the 94th percentile among all pitchers. Prior to June 10, Darvish’s Heart% fell into the 35th percentile. That’s a huge difference, though it’s not unprecedented in the context of Darvish’s career:

Now we can fully understand Darvish’s trade-off. In an attempt to walk fewer hitters, he started throwing more pitches in the heart of the strike zone, resulting in more home runs allowed. Is this an effective change, though? While both are not ideal, home runs are a significantly worse outcome for pitchers than walks. But has Darvish decreased his walk rate by such a significant amount that the relative increase in home runs isn’t impacting him as much?

The answer appears to be yes. Darvish’s ERA, FIP, and xFIP have all improved markedly, as demonstrated in the chart above. But, as with most things, the answer could be more complicated. Of the 15 home runs Darvish has allowed since June 10, nine of them were solo shots. On the surface, that seems unlikely to be sustained over larger samples. Perhaps Darvish is pitching differently with runners on base, but a surface-level look doesn’t suggest that is the case:

Pitch% by Attack Zone, Since June 10 Zone Bases Empty Runners On Heart 29.5% 30.0% Shadow 43.6% 42.6% Chase 20.1% 20.5% Waste 6.8% 6.8%

There must be more going on here. How is Darvish reducing his walks while increasing his strikeouts and keeping his home run rate somewhat in line with where it was to start the year? The first factor I considered was his pitch mix, and there was one stark difference between the two time periods: slider usage. Darvish threw his slider nearly 19% of time in his first 13 starts; in his last 11, he’s thrown it just 10% of the time. In terms of sheer pitch numbers, Darvish has thrown 88 fewer sliders in his last 11 starts than what would be expected had he kept his rate unchanged.

Why is this the case? Perhaps it’s because, unlike in prior years, Darvish struggled to command his slider. Because Darvish only threw 40 innings in 2018, let’s compare Darvish’s 2019 slider to his 2017 slider:

Slider% by Attack Zone Zone 2019 2017 Heart 27.1% 29.4% Shadow 39.1% 44.5% Chase 23.3% 19.6% Waste 10.4% 6.5%

There’s a near four-point jump in Waste% in 2019 when compared to 2017, and I wonder if the changed baseball could be having an impact here. Pitchers across the league have struggled with breaking ball command. Over the past five years, the league-wide slider Waste% has increased by 1.7 points; the year-over-year change is 0.8 points. The 2018 to 2019 difference is statistically significant. Furthermore, since 2002, sliders have never been less valuable. Their +0.39 runs per 100 pitches is tied for the lowest league-wide mark in this 18-year sample.

Darvish effectively replaced his slider with his cutter, a pitch that he’s thrown with much more success this year. Again, let’s compare his 2019 numbers to 2017:

Cutter% by Attack Zone Zone 2019 2017 Heart 28.8% 34.6% Shadow 44.4% 41.9% Chase 20.3% 15.7% Waste 6.6% 7.7%

One could argue that Darvish’s command of his cutter has actually improved, with more of these pitches being located in the shadow and chase zones in 2019 when compared to 2017. As a result, his swinging strike rate (17.5%) on the pitch is in the 83rd percentile among all cutters. His xwOBA against is in the 81st percentile.

Yu Darvish has made a trade-off. He’s cut his slider usage in half in favor of his cutter, a pitch he can control significantly better. With this increase in control, however, Darvish has left more pitches over the middle of the plate, and his home run rate has worsened. Darvish still might not be elite, but he is better now than he was early this season, and that is very good to see.