*Note: all stats are as of August 1, 2017

I originally intended to write a post about the aspects of a four-seam fastball that are most important in generating whiffs. The correlation between fastball velocity and whiff rate on the fastball is only about 25%, so I was interested to find out whether other factors, such as vertical movement, location, or pitch usage, are better indicators of a fastball’s swing-and-miss tendencies. While some of the names at the top of the fastball whiff list were not surprising at all (Chris Sale, Jacob deGrom, James Paxton), there were several others who I was surprised to see, including Brandon McCarthy, Rick Porcello, J.A. Happ, and Clayton Richard. There was one glaring similarity between these seemingly overachieving pitchers: they throw a high percentage of sinkers.

So I looked at the correlation between whiff rate on the four-seam fastball and sinker usage, only to find that it was not only small, but also negative. However, looking at the correlation between these two variables is somewhat like a chicken-and-egg problem: does sinker usage affect a pitcher’s four-seam fastball whiff rate, or does his four-seam fastball whiff rate affect his sinker usage? The latter option certainly seems reasonable: a pitcher who is ineffective with his four-seamer is more likely to develop a sinker than a pitcher with a dominant four-seamer. For this reason, we have to dig deeper to determine if sinker usage has any effect on four-seam whiff rate.

I looked instead at only the 48 qualifying pitchers who throw a sinker at least 10% of the time (and a four-seam fastball at least 5% of the time). I found the correlation between several variables — some relating to the sinker and some unrelated to it — and four-seam whiff rate. If the variables related to the sinker have a significant correlation with four-seam whiff rate, then that implies that a pitcher’s sinker can have an effect on his four-seam fastball. The variables I looked at were the four-seam fastball’s velocity and vertical movement, the sinker’s velocity and vertical movement, and the difference between a pitcher’s four-seam fastball and sinker in both velocity and vertical movement. Here are their correlations with four-seam fastball whiff rate:

There are a few interesting things to note here. First, the four-seam fastball’s velocity seems to be just as important as the difference in velocity between the four-seamer and the sinker. While velocity is often the first thing most people look for to determine if a pitcher has a swing-and-miss fastball, relative velocity is equally as important as absolute velocity, at least when it comes to pitchers who also throw a sinker. This confirms the notion that changing speeds can upset the hitter’s timing and make a fastball seem faster than it is.

Relativity is even more important when it comes to vertical movement. While there is no correlation between four-seam whiff rate and four-seam vertical movement, there is a significant correlation between four-seam whiff rate and the difference in vertical movement between the four-seamer and the sinker (I’ll call this “v-movement difference”). This seems to show that the downward movement of the sinker makes hitters more likely to swing under the four-seam fastball; they keep the sinker in mind, so the four-seamer appears to have more vertical movement than it actually does. If this is true, then we should expect v-movement difference to have a greater effect on pitchers who throw a higher percentage of sinkers. To test whether this is true, I increased the requirement of minimum percentage of sinkers thrown in intervals of 5%, from 10% to 35%. I then found the correlation between four-seam whiff rate and v-movement difference at these different thresholds. Here are the results:

Just as we expected, the correlation between v-movement difference and four-seam whiff rate is higher for pitchers who throw more sinkers. If the relatively high correlation we observed at the 10% threshold were pure luck, then the correlations at higher thresholds would be scattered randomly. The fact that there is a clear upward trend in correlations as the threshold increases proves that v-movement difference does, in fact, have an effect on four-seam whiff rate. While this does not necessarily mean that adding a sinker will help a pitcher get more whiffs on his fastball, it does prove that the quality of a pitcher’s sinker can affect the effectiveness of his fastball. More specifically, we also learn that a good sinker, in terms of generating whiffs on the four-seamer, is one that has little vertical movement (or a lot of sink) in relation to the four-seamer.

Although strikeouts are at an all-time high, Kevin Pillar has continued to make consistent contact. Pillar’s swinging-strike rate is 8.0%, the 115^th highest mark out of 158 qualified major-league hitters. What makes Pillar interesting, however, is that he is near the top of the O-Swing% list (the percent of pitches outside the zone that a batter swings at), where he ranks 15^th in the majors with a mark of 38.1%. A low swinging-strike rate and high O-Swing% is an odd combination to have; it means that Pillar is making more contact than most, despite swinging at more would-be balls than most. It also means that he’s putting in play a lot of bad pitches to hit. Although some hitters are notoriously good at hitting pitches out of the zone (Vladimir Guerrero and Pablo Sandoval come to mind), Kevin Pillar is not, and it’s leading to a lot of weak contact for him.

Pillar’s 27.9 Hard% ranks 141^st in the majors. His 21.9 Soft% ranks as the 20^th highest. Here are Pillar’s average exit velocity, wOBA, and expected wOBA on balls in play, split into pitches in the zone and out of the zone (courtesy of Baseball Savant):

Clearly, Pillar’s weak contact is mostly coming on pitches out of the zone. I used Brooks Baseball’s zone charts to figure out exactly what pitches Pillar is chasing and hitting weakly. The main culprits appear to be fastballs in off the plate and fastballs above the zone.  He swings at these pitches 46.6% of the time and whiffs with only 11.5% of his swings. Here you can see how often he swings at fastballs in each location; here you can see how often he whiffs at them.

According to Baseball Savant, he has an average exit velocity of 73.1 mph, a .224 wOBA, and a .223 xwOBA on fastballs that are in, up, or both. For comparison, on all fastballs, he has an average exit velocity of 85.4 mph, a .302 wOBA, and a .332 xwOBA. Pillar is not only chasing fastballs out of the zone, but he’s putting them in play with regularity. This would not be a problem if he was squaring these balls up, but he’s actually one of the worst hitters in the majors when he puts these pitches in play. Out of the 135 right-handed hitters who have put at least 25 fastballs up and/or in in play, Kevin Pillar ranks 126^th in xwOBA. Meanwhile, only 15 other hitters have put more of these pitches in play.

Pillar’s biggest issue is his pitch selection. He not only swings at a lot of pitches out of the zone, but he swings at pitches that he is especially bad at hitting. However, his ability to make contact on these pitches also seems to be hurting him. Most hitters that chase pitches out of the zone as often as Pillar swing and miss much more often than Pillar does. So when they swing at a pitch out of the zone, it often only costs them a strike. Because Pillar tends to put these pitches in play with weak contact, it generally costs him an out. In fact, this is one of the reasons why we’re seeing so many hitters swing out of their shoes. Of course, part of the reason is a new emphasis on power and the belief that a strikeout is no worse than any other kind of out. But another reason is that with fewer than two strikes, swinging and missing is preferable to putting the ball in play weakly and making an out. Hitters certainly don’t come up to bat trying to swing and miss, but with fewer than two strikes, they would much rather swing and miss than make an out.

Now, I am not suggesting that Kevin Pillar should swing harder. Swinging harder would also lead to more swings and misses on pitches in the zone, which he currently hits very well. The best thing Pillar could do is lower his chase rate, as this would improve the quality of contact he makes while also putting him in more hitter-friendly counts. Of course, this is much easier said than done. While I am not going to try to predict the hitter that Pillar would be if he swung and missed more often — and I definitely won’t try to argue that he should try to miss when he swings — we can at least learn from Pillar that although contact is a good skill to have, it is not very useful without good pitch selection.

On July 19, 2017, the Colorado Rockies beat the San Diego Padres by a score of 18-4. Padres starter Clayton Richard left the game after 3 2/3 innings, having given up 14 hits and with his team down 11-0. After the game, Richard took responsibility for his rough outing, but also pointed out that the Rockies may have benefited from some luck. “It just seemed like mis-hit balls found the right spots,” said Richard. Let’s see if Richard is right; let’s try to eliminate the effects of luck and see how this game should have turned out.

Because the score of the game affects how teams play, I am only going to predict what the score should have been after four innings, at which point the Rockies had a 12-0 lead. In lopsided games, teams often rest their everyday players (as the Padres did with Wil Myers) and don’t bring in their top relievers (Kevin Quackenbush, who gave up six runs, relieved Richard with two outs in the 4^th), so it would be unfair to use what happened after the 4^th inning to estimate what the score of the game should have been.

I looked at Baseball Savant’s hit probability and expected wOBA (xwOBA) of every plate appearance in the first four innings of the game. These stats only consider a batted ball’s exit velocity and launch angle. Although I will generally refer to the difference between xwOBA and wOBA as luck, keep in mind that defensive positioning and defensive ability are also factors that can affect this difference (the Rockies are, in fact, an above-average defensive team, while the Padres are one of the worst in the National League). In the first four innings, the Padres had 16 hitters come up to the plate, and they averaged a .254 xwOBA, compared to an actual wOBA of .281, for a difference of .027 per hitter. I gave Manuel Margot’s first-inning plate appearance, in which he walked but was later picked off, an xwOBA and wOBA of 0. Meanwhile, the Rockies’ 29 hitters averaged an xwOBA of .420 and a wOBA of .664, for a difference of .244 per hitter. Two things are immediately clear. First, the Rockies certainly out-hit the Padres in the first four innings of the game. Second, as Richard noted, the Rockies’ hitters benefited from a lot of luck.

First, I will calculate the number of runs each team would have had through four innings if their wOBA was exactly their xwOBA (this estimate will be a little low for both teams, as xwOBA does not take into account that the game was played at Coors Field). To do this, I will find their weighted runs above average (wRAA), and then add that to four times the average number of runs per inning in the National League.

wRAA = ((wOBA – league wOBA) / wOBA scale) x PA

league wOBA = .320

wOBA scale = 1.25

When calculating wRAA, we run into a problem: we can’t use the actual number of PAs each team had because this number depends on the number of baserunners they had, which should change when we convert wOBA to xwOBA.  To come up with an expected number of baserunners, I added the hit probability of all balls put in play and added 1.000 for each walk and hit-by-pitch (with the exception of Margot’s 1^st-inning walk). Strikeouts, as you might expect, were worth 0 points. The Padres had 3.24 expected baserunners (.203 xOBP) while the Rockies had 11.70 (.404 xOBP). With a .203 OBP, it would take roughly 15 hitters to get through four innings (15 x .203 = 3.045 baserunners; 15 hitters – 3 baserunners = 12 outs). With a .404 OBP, it would take roughly 20 hitters to get through four innings (20 x .404 = 8.08 baserunners, 20 hitters – 8 baserunners = 12 outs). Therefore, we use 15 PAs for the Padres and 20 PAs for the Rockies (notice that reducing the number of hitters doesn’t ignore what happened to the Padres’ last hitter or the Rockies’ last nine, as I use the average xwOBA of all the hitters that came up and simply apply that to a smaller sample).

The Padres’ expected wRAA through four innings is then -.79 while that of the Rockies is 1.60. The National League averages .5533 runs per inning, which comes out to 2.21 runs per four innings. Add each team’s wRAA to this number and a reasonable score of this game through four innings would be 1.42 to 3.81 in favor of the Rockies. It is still the Rockies’ lead, but nowhere near the 12-run difference that actually took place.

Of course, we know that luck and defense do exist. Let’s say that in one of the oddest trades in MLB history, the Padres and the Rockies decided to swap their luck and their defenses before the game. I will add to the Padres’ xwOBA the difference between the Rockies’ xwOBA and wOBA and vice versa (I will call this new number “swapped wOBA”). I will do the same with the teams’ xOBP and OBP to determine the number of hitters that would have come up through four innings in this scenario.  Here’s a chart summarizing all the numbers:

Using the same process as before, we use the teams’ swapped wOBA to calculate their wRAA through four innings and add 2.21 to each. With the Rockies’ luck, the Padres would have been expected to score 4.92 runs (2.71 wRAA + 2.21) through four innings. Meanwhile, with the Padres’ luck, the Rockies would have been expected to score 4.45 runs (2.24 wRAA + 2.21) through four innings. Not only was the game not as lopsided as it appeared, but with the teams’ luck and defense swapped, the Padres would have held the lead (if you round to the nearest whole number) through four innings. That is a 13-run difference solely due to luck and defense!

Now, there is a slight issue with the calculation I performed above. I took data from only 16 Padres hitters and then applied it to 19, assuming the extra three performed at the same level as the first 16. To fix this, we can look instead at the Padres’ expected run value for only the first 16 hitters. We end up with a wRAA of 2.28. Using their swapped OBP of .385, roughly six hitters would have reached base, meaning that these 16 hitters would have come up in 3 1/3 innings. So through only 3 1/3 innings, the Padres would have had basically the same wRAA as the Rockies would have had through four. This is amazing. If only the Padres were given the luck that the Rockies received on this day, they would have at least been tied through four innings, a far cry from the 12-run deficit they unfortunately had to face.