After thinking and reading some... I would say there is a complex relationship between VAA and pitch effectiveness. That is, SwStk% = f(VAA, pitch type, pitch location, ...) -- there are other factors that affect SwStk% than just VAA. For example, this article (https://medium.com/iowabaseballmanagers/fastball-vertical-approach-angle-12e2824d245a) shows that flat VAA is best for fastballs up in the zone, while steep VAA is best for fastballs down in the zone. I'm thinking that VAA(-13 ft) is able to capture some of the dependencies embedded in these other factors. That said, my recommendation (not that you asked for it :)) would be to use the additional data (pitch type, location, etc.) in tandem with VAA to gain insight, rather than rely on the value of a non-physical quantity that is calculated from elements of VAA. In other words, VAA(-13 ft) may be a nice shortcut, but I suspect better insight could be gained by taking the longer route.
FWIW, from a human perception standpoint, I could possibly see the VAA calculated at some point a few feet *front* of home plate being more correlated to SwStk% etc., because VAA in front of home plate would seem to be the basis for a batter's swing decision.
That was my hypothesis as well, but the numbers went in the other direction. It's possible I messed things up! I would love it if someone reproduced or refuted independently.
Identifying the pitch characteristic out of the hand as it relates to swing decisions is compelling, since we know that batters make the call very early in the pitch's flight. But based on what EBP has seen here, VAA isn't that pitch characteristic.
Did you use 13 ft behind home plate? In the coordinate system that Statcast uses, I think the back of home plate is y=0. So "behind home plate" would be -13 in the expressions in the Fangraphs article, but your plots all show positive numbers.
I probably should have kept the same coordinate system. I simply added the distance into the vy_f formula. This means the absolute value of vy_flex (the flexible point) is lower (more time to slow down) and the absolute value of vz_flex is higher (more time for gravity).
13 feet behind the front of home plate, as in, halfway to the backstop, or 13 feet before the ball reaches home plate? If it's literally behind home plate, is the pitch data inferred? Moreover, what the heck could that actually mean if that's the value that correlates with SwStr% and whiff%? If it's 13 feet in front of home plate, as in 13 feet before either the batter or catcher interact with the ball, that's interesting.
I think of VAA as how the ball manages to spend as little time as possible in the path of the swing (this may not be correct - I've also seen descriptions of VAA as how the ball rises or jumps above the bat, but that always strikes me as how IVB works). But if the VAA at 13 feet in front is the value that correlates with SwStr% and whiff%, what could be happening in the final ~25% of the distance to home plate? My understanding is that batters make a swing decision very early, so it's not that they're deciding to choose something 13 feet away.
In either case, is it sufficient to conclude that Bautista and Verlander simply don't make their money through VAA but instead through IVB or IVB/s? There are pitchers who specialize in one but not the other, and some specialize in neither but had quite good fastball run values in 2023 (Webb, Bassitt). That's probably too incurious a tack to take, which is why you're the one researching, and I'm the mere spectator :)
13 feet as in behind the catcher. It’s not intuitive at all. My goal is to spur people better at math to think about VAA and that maybe it should be calculated differently.
After thinking and reading some... I would say there is a complex relationship between VAA and pitch effectiveness. That is, SwStk% = f(VAA, pitch type, pitch location, ...) -- there are other factors that affect SwStk% than just VAA. For example, this article (https://medium.com/iowabaseballmanagers/fastball-vertical-approach-angle-12e2824d245a) shows that flat VAA is best for fastballs up in the zone, while steep VAA is best for fastballs down in the zone. I'm thinking that VAA(-13 ft) is able to capture some of the dependencies embedded in these other factors. That said, my recommendation (not that you asked for it :)) would be to use the additional data (pitch type, location, etc.) in tandem with VAA to gain insight, rather than rely on the value of a non-physical quantity that is calculated from elements of VAA. In other words, VAA(-13 ft) may be a nice shortcut, but I suspect better insight could be gained by taking the longer route.
FWIW, from a human perception standpoint, I could possibly see the VAA calculated at some point a few feet *front* of home plate being more correlated to SwStk% etc., because VAA in front of home plate would seem to be the basis for a batter's swing decision.
That was my hypothesis as well, but the numbers went in the other direction. It's possible I messed things up! I would love it if someone reproduced or refuted independently.
Identifying the pitch characteristic out of the hand as it relates to swing decisions is compelling, since we know that batters make the call very early in the pitch's flight. But based on what EBP has seen here, VAA isn't that pitch characteristic.
Did you use 13 ft behind home plate? In the coordinate system that Statcast uses, I think the back of home plate is y=0. So "behind home plate" would be -13 in the expressions in the Fangraphs article, but your plots all show positive numbers.
I probably should have kept the same coordinate system. I simply added the distance into the vy_f formula. This means the absolute value of vy_flex (the flexible point) is lower (more time to slow down) and the absolute value of vz_flex is higher (more time for gravity).
13 feet behind the front of home plate, as in, halfway to the backstop, or 13 feet before the ball reaches home plate? If it's literally behind home plate, is the pitch data inferred? Moreover, what the heck could that actually mean if that's the value that correlates with SwStr% and whiff%? If it's 13 feet in front of home plate, as in 13 feet before either the batter or catcher interact with the ball, that's interesting.
I think of VAA as how the ball manages to spend as little time as possible in the path of the swing (this may not be correct - I've also seen descriptions of VAA as how the ball rises or jumps above the bat, but that always strikes me as how IVB works). But if the VAA at 13 feet in front is the value that correlates with SwStr% and whiff%, what could be happening in the final ~25% of the distance to home plate? My understanding is that batters make a swing decision very early, so it's not that they're deciding to choose something 13 feet away.
In either case, is it sufficient to conclude that Bautista and Verlander simply don't make their money through VAA but instead through IVB or IVB/s? There are pitchers who specialize in one but not the other, and some specialize in neither but had quite good fastball run values in 2023 (Webb, Bassitt). That's probably too incurious a tack to take, which is why you're the one researching, and I'm the mere spectator :)
13 feet as in behind the catcher. It’s not intuitive at all. My goal is to spur people better at math to think about VAA and that maybe it should be calculated differently.