In an ordinary baseball game, a bloop hit is a fun anomaly, a nuisance to the defense. The batter might smirk knowing that he lucked into a hit, while the pitcher stands annoyed, knowing he got the exact contact he wanted and couldn’t get an out.
In 2001, Luis Gonzalez hit what is perhaps the most famous and unordinary bloop hit in MLB history:
With the weak contact of Gonzo’s hit, I have wondered: what was the probability of a batted ball like that landing for a hit? Were the Diamondbacks supremely “lucky,” or do balls like that land for hits every time?
If that hit happened today, we’d immediately have a hit probability calculation from Baseball Savant to give us an answer. Baseball Savant, of course, did not exist in 2001, so I set out to figure out the hit probability on my own. We’ll use three different methods of calculation throughout the article, starting with an approach similar to what Baseball Savant uses today:
Method 1: Exit Velocity and Launch Angle
Major League Baseball introduced Hit Probability (now called Expected Batting Average, xBA) in 2017 as a way to, well, quantify the probability of a hit using information about the ball’s exit velocity and launch angle as it leaves the bat. The metric asks: if a ball has x exit velocity and y launch angle off the bat, how often should we expect it to fall for a hit? Their model is more complicated than what I describe here, but if there are 10 balls hit at 90 MPH with a launch angle of 30 degrees and 8 of them fall for a hit, then a batted ball with an exit velocity of 90 MPH and launch angle of 30 degrees would have a hit probability (or xBA) of 80%.
Unfortunately, we have a problem: Statcast did not exist in 2001, so we do not know the launch angle and exit velocity of Gonzo’s base hit. We’ll have to use a bit of creativity, math, and Zapruder-ing to come up with an estimate for the two measures.
Alan Nathan is a certified Smart Man at the University of Illinois, and is highly respected for his research on the physics of baseball. He has a lovely tool on his site called the Trajectory Calculator that uses a bunch of Cool Math and Science Equations to spit out a batted ball distance and hang time based on launch angle and exit velocity. By watching the walk-off video, we can come up with an estimate for hang time and distance, then work backwards with the Trajectory Calculator to come up with a launch angle and exit velocity.
Hang time is pretty easy to calculate. There are 74 frames between the moment the bat hits the ball and the ball hits the grass. With a 30 frames per second video, that means the baseball was in the air for 74/30 = 2.47 seconds. A few tests with a stopwatch confirm that that’s a reasonable hang time, let’s call it 2.5 seconds.
Now, we need to figure out the batted ball distance. The video zooms in a bit when the ball hits the ground, so here is an image that is more zoomed out with a red dot showing (approximately) where the baseball lands:
After trying to figure out a precise distance by drawing many, many triangles over a baseball diamond, I couldn’t come up with anything. So, I took a guess!
It is 155 feet between home plate and the edge of the outfield grass right behind second base. The ball lands a bit beyond that point vertically, so let’s say the ball travelled 160 feet in the vertical direction. In the horizontal direction, I a bit more blind. Based on some experimentation with the Trajectory Calculator and other videos of hits that wound up in the same place, I estimate the horizontal distance as 35 feet. Finally, we can use our good friend the Pythagorean Theorem to wind up with 164 total feet travelled from home plate to landing spot.
Wonderful! After plugging in several exit velocity/launch angle combinations into the Trajectory Calculator, I ended up finding that an exit velocity of 58 MPH and a launch angle of 23 degrees results, on average, in a batted ball with 2.5 seconds of hang time, and 164 feet.
Does this estimate seem reasonable? For comparison, here is a clip of a ball hit with an exit velocity of 57 MPH and a launch angle of 24 degrees:
Nearly a mirror image of Gonzo’s hit!
Now that we have an estimate for launch angle and exit velocity, coming up with an approximate xBA is fairly simple.
From 2017-2020, there were 223 batted balls with an exit velocity between 56 and 60 MPH and a launch angle between 21 and 25 degrees. 72 of them fell for a hit. We divide 72 by 223 and find that batted balls which fall into our launch angle/exit velocity group fall for a hit 32.3% of the time. So, if Gonzo did the exact same thing today, you would log onto Baseball Savant and find an xBA for that batted ball somewhere near 0.323.
However... we are missing a couple pieces of information that will dramatically change our hit probability estimate.
Method 2: Add Launch Direction
Let’s look at two more batted balls that fall within the Gonzo walk-off launch angle/exit velocity range. Here’s one with an exit velocity of 59 MPH and a launch angle of 23 degrees:
And another one with exit velocity 57 MPH and launch angle 23 degrees:
Clearly, our first method missed something important: the direction of the ball. On these bloopers, it becomes quite important to know if the ball is going up the line or if it’s going right at a middle infielder.
Let’s look at a spray chart from Baseball Savant that shows us every batted ball that meets our launch angle/exit velocity criteria. Gray dots result in outs, while colored dots are hits:
We see a clear trend where balls hit near the foul line are more likely to result in hits, while balls up the middle are more likely to result in outs. We need some way to account for this in our new hit probability estimate.
Luckily, Statcast measures the launch direction of each batted ball. Where launch angle measures the vertical angle of the ball’s trajectory, launch direction measures the horizontal angle of the ball with respect to the middle of the field. A ball that goes right back up the middle to the pitcher’s mound has a launch direction on 0 degrees. A ball that goes down the third base line has a launch direction of -45 degrees, while a ball down the first base line has a launch direction of 45 degrees.
After watching a handful of batted balls and messing around with the Trajectory Calculator some more, I estimate that Gonzo’s walk-off had a launch direction of -10 degrees.
If we now filter only batted balls with:
- Exit Velocity: 56-60 MPH
- Launch Angle: 21-25 degrees
- Launch Direction: between -12 and 12 degrees
We end up with this spray chart:
(I am not sure what is going with those two crazy points on the chart, Savant occasionally does weird stuff with plotting hit locations)
That is 11 hits out of 89 batted balls, or a hit probability of 12.3%. By removing bloopers that go down the line, hit probability drops dramatically by about 20 percentage points.
These little jam shots up the middle do not result in base hits very often. Was Gonzo just a beneficiary of random variance, or is there something else going on?
Well, we still haven’t accounted for what might be the most important factor...
Method 3: Account for Defensive Positioning
All the batted ball metrics we have used so far completely ignore where the defense is aligned. There are interesting philosophical arguments to be had about whether this is just: for example, xBA treats a weak groundball to the left side of the infield exactly the same whether there is an overshift or not. A power-hitting lefty with the shift on might intentionally slap a groundball to the left side and nearly guarantee himself a hit, but he’ll still end up with a low xBA due to the launch angle and exit velocity of the batted ball.
What does all of this mean for Gonzo’s walk-off? Well, the Yankees shifted the infield way in with the bases loaded and only one out. This dramatically changes the probability that Gonzo’s blooper lands for a base hit.
Here’s a batted ball with almost identical exit velo/launch angle/launch direction numbers as Gonzo:
Due to where the shortstop was positioned, the only way I could see that ball landing for a hit is if Iglesias fell down (and even then, that might go as an error instead of a hit).
I went back and watched all 11 batted balls that fell for a hit that meet our exit velocity/launch angle/launch direction criteria, and assigned an explanation for the hit to each pitch.
Overshift - 3 times
Infield in - 3 times
Moderate Shift - 2 times
Ball directly up middle - 2 times
No “weirdness” - 1 time
8 times, a shift explained the base hit. 2 times, the ball went directly up the middle and split the second baseman and shortstop. Only one hit didn’t have anything out of the ordinary going on:
If the Yankees are playing straight up, Derek Jeter catches Gonzo’s hit almost every time.
Of course, Jeter was not playing straight up. Something I always thought was funny about the play is that Jeter just leaps for a ball that is probably 20 feet above his head, looking like me as a 10-year-old trying to show the coach that I’ll give my best effort for any ball. If he turned and ran to the landing spot, would he have had any chance of catching the ball?
We will now turn to another Statcast metric that focuses on the fielder instead of the batted ball: catch probability.
Catch probability is calculated in a completely different manner from hit probability. Where hit probability asks “given a ball leaves the bat at a certain speed and angle, what is the probability it falls for a hit?”, catch probability asks “given a fielder has to travel x feet in y seconds, what is the probability he makes the play?”. (There are a couple other variables involved, like direction, but this is the basic question being asked).
Baseball Savant has a lovely table that tells us the catch probabilities of a variety of hang time/distance travelled combinations. For example, an outfielder who has to run 90 feet in 4 seconds has about a 5% chance of making the catch, while an outfielder who has 7 seconds to travel the same 90 feet will make the play 95% of the time.
If we can find the hang time and Jeter’s distance from the ball when it is hit, we can come up with a catch probability.
Recall that our estimated hang time for Gonzo’s blooper was 2.5 seconds. Now, we need to know how far Jeter had to travel to catch the ball. I’ll bring back the earlier screenshot that shows the ball’s landing spot and Jeter’s starting location:
It’s a bit tough to approximate Jeter’s distance from the landing spot. I think he is about a third of the way between the second and third base bag, so 30 feet from second base. I also think that he is further from the ball’s landing spot than he is from second base, so let’s call it 35 feet.
Now, we have a hang time and a distance, so we should be able to just plug in our numbers and obtain a catch probability. Unfortunately, we run into another obstacle. Baseball Savant’s catch probability metric is intended to only be used on plays made by outfielders, all of which will have a hang time of more than 2.5 seconds. The shortest hang time that the catch probability tables show is 3 seconds. Perhaps we can extrapolate what Jeter’s catch probability was by looking at comparable hang time/distance combos:
- 3.5 seconds, 35 feet: 95.2% catch rate
- 3.0 seconds, 35 feet: 48.3% catch rate
- 2.5 seconds, 35 feet: ??? catch rate
We see a massive drop in catch probability when we move from 3.5 to 3 seconds of hang time, but again, it’s tough to say what the catch rate would be if we lose another half-second.
Let’s look at a similar situation. Here, we will move from 4 to 3 seconds instead of 3.5 to 2.5 seconds, and will look at batted balls where the defender had to travel 45 feet instead of 35 feet.
- 4.0 seconds, 45 feet: 96.2% catch rate (288 total batted balls)
- 3.5 seconds, 45 feet: 75.0% catch rate (284 total batted balls)
- 3.0 seconds, 45 feet: 1.5% catch rate (132 total batted balls)
The drop in catch probability when we lose that last half-second is massive. I feel comfortable claiming that we would see a similar massive drop in catch probability in our Jeter example. I feel especially confident in this claim when we take into consideration that Jeter needed to run directly backwards, and that he would still be accelerating, having only a second or two to actually run.
Given all of this information, I feel pretty comfortable calling the catch probability given Jeter’s position... 1%? If God came down from the heavens and told Derek Jeter “this is where the ball will land,” perhaps then he could have immediately turned and ran to the spot when the ball left the bat. Even then, I don’t know that he would have made it in time.
We end up with three different ways of calculating the hit probability of Gonzo’s walk-off:
Launch Angle + Exit Velocity: 32.3%
Launch Angle + Exit Velocity + Launch Direction: 12.3%
Hang Time + Distance from Jeter to Ball: ~99%
This is an example of what I find fascinating and fun about sabermetrics. Depending on how you view a problem and what information you decide to use, you can come up with three completely different answers to a question, all of which are completely correct! It’s a matter of figuring out which method is most useful. Sure, numbers never lie, but they also can tell many different truths.