I would like to thank my high school math teachers for the following article.

They always told me that one day the stuff they were teaching me would come in handy. Algebra. Geometry. Calculus. This week I found a way to put those hours in math class to something worthwhile: baseball writing in a pandemic! With nothing else to do, we’re going to try to figure out the math behind one of the most memorable moments in Cardinals’ baseball history: Ozzie Smith’s 1985 NLCS Game 5 walk-off home run.

Rick Hummel’s original article from October 15, 1985 is still available at the Post-Dispatch. The Hall of Fame writer called the moment a “3000-1 shot”. Smith, a switch-hitter, had 3009 career left-handed at-bats and had not yet hit a home run.

With the game and series tied 2-2 in the bottom of the ninth, Smith stepped in to face Tom Niedenfuer. The Cardinals’ shortstop was set-up at 1-2 when catcher Mike Scioscia called for a fastball. Here’s what happened:

Let’s take this pitch and its result step-by-step, starting with velocity and location.

We have no radar gun to go by, so how do we calculate pitch velocity? Easy: *V = D/T* (velocity = distance divided by time.)

In the video above, there are 12 frames between the point the pitch leaves Niedenfuer’s hand and to when it connects with Smith’s bat. At 30 frames per second, that makes the “T” - time - .4 seconds.

What about “D” - distance? This requires some guessing. Niedenfur’s wind-up and stride (height and length) both impact the pitch’s traveled distance. A Google search produced a satisfying cheat: a pitcher’s stride averages 80-90% of his height. Niedenfuer is listed at 6’5” (77”). That nets us a stride of 62-69”, and 65.5” as a midpoint. The pitch does have a downward plane that we should account for, but without a side-angle camera, that’s hard to do. There probably is a way to use geometry here, but I’m not sure it would significantly alter the result. My simpler approach is to just subtract the stride-length from the total distance between the mound and the plate. That gives us a usable “D” of 660.5 feet from the front Niedenfur’s foot to the plate.

Following this formula, my estimated pitch speed is a satisfying 93.8 mph. A little under 94 for a hard-throwing reliever in 1985 fits well enough, as long as we acknowledge we’re fudging the numbers.

What about location? If we account for the camera angle, it appears that Scioscia set up low and slightly away. The giveaway is the position of the umpire – who appears to be looking down the inside black.

At a 1-2 count, a hard fastball low and away makes sense. Smith doesn’t have the power to turn on an outside pitch, so the Dodgers are trying to entice a weak grounder.

Smith sets up relatively close to the plate, so he can cover the outside corner in a pitcher’s count. It’s a great adjustment and it puts Smith in position to foul off anything at the knees and on the black, and the potential for solid contact if Neidenfuer misses over the plate.

Niedenfuer could not have made a worse pitch. Instead of low and slightly away, below Smith’s knees, the ball drifted back across Scioscia’s middle and up, reaching the plate belt-high.

At the point of contact, the pitch might be somewhere between 2-3 inches inside and middle/middle. The angle makes it hard to pinpoint. Regardless, it’s in the exact location for Smith to use the full force of his less-than-prodigious power.

That’s the pitch. What about the homer? Today, Statcast would immediately populate the database at Baseball Savant with the exit velocity and launch angle. Can we do the same with a calculator and some ingenuity? Probably not. But, let’s try anyway!

The video provides us with four frames of reference for the ball’s location from point-of-contact until it exits the camera’s view - which takes about .13 seconds. That gives us a clean line to calculate an angle from, if the world was 2-dimensional. It’s not, though. So we have to try and find the actual plane of the ball. The image below attempts to capture that, with the red plane roughly parallel to the foul line and the protractor image adjusted toward to match the plane. Is this perfect? Nope! The actual path of the ball is inside the plane of the foul line. The camera would cause the angle of the hit to increase the more toward center it traveled. Fortunately, as Buck says, Smith “corked one *down the line”*. Not on the line, but pretty close. So, our actual launch angle will be slightly less than what the image shows - 43 degrees. How about we say +/- 40?

That’s a great result. +/- 40 degrees places this ball at the upper end of Baseball Savant’s barrel zone but firmly in the “likely homerun” range, if the contact was hard enough. It’s the launch angle + a high *exit velocity *that produces the best chance at a HR.

I laid in bed all night Wednesday trying to figure out a way to calculate the exit velocity of Smith’s homer and I ultimately decided that I can’t

I mean, I can. Maybe. But, I won’t.

The formula would involve multi-variable integrals – a calculus concept – to calculate the rate of change in velocity of an object traveling along an arc. I did take calculus in college… a 5-hour course that met at 4:00 pm every Monday-Friday of the first semester of my freshman year at Truman State in 1996. I did manage to show up to class once or twice a week when I wasn’t busy playing soccer on the quad, and by the miracle of extra credit, I squeaked out a 79.5 in the course. Rounding for the win! All that means is that you don’t want me to do calculus.

The good news is that we don’t actually have to. Instead, we can fall back on our tried and true process of searching for comparables.

To find Smith’s exit velocity, we have to search for other balls struck with a similar launch angle – +/- 40 degrees – and distance traveled. Theoretically, balls hit the same distance at the same angle at the same altitude would have about the same velocity.

It’s a simple thing to calculate the distance of Smith’s HR: the ball struck the concrete pillar to the left of the 330’ sign, roughly 340’ from home. Since absolute precision isn’t necessary, we can set a search range of 330-350’ to go along with a 37-43 degree angle. That nets us a nice result:

This video has important significance in understanding what happened in the ninth inning of a game played on October 14, 1985... pic.twitter.com/DFnpR1rlt8

— Jason Hill (@JPHill_Cards) April 1, 2020

How rare was Ozzie’s feat? Since 2015, Cardinals batters have hit 162 balls between 37-43 degrees that traveled 330-350 feet. 159 of them were outs. Only one other ball left the ballpark. The exit velocity on Tommy Edman’s corker was 98.4 mph. Baseball Savant gathered all the results (159 outs, 1 misplayed DeJong double, 1 off-the-wall Wong triple, and 1 Edman HR) into a handy chart keyed by exit velocity and distance to give us a data cluster.

Based on these comparables, the exit velocity of Ozzie’s home run in the ’85 NLCS was probably between 94-98.5 mph.

There we go! Pitch velocity, location, launch angle, distance and exit velocity. No fancy computers or calculus required. But, did we successfully Statcast an event from nearly four decades ago? Honestly, the best we can do is make some educated guesses using fuzzy math, a bunch of assumptions, and a handful of modern comps. At best all of our results are best viewed as a range, and need to be stated with sufficient qualifiers. But, those results, qualified and ranged as they are, do help us better understand one of the more unlikely and memorable events in Cardinals history. A homer-less left-handed slap-hitter turned on a (roughly) 93.8 mph fastball that missed middle-middle (or so), driving it at (about) 96 mph over a 40 (‘ish) degree elevation to barely clear the wall and deliver a (*definitive*) NLCS win for the ages! 35 years later, I agree with Jack: Go crazy!

Credits:

Baseball Savant search parameters.

Tommy Edman HR video by MLB at Baseball Savant.

Ozzie Smith HR video by MLB on YouTube.

Special thanks to Birds on the Black’s Zach Gifford (@zjgifford) for helping me tame some unruly search parameters.