Home Run Trajectories and Pitchers

On a recent episode of the Effectively Wild podcast, a possibly (probably?) apocryphal tale was discussed that went roughly as follows: In the late 1980s, Bo Jackson hit such a low, fast, line-drive-type home run to dead center that the pitcher at the time, Nolan Ryan, made an effort to try to catch the ball as it passed the mound.  It was discussed whether or not it was possible for a pitcher to rob a batter of a home run this way; the consensus opinion was that this was something for the online baseball world's best physicist, Dr. Alan Nathan, to look into.  While he would certainly do a better job of it than I'm about to, he does provide a trajectory calculation Excel file on his Physics of Baseball website that can provide an initial answer.

There are a number of variables that come into play here. Speed off the bat is important, of course. As a reference point, I searched around for the fastest-hit home run I could find.  This lead me to an August Fagerstom post at FanGraphs about 2014's most extreme home runs and a ball hit by Cleveland's Zach Walters in late September. Walters' home run left the bat at 122 MPH, and since I'm trying to figure out if this is even possible at all I'm going to use that as my go-to exit velocity. Park dimensions are hugely important as well, of course; any home run ball that a pitcher has a chance at will also just barely clear the fence.

Using a variety of online sources, including the Seamheads ballpark database, I collected the centerfield distances and wall heights for all active parks (summarized in a table after this paragraph).  Fenway is shortest at only 390 feet in center, but it's offset a bit by the wall being 17 ft tall there.  The optimal stadiums for this to have a chance at happening look to be Petco (396 ft x 8 ft), AT&T (399 ft x 8 ft), and Camden Yards (400 ft x 7 ft).  Horizontal launch angle was fixed at 0 degrees (that is, true dead center).  Backspin on the ball is a hugely important factor in this, but for the sake of simplicity (and this is why Alan could do it better) I kept it fixed at the spreadsheet's default 1500 RPM (and ignored any other spin directions).

Lastly, the ball's height when hit plays an enormous role. The spreadsheet was preset to two feet when I opened it, but I quickly found out that in all but the most extreme circumstances there were no catchable balls hit at two feet, so I also looked at one foot high (the lowest pitch struck for a home run last year) and 0.2 feet (approximately the lowest a ball could be without being literally in the dirt). To judge catchability I looked at ball height when it passed over the pitching rubber itself, taking the mound height into account, and the parameter I varied to look for catchable home runs was vertical launch angle.

As I briefly mentioned above, at an initial height of two feet it takes some extremes to find a catchable ball. Coming off the bat at 122 MPH, a ball hit at a vertical launch angle (VLA) of 8.9 degrees will scrape the top of the fence at both Petco and Camden, and will pass over the pitching rubber at 10.097 feet roughly a third of a second after it's hit. Now, I have absolutely no information on the vertical leaping ability of major league pitchers, but I wouldn't put it past, say, 6'10" Chris Young to be able to get that much air.  Any slower, though, and the ball won't clear the fence.

Reducing the initial height to one foot opens the possibilities up a bit wider. Sticking with 122 MPH, a VLA of 9 degrees will leave the park at Petco only and will pass over the mound at just 9.2 feet (in about the same amount of time, a third of a second from impact). An extra half-degree of VLA raises the over-mound height to 9.7 feet - still potentially in range of many pitchers - while bumping the number of parks in which it's a home run to 16!

Dropping even further to the 2" initial height allows the VLA to be as much as 10.55 degrees while still passing less than 10 feet over the mound, leading to a home run in all parks except Chase Field, Marlins Park, and Minute Maid park. However, we may have left the realm of plausibility here with our 122 MPH, 10.55 degree VLA perfectly straight, 1500 RPM backspin home run hit basically in the dirt.

Actually, we might be well out of the realm of plausibility anyway with this whole thing. A 90 MPH pitch reaches the plate in just under half a second, and for all these low-trajectory hits the time it takes to return to the mound is about 0.35 seconds, so the total elapsed time from the pitcher's release of the ball is around 0.8 seconds. I don't know enough about human reaction times to say for sure whether it's possible for a pitcher to complete their follow-through, recognize the catchable line drive, and jump high enough accurately enough to actually catch the ball in such a short period of time, but I suspect it isn't.

So, the takeaway I hope you all get from this, then, is that from a strictly physics-of-a-batted-ball perspective it almost certainly is possible for a pitcher to be able to stop a home run, but from a practical perspective I doubt it could/will ever happen.

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John Choiniere is a researcher and occasional contributor at Beyond the Box Score. You can follow him on Twitter at @johnchoiniere.