Out of Left Field

Major League Hall-of-Famer Branch Rickey once said, "When I hit a home run I usually didn't care where it went.  So long as it was a home run was all that mattered."

While that's a totally reasonable philosophy — after all, you don't earn extra runs based on distance or anything — if you want to hit home runs in the first place, where the ball goes actually matters quite a lot.  It also matters where you happen to be standing when you swing the bat.

Baseball is a little strange, as team sports go.  If you're a basketball fan, you'll remember that great scene in Hoosiers where Gene Hackman's scrappy underdogs are wandering around the enormous gym where they're about to play for the state championship, and they're looking all kinds of nervous.  He pulls out a measuring tape to check the height of the basket and says, "Ten feet.  I think you'll find it's the exact same measurements as our gym back in Hickory."  In other words, any basketball player, stepping onto any court, knows exactly what the playing field looks like.  But that's not the case in baseball: not all ballparks are created equal.

In fact, many ballparks aren't even created symmetrical.  So Branch wasn't being completely honest about his preferences.  You should care where your home run to right field went, because it's entirely possible that same shot to left field wouldn't have made it past the warning track.  And the same exact fly ball that ends up being a home run in Yankees Stadium might be an easy out in St. Louis.

Fenway Park in Boston offers maybe the most obvious example of what we're talking about.


A little weird, right?  Left field is strangely shaped,1 and at a relatively puny 315 feet, it's a lot shorter than center.   To compensate for the weirdness, so that right-handed hitters aren't constantly blasting home runs, the left field wall -- the famous "Green Monster" -- is a whopping 37 feet tall, the highest among all current MLB stadiums.

This means that a lot of deep line drives that would be home runs in other parks get sucked up by the Green Monster.  In other words, it's not just the distance of a hit that determines whether or not it will result in a home run; the trajectory matters too.  And, with a little more information, we can start to work out some facts about trajectories.

Let's say the path of any given ball is roughly parabolic.2  The average home run to left field in 2013 reached a maximum height of about 81 feet and traveled a distance of 378 from home plate.3  If we reckon that most home runs begin about three feet off the ground (roughly the middle of the strike zone), that gives us enough info to calculate an "average" trajectory that can be modeled by the equation:

height ≈ -0.0022(distance — 187.2)2 + 81

As you can see, even though the Green Monster gobbles up line drive homers, the average home run would still get out of left field in Fenway.  But what about the other stadiums?  Would the average home run be good enough in most parks?  The interactive below lets you explore this question (you can very the trajectory, too):

As you can see, the average home run would be a home run anywhere, so maybe the fact that baseball stadiums are designed so differently doesn't actually matter so much for home run hitters.  Maybe Branch was right after all.

Teachers: want to have this conversation in your class?  Check out our latest lesson, Out of Left Field!

1.  That's Lansdowne Street running right behind the stadium and screwing everything up for everybody.

2.  It's not.  Unless your stadium is in a vacuum, which is uncomfortable for fans and players alike.  But this gives us a first approximation and some tidy math.

3.  That's the estimated total distance the ball would have traveled before returning to a height level with home plate, had it not been impeded by things like bleacher seats, light poles, and spectators' faces.

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