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The Russell Branyan
homer on Aug. 21, 2010: how Hit Tracker arrived at 440 feet.
There has been a lot of
discussion about the home run Russell Branyan hit into the 4th
deck in right field at Yankee Stadium on Aug. 21, 2010. He is the
first player to have reached this deck during a major league game,
and in the wake of this notable achievement, many people quite
naturally speculated as to how far Branyan’s ball would have
gone if it been permitted to make it all the way back to field level
(this is the most widely accepted definition of a home run’s
distance).
The Hit Tracker method
of home run distance measurement involves an observation of the ball
near the end of its flight path (typically the landing location),
weather and altitude data, and a measurement of the time of flight.
These values are fed into an aerodynamic model that progressively
searches through a series of aerodynamically valid flight paths until
it finds the one that matches the observation data. It then projects
the continuation of this flight path all the way back down to field
level, and determines the home run distance.
In the case of the
Branyan homer, the ball was observed to land at a point 380 feet
horizontally from home plate, 75 feet above field level, after a
flight time of 4.69 seconds. The weather was a warm 83 degrees, with
a mere breath of wind, 3 mph, blowing in from right-center field.
The altitude of Yankee Stadium is approximately 55 feet above sea
level. When these values are fed into Hit Tracker, it determined the
trajectory as shown in the following diagram. The red dots indicate
the ball’s position every 1 second, while the green dot is the
landing point; the trajectory path after the green dot is its
hypothetical continuation down to field level.
The following screen
capture from the Hit Tracker tool illustrates just how close to home
plate the front-left corner of the 4th deck really is.
The diagram shown was created using actual blueprints from the new
Yankee Stadium, acquired by me.
The light green lines
in right field are the 2nd deck, and the yellow lines are
the 3rd and 4th decks, with heights above field
level indicated. The concentric circular arcs show the distance to
home plate in 50 foot increments. You can check these distances by
recalling that the RF pole is 314 feet from home plate, and the LF
pole 318 feet, while center field is a bit over 400 feet.
So why did this home
run seem like it went farther? First of all, any “first”
accomplishment is likely to seem magnified: after all, if no one has
done something yet, that something must be difficult, unusual and
extreme, right? However, it is worthwhile to recall that at the time
of the Branyan homer, there had only been 143 regular season games,
plus a handful of playoff games, in the history of the still-new
ballpark. Contrast this with Fenway Park, which has hosted more than
7,500 regular season games and numerous playoff games. I expect that
home runs to the 4th deck in right field at Yankee Stadium
will be infrequent, but not truly rare.
Second, nearly all home
runs that impact something high in the air (an upper deck, a foul
pole, a catwalk) seem longer than they are, because of the way air
resistance shapes the flight path of a long fly ball. The flight
path of a ball is quite asymmetrical, rocketing off the bat at high
speed and a relatively low angle, but slowing down by 50% or more
during flight and ultimately descending at a much more steep angle
(don’t believe me? ask yourself, would you rather catch a
Branyan home run just as it leaves his bat, or as it gently settles
into your bare hands in the upper deck?) All of this is due to air
resistance, which takes what would be a parabolic flight path in a
vacuum, and “flattens” it towards home plate, as can be
seen in the first diagram above. Thus when a ball hits something
high in the air, we see primarily the high-speed, flat-angle part of
the flight path, and we don’t see as much of the dying,
fluttering ending. For this reason, we attribute much longer
distance estimates to balls that land high up than we do those that
make it all the way back down to the field.
Finally, I think many
people expected a larger number for the distance on this homer
because they know Russell Branyan is an immensely powerful slugger,
and they know he can hit the ball farther than 440 feet. I can
personally attest to this; once, after taping a segment with Channel
4 in San Diego on the field at PETCO Park in June, 2007, I got the
opportunity to meet Russell Branyan, and inform him that one of his
recent home runs there, a blast to deep right center field in the
vicinity of the palm trees, had traveled 461 feet. Funny, at the
time, he didn’t seem as happy with that number as I thought
he’d be…
I guess I have some
work to do to accomplish what I’ve set out to do: help people
understand how far home runs really go, without exaggeration or
hyperbole. When I’ve succeeded, instead of being disappointed,
people will be mightily impressed when they hear that a home run went
440 feet.
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