What does a 100mph swing speed mean?

High school senior Luke Shilling made a big impression at this weekend's Perfect Game Pitcher/Catcher Indoor Showcase in Cedar Rapids, Iowa. Shilling, ranked by Perfect Game as one of the top 100 high school pitchers, dazzled with his offerings and is now hoping for an early selection in MLB's Rule 4 draft this June.

But this showcase is one of dozens, with hundreds of prep standouts and would-be pros showing off their stuff. What made Shilling's outing worth writing about was his performance in the batting cage. According to the Zepp sensor affixed to the bottom of his bat, the Pontiac, Mich., product had a bat speed at impact of 103 mph. It was the highest bat speed recorded by Perfect Game since they began their partnership with Zepp last summer.

New @PerfectGameUSA bat speed impact record set by Luke Schilling @PGShowcases! #ZeppYourSwing http://t.co/07SabHe5VX pic.twitter.com/ViM6XTxAnU

— Zepp Labs (@ZeppLabs) February 8, 2015

Zepp, naturally, was only too happy to share this impressive feat. And the truth is, as this type of sensor becomes more widely used, these types of readings will become as common as radar gun readings* for pitchers. It's up to us, then, to determine how impressive a 100-mph swing is, and how it translates into the pros.

* - Sorry, TrackMan: As common as radar gun and spin readings.

The first point of reference is to compare this bat speed to the professionals. Based on their testing of professional hitters, Zepp's app says the typical bat speed at impact is between 70 and 90 mph. Additional data from the app seems to confirm this: most of the example swings from major league stars are in the high 80s or low 90s, with one swing from Mike Trout producing a bat speed of 99 mph at impact, and one from Hunter Pence topping out at 106 mph.

It's not fair to compare the reigning AL MVP's swing to that of a high school senior, but it's worth noting Shilling's attack angle was negative, suggesting a hard-hit ground ball, whereas both Trout and Pence's attack angle was positive, which is more likely to produce a line drive.

Leaving that aside, I'll look at a 100-mph swing in a vacuum. How does that swing translate into a batted ball distance? To start, consider this formula from baseball physics guru Alan Nathan to determine the batted ball exit speed (v_b) from swing speed (v_s) and pitch speed (v_p):

v_b = e_av_p + (1 + e_a)v_s

The final missing piece, e_a, is the collision efficiency of the bat and depends on where the ball impacts the bat. For the "sweet spot" of a typical wooden bat, this variable is usually around 0.1, but can top out around 0.2. That means that, for a ball hit off a tee, a 100-mph swing will produce an exit velocity of 120 mph in the best-case scenario, and a 110 mph exit velocity for the average "well-struck" ball. Using this Baseball HR Simulator, it is estimated that a baseball that leaves the bat at 120 mph, launched at the right angle, could travel as far as 470 feet!

Even with all the caveats and conditions in that last paragraph -- the batter has to hit the ball dead center on the sweet spot with the exact right launch angle -- that number seems awfully high. It gets even worse when we add an actual pitch to the equation. Let's take an average four-seam fastball, which leaves the pitcher's hand between 90 to 95 mph and crosses home plate around 85 mph. Plug that into the equation above and the resulting exit velocity is 137 mph, enough for a 560-foot home run!

This number also seems crazy high, but there's a little bit of public tracking data of batted ball speed in MLB to make this seem more reasonable. Sportvision's HITf/x does estimate exit velocity, but we don't have access to most of that information. What we do have is the sample data from April 2009, where the maximum exit velocity recorded is 138.5 mph on a Ronnie Belliard line out off an 87 mph Ricky Nolasco offering. Plug this back into the formula (with an e_a of 0.2), and it suggests a bat speed of 101 mph. But Belliard's liner and a Placido Polanco double-play grounder are the only two balls hit in that month with exit velocities over 130 mph.

The other HITf/x source is from ESPN's Home Run Tracker. As a sample, here are the top home runs hit in each of the last five seasons by exit velocity, along with the speed measured by PITCHf/x when the pitch crossed the plate and the estimated bat speed. Note that the estimated bat speed was calculated assuming an e_a of 0.1: that most home runs were hit off the sweet spot of the bat seems like a reasonable assumption.

This chart makes it seem like a 100-mph swing is right around the upper limit of what the best hitters in the world can achieve. Still, there are a lot of assumptions to get here. For starters, I'm assuming that both the HITf/x exit velocity (which is actually measured a few feet after impact and then, I imagine, adjusted for the loss of velocity caused by air resistance) and the Zepp sensor (which the company claims is accurate to within a few miles per hour) are accurate.

The biggest assumption involves where the ball impacts the bat and thus the collision efficiency. I've assumed that these balls are hitting an inch or so off the exact sweet spot of the barrel, but if I instead assume that the fastest home runs are hit right at the node, then MLB swing speeds seem to top out around 90 mph. A 100-mph swing is probably behind the legendary homers of Ted Williams and Mickey Mantle, but whether those particular home runs are remarkable because they swung much harder than their peers or because they happened to get an impact exactly six inches from the end of the bat is hard to say.

And of course, this is not to suggest that Luke Shilling could be dropped into a major-league game tomorrow and start hitting tape measure homers. As Zepp's baseball product manager Trevor Stocking pointed out on Twitter, it's likely that not every MLB swing is at max effort, since that swing is more difficult to control, and perhaps less likely to lead to solid contact. Other people I talked to agreed: youth baseball coach Bryan Eisenberg suggested swinging down on the ball (as evidenced by Shilling's attack angle) tends to produce higher-than-usual bat speeds at impact. But, of course, swinging down like that won't necessarily produce the best results, no matter how much bat speed you generate. A triple-digit speed reading will always be sexy, but as with pitchers, there's more to a good swing than just that headline number.

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Home run batted ball data courtesy of ESPN's Home Run Tracker. PITCHf/x data courtesy of MLB Advanced Media.

Bryan Cole is a featured writer for Beyond the Box Score. His own swing speed leaves a lot to be desired. You can follow him on Twitter at @Doctor_Bryan.