The greatest hitter of our generation was 101st last season in average exit velocity. One Hundred and First. Despite this, we still obsess over exit velocity and generally hate the Yankees more (if that is possible) for having the two hardest hitters in baseball at the same time. Today, we’re going to visually explore the importance of keeping a narrow range of launch angles (read: lower standard deviation of launch angle), as well as the benefit of a picking when to max out your swing (aka: higher standard deviation of exit velocity).

TROUT = (Average Exit Velocity)*(St. Dev. of Average Exit Velocity)/(St. Dev of Launch Angle)

Essentially, the formula rewards players who hit the ball harder on average, pick their spots (show a greater spread in their exit velocities) and have consistent launch angles. Having a higher exit velocity is fairly straightforward; generally speaking, hitting the ball harder is better. The other two ingredients are less intuitive at a glance, but we’ll explore visual evidence as to why they are important.

Let’s begin with a simple chart, wOBA (on balls in play) by Launch Angle, for all balls in play captured by StatCast. wOBA values are calculated based on 2017 weights for all seasons in the data set.

wOBA by Launch Angle (2015-2017)

Launch angle, when ignoring velocity, shows an interesting value curve, with a steep, exponential gains in wOBA, peaking at 12 degrees, followed by a valley which peaks again around 24 degrees, then falls sharply as you get into the proverbial “can of corn” type of fly balls. This brings us to our second chart, this one with the percent of balls in play that occur at each launch angle bucket overlaid on the wOBA curve.

wOBA by Launch Angle and % of BP by Launch Angle (2015-2017)



The lavender line represents the frequency that a ball in play is recorded at that launch angle. Bear in mind that certain launch angles may be biased by StatCast’s inability to capture certain data points, however, it is interesting that the wOBA peak intersects quite neatly with the In Play % peak at around 12 degrees, suggesting that batters do optimize their launch angles for wOBA. The important takeaway from the above chart is that the distribution of launch angles is wider than the distribution of value, implying that a tighter distribution of launch angles, which in mathematical terms implies a lower standard deviation, will generally be better.

If we assume that a batter has already optimized his swing so that his mean launch angle will fall in an area that does maximum damage, he will benefit greatly by keeping as many balls in play as possible closer to that mean. Thus, players who exhibit a lower standard deviation of launch angle should, in theory, provide more baseball value for the same exit velocity.

No Relationship Between Standard Deviation of Launch Angle and wOBA

Looking for a correlation between standard deviation of launch angle and wOBA will give you a big fat goose egg. How do we square that with the argument presented above? Two ways: First, not all players are optimizing their launch angle, meaning some players may benefit from a wider distribution (if their average is out of the sweet spot). This is likely true for lesser players who lack the ability to control launch angles. However, for a player of Mike Trout’s caliber, who makes consistently solid contact, tightening up his distribution of launch angles will generate significant value.

Second, some players will employ different swings for different counts, with a bigger, higher launch angle swing earlier in the count and a tighter, line drive, lower launch angle with two strikes. For certain players, a higher standard deviation would be a good thing (see Josh Donaldson later).

Smaller Spread of Launch Angles = Higher BABIP

Standard Deviation of Launch Angle to BABIP | R2 0.13

We see some evidence that having a lower standard deviation of launch angle is an important contributor to having a higher BABIP. This makes intuitive sense, since presumably this is in a sense measuring a player’s hit tool — the ability to make consistent, optimal launch angle contact. In case you were wondering, lower standard deviation of launch angle is not correlated to a lower average launch angle:

St Dev. of Launch Angle to Average Launch Angle | R2 0.00

In fact, it appears there’s even a slightly opposite relationship; i.e., higher average launch angles lead to a smaller range of launch angles.

What we’ve established is that there is a benefit (at least for BABIP) in having a tighter distribution of launch angles. Let’s see if this passes the sniff test and look at the top 20 and bottom 20 performers by this metric during the StatCast Era (minimum 400 balls in play).

Top 20 (Lowest St. Deviation of Launch Angle, 2015-2017, min 400 BIP)

Votto, Freeman, Cabrera, Mauer, Turner and Trout all make a lot of sense on this list.

Bottom 20 (Lowest St. Deviation of Launch Angle, 2015-2017, min 400 BIP)

Odor, Bautista, Pederson and Reynolds are all good examples of guys who are consistently inconsistent and make sense on this list. Josh Donaldson is a surprise; I’m not sure what to make of that, but it may be a picking-his-spots type of strategy, as referenced above.

Let’s detour and focus on home runs, since many players aren’t optimizing for wOBA; some are purely optimizing for homers. Additionally, some players may pick their spots when they go for a home run swing. Specifically, if a batter keys in on a pitch that he knows he can drive at the optimal home run launch angle of 28 degrees, the gains for hitting it harder are exponential.

A Hardball Times Update by Rachael McDaniel Goodbye for now.

Probability of a Homer Run, by Launch Angle and Exit Velocity

There is exponential benefit to hitting the ball harder once you hit that 95 mph-plus threshold. An exit velocity of 105 mph hit at an approximate launch angle of 28 degrees will be a home run approximately 90 percent of the time, compared to 50 percent at 100 mph and 17 percent at 95.

Probability of a Home Run, 28 Degree Launch Angle by Exit Velocity

The above chart paints a clear picture of the incremental benefits of swinging harder, with near linear gains from 95 mph to 105 mph. This indicates that picking spots to swing harder, as measured noisily by the standard deviation of exit velocity, is a potential indicator of success. This is not a new concept; Mike Podhorzer introduced this for his pre-StatCast xHR/FB formula, where a greater distribution of fly ball distance was a strong predictor for HR/FB. Not surprisingly, Mike Trout did well in this metric as well.

Let’s tie this back to the formula introduced at the top of the page, specifically a metric that involves just three ingredients, average exit velocity (higher = better), standard deviation of exit velocity (higher is better) and standard deviation of launch angle (lower is better). While these standard deviations may work this way for some batters, it may not work for all batters. One batter it most certainly works for is Trout, who ranks first for all batters with at least 400 balls in play in the StatCast era.

TROUT = (Average Exit Velocity)*(Standard Deviation of Average Exit Velocity)/(Standard Deviation of Launch Angle)

TROUT 2015-2017 (Min 400 BIP) Batter Name TROUT avg Exit Velo SD Exit Velo SD Launch Angle wOBA Mike Trout 65.57 91.65 15.30 21.39 0.491 Brandon Belt 63.18 89.01 14.02 19.76 0.427 J.D. Martinez 61.77 91.68 14.94 22.17 0.506 Miguel Cabrera 61.53 93.59 13.73 20.88 0.425 Domingo Santana 61.04 90.35 14.25 21.09 0.475 Willson Contreras 60.53 88.64 16.41 24.03 0.428 Giancarlo Stanton 59.75 94.83 16.63 26.39 0.499 Avisail Garcia 59.50 90.12 15.34 23.24 0.388 Wilson Ramos 59.21 90.40 15.31 23.38 0.353 Starling Marte 59.03 86.95 15.94 23.47 0.387 Tommy Pham 58.77 91.21 15.27 23.70 0.464 Tim Beckham 58.56 88.78 15.64 23.70 0.428 Paulo Orlando 58.36 89.80 14.22 21.88 0.361 George Springer 58.06 89.91 15.82 24.51 0.412 Corey Seager 58.05 90.75 14.17 22.15 0.436 Carlos Correa 57.97 91.08 15.03 23.61 0.417 David Freese 57.89 89.98 14.44 22.44 0.387 Trey Mancini 57.71 89.14 15.93 24.61 0.447 Anthony Rizzo 57.63 89.35 15.05 23.33 0.398 Steven Souza Jr. 57.63 89.70 15.32 23.85 0.434 Eric Hosmer 57.52 91.59 14.78 23.53 0.390 Jorge Soler 57.48 91.80 14.32 22.87 0.390 Freddie Freeman 57.40 91.03 13.14 20.84 0.466 Nicholas Castellanos 57.33 89.10 12.88 20.01 0.404 Christian Yelich 57.29 92.11 13.81 22.21 0.398 Derek Dietrich 57.23 86.36 15.43 23.29 0.377 Joey Votto 57.21 89.18 13.17 20.53 0.455 Brandon Moss 57.14 89.68 15.26 23.94 0.405 Chris Davis 57.06 91.80 13.45 21.64 0.481 Jose Abreu 56.76 91.00 14.54 23.31 0.425

We see an interesting list of names, with a couple of weird ones like Brandon Belt, Tim Beckham and Paulo Orlando. This metric is more of an elucidation of what Trout is trying to do, rather than a metric looking to unearth value in heretofore undervalued guys like Paulo Orlando. Here’s the same metric, broken out into player-seasons:

TROUT by Season (2015-2017 min 150 BIP) Batter Season TROUT avg Exit Velo SD Exit Velo SD Launch Angle wOBA Aaron Judge 2017 70.73 95.45 16.92 22.84 0.592 Mike Trout 2015 67.35 93.26 14.75 20.43 0.506 Giancarlo Stanton 2015 67.16 98.60 14.73 21.63 0.533 Domingo Santana 2016 66.88 93.84 14.26 20.01 0.464 Brandon Belt 2016 65.63 87.54 14.55 19.40 0.426 Ian Happ 2017 65.48 89.31 16.54 22.56 0.488 Mike Trout 2017 65.16 89.33 17.00 23.31 0.491 Jorge Soler 2015 64.29 92.65 14.39 20.74 0.424 Alex Avila 2017 64.19 91.35 13.28 18.90 0.483 J.D. Martinez 2017 63.60 91.34 16.24 23.32 0.573 Brandon Belt 2015 63.51 90.03 13.66 19.37 0.450 Miguel Cabrera 2016 63.41 94.56 13.42 20.01 0.453 Steven Souza Jr. 2015 63.34 89.43 17.05 24.07 0.425 Michael Morse 2015 63.02 91.35 14.43 20.91 0.360 Mike Trout 2016 62.98 91.76 14.28 20.81 0.476 Tommy Pham 2017 62.90 90.08 15.92 22.80 0.467 Nelson Cruz 2015 62.54 93.61 15.12 22.63 0.499 Jonathan Schoop 2015 62.52 90.45 15.19 21.97 0.416 David Freese 2016 62.38 91.30 13.57 19.86 0.426 Wilson Ramos 2015 62.23 91.18 14.91 21.85 0.303 Miguel Sano 2017 62.16 93.32 16.68 25.04 0.550 Willson Contreras 2017 62.12 88.94 17.52 25.08 0.426 J.D. Martinez 2015 61.91 91.82 14.81 21.96 0.475 Matt Carpenter 2015 61.84 89.35 12.97 18.75 0.425 Avisail Garcia 2016 61.65 91.08 15.46 22.84 0.360 Yasmany Tomas 2015 61.30 90.26 14.26 20.99 0.390 Joey Votto 2015 61.10 90.44 13.31 19.70 0.471 Miguel Cabrera 2015 61.04 94.45 13.45 20.82 0.454 Anthony Rizzo 2015 60.90 89.18 14.69 21.51 0.392 Rafael Devers 2017 60.87 90.27 17.95 26.61 0.415 Joey Gallo 2017 60.83 93.89 15.99 24.68 0.542 Kennys Vargas 2017 60.62 86.59 16.62 23.74 0.442 Paulo Orlando 2016 60.60 90.62 13.96 20.87 0.387 Starling Marte 2016 60.56 87.88 15.36 22.28 0.410 Jorge Bonifacio 2017 60.46 88.04 16.38 23.85 0.414 Brandon Moss 2015 60.37 89.75 15.65 23.27 0.380 George Springer 2015 60.30 90.38 15.59 23.36 0.424 Carlos Correa 2017 60.25 90.89 15.68 23.65 0.460 Robinson Cano 2015 60.20 91.57 14.58 22.18 0.370 Chad Pinder 2017 60.15 90.04 15.30 22.91 0.407

Trout clearly dominates this metric, checking in with the second, seventh and 15th best seasons, bested only by the inconspicuous Aaron Judge.

Conclusion

The TROUT metric gives us a little insight into the game plan that Trout employs: hit the ball hard, but not too hard that it will throw off his launch angles, and pick his spots to max out and go for the home run. While this is not an approach that works for everyone, it is one Mike Trout has perfected.

References and Resources