Two years into the Statcast era, much work has been done on understanding the value of a batted ball, based on its trajectory. For example, on the first day of this year's Saberseminar Glenn Healey discussed the intrinsic value of a batted ball, modelling run value as a function of exit velocity, launch angle and batted ball direction.
What has not received any attention publicly is the probability distribution of batted ball trajectories. Understanding this distribution could inform fieder position and batter/pitcher evaluation. In this project, presented at Saberseminar 2016, I present an early attempt at methodology for predicting the joint distribution of exit velocity and launch angle, given the batter and pitcher involved in the matchup.
The Hardball Times published my article about this project on August 19, 2016. http://www.hardballtimes.com/toward-a-probability-distribution-over-batted-ball-trajectories/.
You can easily explore the results for the batter and pitcher of your choosing at https://saberpowers.shinyapps.io/trajectory-distribution.
This project is far from complete. Some potential improvements are:
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As Alan Nathan pointed out to me at the FanGraphs meetup on the Friday before Saberseminar, (roughly) 10 degrees will not be the optimal launch angle for all batters. Batters whose swing plane is 10 degrees probably have an optimal launch angle close to 10 degrees. Batters whose swing plane is 25 degrees probably have an optimal launch angle closer to 25 degrees.
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I ignore pitch type and location, but obviously these are two variables that strongly inform launch angle.
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I have presented this model, but I have not presented any validation of it. That is coming.
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The next thing to incorporate is batted ball direction (horizontal launch angle). This is a necessary step if this is ever going to be used for fielder positioning.
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Also worth including are data on non-batted balls. For example, I currently ignore swing-and-misses because there is no way to define exit velocity or launch angle on these swings. But combining these data with batted ball data are necessary to get a complete picture of the player.
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I have not (yet) considered biases due to data missing at non-random.
To conclude, this is early stage research with much room for improvement. There are aspects of the currently methodology which I find unsatisfactory. If you are interested in this endeavour or have suggestions for improving some of the methodology, please reach out to me.