The past couple of years have been a renewed focus on the venerable popup (infield fly). Once lumped in with all other batted balls on the other side of the fielding independent street from strikeouts, walks and home runs, they are now seen as mostly akin to strikeouts. Popups are essentially automatic outs that are reflective of pitcher skill almost completely independent of the defensive skill behind a pitcher, and have also been shown to be a repeatable skill. Hence, there has been renewed interest in popup artists like Marco Estrada and Chris Young, whose peripherals might be mediocre, but pile up these free outs at nearly double the league rate.
This got me to thinking, what is exactly is a popup? Where should the line be drawn between popups which are free outs, and flyballs or (soft) line drives that are not? If you go to Fangraphs and look at their batted ball leaderboards, which are based on play-by-play stringing from Baseball Info Solutions (BIS), you'll see a fly ball rate of 33.8%, and a popup% (IFFB%) of 9.5% of all fly balls, meaning popups are about 3.2% of all balls in play (roughly 1 in 30). This has been pretty stable over time, ranging from 3.2% to 4.2% since 2002 when the data became available.
However, there are other estimates, which tend to be much higher. Searching Baseball-Savant, which uses MLBAM/Gameday data, for balls classified popups returns 8,680 balls in 2015, which is about 6.6% of the ~130,000 balls put in ball. That's nearly twice as high, and thus twice as many implied free outs. So which is right? Anecdotally, one thing I noticed is that BIS/Fangraphs seems to have a roughly 100 foot cutoff - basically literally within the basepaths, which feels somewhat a somewhat overly strict standard since balls beyond are very routine.
It seems me to the best approach to differentiate is to look at the distance when balls start falling in, and use that as a cutoff. I downloaded all 2014 data for balls
in the air (edit: see comment below) classified as fly balls or popups by MLBAM from Baseball-Savant, and binned the data into 25 foot intervals by distance recorded, and looked at the percentage of balls that were turned into outs (avoiding any hit/error bias):
One limitation is that to the best of my knowledge these distances are estimates by the Gameday stringer, so they're not completely precise. At some point, it would be interesting to repeat this with Statcast when there's more and better data available.
As expected, balls under 125 feet are basically automatic outs. Balls under 25 feet are turned into outs 99% of the time; the intervals between 25 and 125 feet are all over 99.5%. It's only the interval of 125 to 150 feet where it falls to 98%, which is still pretty automatic. Between 150 and 225 feet, more balls fall in: bloopers between the infield and outfield, and soft liners. At this point, balls are definitely not automatic outs and so we're clearly out of popup territory. From 225 to 300 feet, almost all balls are caught again, some hard liners excepted. It's once a ball is hit 300 feet that there's a better than even chance of it going for a hit, and anything over 375 is basically never caught.
Going back to the question of what exactly should be considered a popup, it's basically impossible to distinguish any ball under 125 feet from another in terms of likelihood of becoming an out. Balls over 150 feet are not automatic outs, and shouldn't be lumped in with popups. 125 to 150 feet is a gray zone. But over 100 feet the number of batted balls (light blue on the chart) jump high enough that it's possible to drill down further, using 10 foot intervals:
Here we see the ~99% rate of turning balls in to outs extends extends to about 140 feet. From 140 to 150 feet, it falls to 97% which, is still very high, but there's a pretty clear break in the trend which continues quite linearly as distances increase.
It seems to me that roughly 140 feet is a good line for what should be considered a popup/automatic out for pitchers, and what should be classified either a fly ball or line drive. In terms of numbers, this works out to about 6,550 popups in 2014, roughly 5%. That falls neatly between the 3.2% at Fangraphs and the 6.6% Gameday number.