Unlike many baseball fans, Furman math majors Andrew Hartley ’20 and Ella Morton ’20 don’t have a problem with the rise of the shift. What they do have a problem with is teams like the Houston Astros, currently battling the Washington Nationals in the 2019 World Series, earning a reputation for “radical” defensive alignments when the reality is, just like everybody else in the league, they’re not shifting nearly enough.
At least, that’s according to the results of their two-year research project, “Swing Shift: A Mathematical Approach to Defensive Shifting.”
According to the math, Hartley says, “if you’re shifting, you might as well go all the way and try to cover as many points as possible. To do that, if there’s nobody on base you really only need three infielders (not counting the pitcher and catcher).”
Hartley and Morton conducted the research with three Furman faculty members who have carved a national niche for themselves with sports-inspired mathematical research – John Harris ’91 and Kevin Hutson, both professors of math, and Liz Bouzarth, an associate math professor – as well as Ben Grannan, an assistant professor of business and accounting. Grannan helped Hartley and Morton code the program they used to solve the model they created.
A shift is when players move away from their traditional positions to areas where data show the batter is most likely to hit the ball. For example, most right-handed batters hit the ball to the third-base side of the field, and vice versa for lefties.
Shifts – even “radical” ones – are almost always limited to teams sliding their third baseman and shortstop one position to the right, or they’ll move the second baseman to the left side of the infield with the third baseman and shortstop. The outfielders remain generally where they usually are.
“We’re only putting three people in the infield, which is very different from how baseball is traditionally played. And it’s doing better than a traditional placement,” Morton said. “What’s special about what we’re doing is we’re looking at all the players. The first baseman has to stay around first base, but the other six can go anywhere.”
And that’s something even the Astros – who have ranked first, first and second over the last three years in percentage of plate appearances with a defensive shift – haven’t been doing with anything approaching regularity. The study shows that’s a mistake.
To determine where to place defensive players, Hartley and Morton collected data on every fair ball hit by 20 major league batters – 10 right-handed and 10 left-handed – from 2014 to 2018 and developed a coordinate system for the field. Then they determined the chance a fielder has of covering a given point based on his distance from it and employed integer programing to maximize batter-specific coverage, adding extra weight to areas most likely to result in extra-base hits if the ball is hit there.
They assumed no runners on base, and the pitcher and catcher weren’t part of the equation. Constraints were the first baseman had to remain close enough to cover first, and two other players had to remain in the infield.
Once they had come up with their defensive positioning, Hartley and Morton tested their model using 2019 hit data to simulate 10,000 balls in play by each of the 20 batters. The result was a 5.9-percent average drop in predicated BABIP (batting average on balls in play) for right-handed batters and 8 percent for left-handers.
For lefties, that turns a .300 hitter into one with a much-more-pedestrian .276 batting average.
“The main takeaway was four infielders was great, that’s standard, but what if you did three? Hartley said. “You might get a much better coverage because that fourth infielder might not really be doing a ton for you if you’re using the other three optimally.”
Televised games will frequently feature “spray charts” — colorful graphics that slice the field into pieces based on the percentage of time a batter hits to those areas. But moving individual players based on that information doesn’t reflect the most efficient way for a team to defend the hitter, which is what sets the Hartley-Morton model apart.
Their system places fielders in relation to one another while also incorporating risk of extra-base hits.
The students’ results “showed the optimized defensive player locations,” Grannan said. “As far as we can tell, teams were doing more of an ad-hoc approach or quick rule-of-thumb approach instead of actually trying to build a novel, mathematical model to try to best shift the players.”
Hartley and Morton didn’t realize how cutting-edge their results were until they presented at the Saberseminar in August in Boston. The Saberseminar is an annual conference devoted to the latest in baseball research and analysis and featured representatives from all 30 major league teams.
“I thought that what we were doing was kind of unoriginal; it was just uncovering what they were doing,” Hartley, a native of Annapolis, Maryland, said. “But when I talked with the head of the Astros analytics department, he was like, ‘It’s not even certain if all 30 of the teams are asking the same questions, and if they are, they’re being answered in 25 completely different ways.’ That’s pretty shocking.”