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The math behind hitting in baseball when the game's not on the line

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Now 34 and preparing for his 13th year in major league baseball, Orioles shortstop J.J. Hardy is perceived by some to be in a state of athletic decline.

The player who slugged 30 home runs as recently as 2011, for example, belted just eight last year, and injuries have forced him to miss about 30 percent of his team's games over the past two years.


But there are many ways to measure success in a sport as complex as baseball, and if a team of computer scientists at the Johns Hopkins University is to be believed, Oriole fans might have reason to feel hopeful about the two-time All-Star.

A study led by Anton Dahbura, a research scientist in the computer sciences department at Johns Hopkins, revealed a striking dichotomy: While Hardy was all but useless as a hitter in 2016 when the outcome of games was already more or less decided, he hit nearly 200 points higher — more than .290 — when the results hung in the balance.


The finding is among the more interesting nuggets to appear in "Padding the Stats: A Study of MLB Player Performance in Meaningless-Game Situations," a 55-page paper that Dahbura made public in December. A lifelong baseball nut, Dahbura wrote with the help of Jaewon Lee and Evan Hsia, student researchers and engineering undergraduates who also love the game.

The project examined how every major league hitter performed last season when, by the authors' calculations, either team in a given game had at least a 95 percent chance of winning.

Dahbura said it's beyond the study's scope to assign definitive meaning to such figures, but the baseball fan in him can't help speculating that they open up new lines of inquiry in a sport that is already one of the most rigorously analyzed in the world.

"What does it tell you that Hardy did so poorly when a game was already decided, batting a mere .100 in those situations, but so dramatically better when it wasn't?" he asked. "It's hard to say with certainty at this point, but the numbers are so striking they're very likely telling us something."

The goal of the study, Dahbura said, was to raise awareness about the fact that not all at-bats during a season are equally important.

Hardy's performance was actually a striking exception to the trend the team set out to explore.

"Some players have been able to significantly improve their overall season statistics by maximizing their performance" in so-called meaningless game situations, the article reads.

Dahbura, 56, is one of those baseball geeks lucky enough to have a passion and a gift for mathematics and statistics. It's a blend of talents in growing demand in baseball front offices as franchises increasingly seek to blend the benefits of computer-aided analytics with the intuitive wisdom of more old-fashioned scouting.


A former player, coach and manager at Johns Hopkins, Dahbura — now executive director of the Information Security Institute, a center for cybersecurity education and research within the university's computer sciences department — said he first became interested in how players perform in meaningless-game situations in 1999 and 2000, when temperamental slugger Albert Belle played for the Orioles.

He always suspected Belle tried harder, upped his game and padded his personal stats in low-pressure situations that mattered little to his team. But the databases of baseball information needed to test his hunch had not yet been created.

In the years since, Dahbura — who earned a doctorate in electrical engineering and computer science from Hopkins in 1981 — made his way through a variety of successful gigs in private business, including at Hub Labels Inc., a Hagerstown printing company his parents founded.

In 2010, Dahbura, who is known for his work with multiple community organizations in Hagerstown, became a partial owner of the Hagerstown Suns, a Class A minor league affiliate of the Washington Nationals.

His practice of donning a Suns uniform and shagging flies during batting practice has made him a local celebrity — several articles in the Hagerstown Sun have noted that the players call him "Shag" —and he counts several current big-leaguers as friends, including San Francisco Giants pitcher Matt Cain and Nationals right-hander Steven Strasburg.

The irascible Belle retired years ago, but Dahbura's interest in meaningless-game situation performance has persisted.


Last year, he and his research team began tapping into baseball databases now available to the public to quantify the effect.

They divided their project into two phases. First the researchers defined "meaningless-game situations" — somewhat arbitrarily, Dahbura conceded — as scenarios in which history shows there is less than a 5 percent chance of the trailing team overcoming its deficit.

A sample of more than 9,600 big league games played between 2013 and 2016 revealed that the threshold is met if a team has a seven-run lead in the first inning, a six-run lead in the second through seventh innings, a five-run lead in the eighth or a four-run lead in the ninth or later.

Nearly 22,000 plate appearances by 781 hitters took place under such circumstances in 2016, 11.4 percent of the more than 184,000 total plate appearances by hitters that season.

In the second phase, the team ran the numbers on every major league hitter for the year, working up lists of the top 10 players in several offensive categories. Even longtime fans might find many of the results surprising.

Some of the sport's most feared hitters performed formidably when it mattered least. Those included the Colorado Rockies' Carlos Gonzalez (10 homers) and the Toronto Blue Jays' Edwin Encarnacion (a .442 batting average, 179 points higher than his overall mark).


Closer to home, the Orioles' Manny Machado led the majors in runs batted in during meaningless-game situations — 30 of his 96 RBIs fit the category — and finished third in home runs during such situations with eight.

Utility outfielder Nolan Reimold was the only Oriole to finish in the top 10 for batting average in meaningless situations: His .400 mark topped his overall average for the season by 178 points, the sixth-highest positive differential in baseball.

The leader in that category was Seattle Mariners outfielder Seth Smith, whose .488 average and 239-point spike in meaningless-game situations easily topped his nearest competitor, former Oriole Jimmy Paredes, who played for the Toronto Blue Jays and Philadelphia Phillies last year. The Orioles acquired Smith in a trade this month.

What such figures say about a player, Dahbura said, is too early to ascertain. The success of Gonzalez, Encarnacion, Machado and others in what some call "garbage time" doesn't necessarily mean they faltered in high-leverage situations.

Baseball analysts will point out that managers routinely alter their lineups and strategies during one-sided games — putting in lesser pitchers, for example, in games that appear lost, or asking pitchers to throw more strikes when their team is far ahead.

But Dahbura is hopeful the data will inspire conversation.


He envisions a time when general managers use the statistics during contract negotiations or when coaches work with hitters to explore whether they're experiencing stress during certain game situations and how they can improve.

In his next research phase, he said, he'll work up statistical profiles for batters throughout history, including Belle, and he's working with Johns Hopkins colleagues to develop an undergraduate course in sports analytics.

Dahbura said it wouldn't shock him to see Hardy have a better-than-expected year at the plate in 2017, and he expects to keep on learning as much about baseball as he does about the complexities of business, applied math and cybersecurity.

It's a game he has loved for a long time, he said, and the possibilities are without limit.

"It's this challenge of trying to understand a game that has captured me," he said. "I've never really gotten my fill."


Mark Trumbo had 20 RBI in MGS (eighth in MLB).

Playing better in meaningless games

These major league baseball players most improved their batting averages when playing in "meaningless-game situations" (MGS).

Player - 2016 team - MGS hits/at bats - MGS batting average - overall batting average - differential

1 Seth Smith Seattle 20-41 .488 .249 0.239

2 Jimmy Paredes Tor./Phi. 12-29 .414. 222 0.192


3 Rene Rivera NY Mets 12-29 .414 .2220.192

4 Chase Utley LA Dodgers 17-39 .436 .252 0.184

5 Edwin Encarnacion Tor 23-52. 442 .263 0.179

6 Nolan Reimold Bal 12-30 .400 .2220.178

7 Kevin Kiermaier TB 12-29 .414 .246 0.168

8 Adam Lind Sea 16-40 .400 .239 0.161


9 Yangervis Solarte SD 21-48 .438 .2860.152

10 Eric Fryer StL/Pit 10-24 .417 .2670.150

Other MLB Players of note:

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12 Carlos Gonzalez COL 30-68. 441. 2980.143

19 Yasiel Puig LA Dodgers 12-30 .400 .2630.137

28 Hanley Ramirez Bos 24-59 .407 .2860.121


Orioles MGS leaders:

Manny Machado had 28 total hits in MGS, the second-highest total in baseball. He also hit 8 home runs (third in MLB) and had 30 RBI (first) in MGS.

New Oriole Seth Smith, who played for the Seattle Mariners in 2016, led the majors in MGS batting average (.448). He also hit 8 home runs (third in MLB) and had 25 RBI (third) in MSG.

Mark Trumbo hit 7 home runs in MGS (third in MLB); Chris Davis and Adam Jones hit 6 each (fourth).