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The "What If's" of Win Expectancy Swings in the Cardinals-Braves Wild Card Game

The infield fly call has gotten all of the attention, but it was not the biggest swing in Win Expectancy during the National League Wild Card Game.

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In this morning's post, Dan beautifully describes MLB's new Hobbesian play-in game as a "nasty, brutish, and short Wild Card series." The all-or-nothing nature of this Leviathan has understandably caused Braves fans and the national media to latch onto the controversial infield fly rule call in the bottom of the eighth inning. The "what if" nature of the call and the game of baseball make it an enticing play; however, if we play the "what if" game, the call was not the most significant swing in Win Expectancy of the game.

The Fangraphs glossary defines the stat Win Expectancy (WE) thusly:

In the words of David Appelman, Win Expectancy (WE) is, "the percent chance a particular team will win based on the score, inning, outs, runners on base, and the run environment." These percentages are calculated using historical data, meaning if a team is losing and has a 24% win expectancy, only 24% of teams in similar situations in the past have ever come back to win.

After David Ross singled to center field off Mitchell Boggs, the Cardinals Win Expectancy (WE) fell from 91 percent to 86 percent. As you know, Andrelton Simmons hit a popup that fell after an umpire called "infield fly," which meant Simmons, the batter, was the second out. The runners advanced when the popup fell, giving the Braves runners at second and third with two outs. The Cardinals' WE shot up from 86 percent to 90 percent on the play. Had an infield fly not been called, the Braves would have had the bases loaded with one out in the bottom of the eighth. Using The Hardball Times WinProbability Inquirer, this situation would have dropped the Cards' WE to 76 percent. So, the out due to the infield fly call caused a WE swing from 76 percent to 90 percent; or, 14 percent.

The infield fly call resulted in a significant 14 percentage point swing in WE between what happened on the field and what might have happened on the field. Using the Baseball Reference WE graph as our starting point, we can see that that infield fly call wasn't the most significant swing in WE of the game if we play the "what if" game.


The Cardinals comeback and subsequent late-inning dramatics seem to have pushed the second inning out of the collective memories of baseball fans and press. In the bottom of the second, Dan Uggla drew a walk off Kyle Lohse with two outs. Ross dug in and Lohse quickly induced a 1-2 count. Working out of the stretch, Lohse threw a nasty changeup to Ross. Ross swung and missed for the third strike of the third out of the inning. But, home plate umpire called timeout after Lohse started his delivery, a questionable call that negated the strikeout. On the next pitch, Lohse threw a change that hung up and over the plate. Ross drove it into the left field bleachers to put Atlanta up 2-0 and Braves fans swung the foam tomahawks the Braves gave them for free and went into a round of their disgustingly racist chant as the Native American Lohse got a new baseball from the home plate umpire.

The WE for the Cardinals entering the Ross plate appearance was 48 percent. After the Ross two-run dinger, it plummeted by 21 points to 27 percent. Had the home plate umpire not made the timeout call after Lohse started his delivery and the strikeout had stood, the Cardinals' WE would have been 50 percent. The Cards' WE swung 23 points as a result of the strange timeout call that negated the Ross homer.


With the Braves leading 2-0 in the top of the fourth, Carlos Beltran singled to lead-off the inning. With Beltran on first, Matt Holliday dug into the batter's box. At this point in the inning, St. Louis had a WE of 31 percent. Holliday hit a grounder to third baseman Chipper Jones for what should have been a double play, but the future Hall-of-Famer slung his throw over the second baseman's head and into right field. Due to the error resulting in runners at the corners, the Cards' WE shot up by 11 points from 31 percent to 42 percent. If Jones had made a good throw and Atlanta had turned two, the Cardinals' WE would have been 22 percent. The Jones error swung the Redbirds' WE by 20 percent.

The plays that followed the throwing error by Jones made the play even bigger. By the end of the visitors' half of the fourth, the Cardinals had turned a two-run deficit to a one-run lead. Their WE rose from 26 percent to 58 percent, an increased of 32 percentage points.


With nobody out and runners on the corners in top of the third, Allen Craig came to bat. The Braves led 2-0 and the Cardinals had a WE of 42 percent. Torty's master took a great plate appearance and worked a 3-1 hitter's count. Medlen gave this professional hitter a pitch to drive and he did, sending a laser beam that short-hopped the left-field wall. Beltran scored and Holliday went from first to third on Craig's double. The Braves' lead was halved and the Cardinals' WE increased by 14 percentage points, from 42 percent to 56 percent.

If Medlen had retired Craig without a run scoring, the Cards' WE would have fallen to 34 percent. If Craig had grounded into a double play and scored Beltran, their WE would have fallen to 32 percent. The WE difference between these alternate reality outcomes and Craig's real-life double ranged from 22 to 24 points.


The second most clutch play for the Cardinals' chances of winning the Wild Card play-in occurred with Holliday at the bat in the top of the sixth. The Cardinals led 3-2 after plating three runs in the third on Kris Medlen. The young righthander had hit Holliday with a sinker that ran in during the first inning. In the third, Holliday took a similar fastball that bore in on him for a called "ball." In the fourth, Medlen ran another two-seamer in on Holliday and the slugger mashed it into the bleachers to give St. Louis a two-run lead. The Holliday homer caused the Cardinals' WE to shoot up by 13 points, from 64 percent to 77 percent. Had Medlen retired Holliday and given the Braves two outs in a one-run game during the top of the sixth, the Cards' WE would have dropped to 62 percent. Holliday's dinger pushing the St. Louis lead to two with one out was a 15 percentage point swing in WE from a Holliday out.


I'm going to cheat a little bit with this last entry. It isn't one play, but two. The Braves made two throwing errors that significantly helped the Cardinals' chances at winning the game in the top of the seventh inning. Since we're creating fanciful "what if" scenarios in the spirit of pinning last night's Cardinals win solely on an infield fly call, I'm okay with stretching my premise a bit. After all, this is an alternate reality we're imagining.

Heading into the top of the seventh inning, St. Louis led 4-2 and had a WE of 82 percent. David Freese led off the inning and reached on an Uggla throwing error. Uggla's error put a runner on second with nobody out and raised the Cardinals' WE from 82 to 87 percent. Matheny ordered Daniel Descalso to lay down a sacrifice bunt that moved Chambers to third with one out and dropped the Cards' WE by a percentage point to 86 percent.

Pete Kozma, warlock shortstop, stepped to the plate with the Braves infield drawn in and hit a grounder to short. Simmons knocked the ball down and then threw it away. Perhaps if Simmons fields the ball cleanly and makes a good throw to the plate, Chambers is cut down for the inning's second out and Kozma does not advance to second base and score on Matt Carpenter's infield single. However, Simmons made the error. After the play, the Cardinals' WE was 91 percent. After the Carpenter single, it was 95 percent.

Without the Braves' errors that helped the Cardinals to plate two runs, the St. Louis lead would have been ahead 4-2 entering the bottom of the seventh and had a WE of 78 percent. The two Braves errors in the top of the seventh contributed to a 17 WE percentage point swing in the Cardinals' favor.


Right after the infield fly call, Mike Matheny summoned Jason Motte out of the Cardinals bullpen to face pinch-hitter Brian McCann. The Atlanta backstop drew a walk, loading the bases with two outs in the bottom of the eighth of a 6-3 game. The Cardinals WE was at 87 percent as Michael Bourne dug in against Motte. The flame-throwing closer struck Bourne out to escape the bases-loaded jam. With the inning-ending out, the St. Louis WE increased 10 points to 97 percent.

If Bourn had singled home two runs, the Cardinals' WE would have fallen to 72 percent. If Bourne had singled in one run, the Cardinals' WE would have fallen to 77 percent. If Bourne had cleared the bases with a double, the Cardinals' WE would have plummeted to 42 percent. Had Bourne hit a grand slam, the St. Louis WE would have been a mere 15 percent after Bourne touched the plate to give Atlanta a 7-6 lead. Motte striking out Bourne had a WE swing of between 20 and 82 points between other "what if" occurrences.


There is no denying that the infield fly call during the NL Wild Card game was an important one. The Win Expectancy metric gives us an idea of just how important it was compared to historical outcomes and other events in the game. While the importance of the infield fly call is as plain as day, if we use the "what if" imaginings that are at the heart of the outcry over the call, it is also quite clear that it was not the most important play of the Wild Card game.