Bad call, legitimate victory. The Cards won fair and square.

During the first ever National League Wild Card game, the umpires blew a big call during an important situation in the eighth inning.  See for yourself:

First off, that was a horrible call.   I know that the infield fly rule can be called even when the play is not in the infield.  Still, the ball was hit so far into the outfield, that there was no chance the baserunners could be duped into a double play.  How do we know?  The ball actually landed and the runners advanced safely.  It didn't look even close to a play that should have been an infield fly.  If infield fly had not been called, and the runners had been doubled up, there was no way the Braves were going to argue that it should have been an infield fly.  Beyond that, it was not a routine play.  The umps should not have called infield fly.  They should have just let play continue.

Side note: the Braves and their fans had every right to be upset, but throwing trash on the field was uncalled for and classless.  Yell "infield fly" at the umps, but don't create unnecessary delays and unnecessary safety risks just because there was a bad call.

So, how costly was this blown call?  We will never know, at least not until time travel is invented.  But we can make an educated estimate.  The botched call left the Braves with runners at second and third with two outs.  The Braves did not score that inning, drawing a walk but then striking out to end the frame.  Had the umpires let the play continue, like they should have, the Braves would have had the bases loaded with only one out.

What's the difference, then, between one out with the bases loaded and two outs with runners at second and third?  The best way to quantify this is run expectancy.  Run expectancy looks at the average number of runs scored, based on historical data, for every possible combination of baserunners and outs, or base/out states.  The incomparable Tom Tango has laboriously looked at every inning of every game from 1950 to 2010 and compiled data on the average number of runs scored from each base/out state.  He has compiled this data and presented it cleanly by era.

Using data from the current era of baseball (1993 to 2010) the run expectancy of the base/out state where runners are at second and third with two outs is 0.626.  In other words, with that combination of baserunners and outs, on average 0.626 runs score before the third out happens.  Slightly over a coin flip.  The Braves were on the losing side of such a coin flip during the NL Wild Card game, as they did not score that inning.

But what if there was no infield fly call?  What if the Braves had the bases loaded with only one out?  In that situation, the run expectancy is 1.631.  Or put another way, on average 1.631 runs score when a team has the bases loaded and only one out.  That is a difference of over one full run, 1.005 to be exact.  Historical data tells us that the blown infield fly call cost the Braves one run.

So did that call change the outcome of the game?  Again, we will never know for certain.  But, history shows that the Braves would have scored one additional run.  At the time, the Cardinals had a three run lead, which they maintained to the end of the game.  One more run would not have changed the outcome.  It would only make a three-run loss become a two-run loss.  Had the Braves scored that lost run, it on its own would not have been enough to win.

People will remember this game for many reasons.  It was the first game in the new playoff format.  It was Larry Jones Jr.'s last career game.  But people will most likely remember the botched infield fly rule more than anything else.  This is unfortunate, because, as the win probability chart for the game shows, the numerous fielding errors by the Braves contributed more toward the loss.

In the end, there was a bad call during an important situation, but it did not invalidate the Cardinals' win.