Down by a run in the top of the ninth inning, with two out, and base runners on first and second, left-handed batter Raul Ibanez was due up for the New York Yankees. Waiting on the pitching mound for Ibanez was left-handed pitcher Phil Coke of the Detroit Tigers. In the history of baseball, this specific pitcher-batter match up had occurred four times previously, with Coke getting the upper hand in all but one occasion, which was a home run in 2009.

During the first two games of this American League Championship Series, these two player faced each other twice. The first occasion resulted in a ground out; the second, a strike out. At the time, both of these plate appearances were thought to be high leverage situations, but they pale in comparison to Tuesday night’s confrontation which would only be slightly hyperbolic to suggest was the most important at-bat of the Yankees season. The outcome of the Coke vs. Ibanez battle would decide the difference between a likely insurmountable 3-0 ALCS lead for the Tigers, and a tight 2-1 ALCS deficit for the Yankees.

Over the course of his career, Ibanez has made 1873 plate appearances against left-handed pitching, and from this sample which started being collected in 1996, we can safely say that he is a below average batter against southpaws. Over the last four years, his numbers have declined steadily, likely due to his own aging, and the fact that managers handling him have reduced his opportunities to hit against left-handers.

We consider Ibanez to be a poor hitter against the average left-handed pitcher. Phil Coke is not your average left-handed pitcher. He specializes at getting left-handed batters out. Over the course of his career, he’s faced 584 batters on the left side. Only 170 times has a lefty been able to avoid getting out. If we were to take the numbers of the left-handed batters that Coke has faced and add up their totals to pretend as though it was one player, he would be the third worst offensive player in baseball this past season.

So, we can safely say that Ibanez vs. Coke is not the best of match ups for the New York Yankees, to whom the outcome of this plate appearance is critical. We might even go a bit further and suggest that the manager of the team, Joe Girardi, should consider the other options at his disposal, which, looking at his bench, include Alex Rodriguez and Nick Swisher, both excellent hitters against left-handed pitching. So excellent in fact, that the match up would go from favoring Coke, to favoring either of these batters.

However, we can’t look only at Girardi’s bench because it’s not realistic to assume that him bringing in either Rodriguez or Swisher wouldn’t result in a counter move by Tigers manager Jim Leyland. At the time, right-handed reliever Joaquin Benoit was up working in the Detroit bullpen, and he was the most likely response to Girardi pinch-hitting with either of his two best options.

Benoit has fairly even splits. In fact, despite being right-handed, he’s been slightly worse against right-handed batters than left-handed batters over his career. During the 2012 regular season, batters performed exactly the same against him in terms of weighted on base average whether they faced the reliever from the right or left side of the plate.

Meanwhile, both Rodriguez and Swisher remain above average bats against right-handed pitching. While A-Rod has actually performed better against righties over his entire career, the switch-hitting Swisher has been only slightly worse than his average performance against lefties. More recently, Rodriguez had a below average performance against right-handers this season, while Swisher had the best year of his career against right-handed pitching.

So, again, we find that even with this counter move, going by both recent and career numbers, there’s a far superior option in Nick Swisher (and maybe Alex Rodriguez) available to Joe Girardi. However, the manager stuck with Ibanez, and he struck out on the seventh pitch from Coke.

Game over.

Now, the defense for Girardi is that Ibanez had been playing well extremely recently, while Rodriguez and Swisher had been playing poorly extremely recently. The predictive nature of hot/cold streaks was studied in The Book, and the conclusion drawn was that it’s always better to assume that a player will hit at his projected norm regardless of how he’s hit in the very recent past.

Now, there is the additional possibility that an injury or bout of tiredness that we might not know about has emerged for Rodriguez or Swisher, but if such a thing has affected them to the degree that Girardi considers Ibanez the better option in this situation, then they probably shouldn’t be on the team’s roster at all.

Further to the idea of playing the hot hand, if you’re going to argue that this is the right move, then you also have to consider that Coke, too, has been “hot.” In fact, over six appearances, pitching five and a third innings, he has yet to allow a run this postseason. So, if you’re going to place so much of an emphasis on recent performances, shouldn’t you maybe give more consideration to the strategy that would force the opposing manager’s hand into playing the less “hot” pitcher? Benoit, has made four appearances this postseason, pitching three and two thirds innings, and allowing two runs in that time.┬áSurely, if recent performances is so important, this is the preferable pitcher to face.

What we’re left with is absolutely no reasonable justification for what Girardi decided to do last night, in letting Ibanez bat against Coke. It’s like sending in a cockroach to fight an exterminator, when you have a lion. Yes, as soon as you unleash the lion, the other combatant will up the ante with a Rhodesian Ridgeback, but I like the odds of winning that battle a heck of a lot more than the alternative. I’m not sure why the same wasn’t true for Joe Girardi on Tuesday night.

And now, the Detroit Tigers are a win away from the World Series, and the New York Yankees are a loss away from their season being finished.