Should the Pirates have started Gerrit Cole on Sunday?

Entering Sunday, the Pirates had clawed their way to within one game of the Cardinals for the NL Central lead. With both teams already having clinched at least a wild card, there was a lot on the line. The winner of the division would avoid the dreaded "coin-flip game" and move right to the division series against the Dodgers, while the loser would host the Giants in said toss-up.

Manager Clint Hurdle had an important decision to make: pitch Gerrit Cole, his ace, in the season finale against the Reds and hope that the Diamondbacks were able to beat the Cardinals to force a game 163 Monday, or spot start someone like Stolmy Pimentel or Casey Sadler as a sacrificial lamb and keep Cole on extra rest for Wednesday's wild-card game. You all know what happened: He opted for Cole, who pitched well but not well enough to beat Johnny Cueto; a gaggle of Cardinal relievers took Adam Wainwright's turn and shut out the woeful D-Backs; and the Cardinals won the division by two games.

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We won't know until after Edinson Volquez and Madison Bumgarner face off on Wednesday whether Hurdle's choice proved to be a good one or not. However, we can examine the Pirates' chances of reaching the division series in several hypothetical scenarios.

For many of the odds given below, I'll use former BtBS contributor Matt Hunter's SaberSim tool to calculate probabilities.

We'll start with what actually happened: Gerrit Cole got the ball on Sunday. There's a tree of possibilities we have to go down to see what the Pirates' chances of reaching the division series were. (I'm not dealing with rotation ordering for the division series itself, partly because there are so many possibilities and partly because Cole, Francisco Liriano, and Volquez will pitch the first three games in some order regardless.) First, we'll look at the chances that the Pirates didn't tie the Cardinals at the end of the day.

SaberSim has Cole as winning 48.6% of his games against the Reds, and the Cardinals losing 55.1% of their games in Arizona. Some basic probability (multiply the two) tells us that the Pirates would go to a game 163 against the Cardinals 26.8% of the time. That game, however, would pit Jeff Locke, he of the 4.37 FIP, against Adam Wainwright. It's not exactly a fair matchup, and SaberSim has the Pirates winning only 41.2% of the time.

Next, we have to examine the wild-card game. Edinson Volquez would likely have started it even in the case of a game 163, which simplifies things a bit.

Fangraphs puts the Pirates at 52:48% over Bumgarner and the Giants, mostly because the home-field advantage offsets the Giants' clear edge in pitching. SaberSim disagrees, putting the Giants ahead by 56:44%. Then again, Volquez has outperformed his FIP by over a run this year, with a 3.07 ERA and 4.18 FIP, so SaberSim may be underestimating his ability to beat peripherals. Let's split the difference and call this scenario 52:48% Giants.

I won't bore you with descriptions of the scenarios for saving Cole for game 163 or the wild card, but here are the outcomes in tabular form.

What with all the chains of possibilities, it boils down to this: Starting Cole gave the Pirates a 55.1% chance of reaching the NLDS. There are myriad options and calculations for saving Cole and going with Sadler or Pimentel (pretty much the same chain of events, just with different pitchers), but those probability comes out to 55.5%. (Note: Fangraphs seems a bit more bullish on the Pirates in general, as their odds before Sunday's games had them reaching the division series 57.8% of the time.)

Four-tenths of a percent. Saving their best pitcher, and essentially conceding defeat in the division to a bitter rival, would have netted the Pirates a whopping four-tenths of a percent in their quest for the NLDS. While any gain is a good gain, simulations are by no means baseball, as Hurdle pointed out:

There is no way we're going to walk away from the opportunity to win the division...This is not about theory. This is not about analytics. The only analytics that played into this decision was human analytics.

I could have gone even farther down the rabbit hole by looking at scenarios involving Wainwright starting on Sunday after a Pirates win and the options for game 163, but that would just redistribute some of the probabilities and not change things much in the aggregate. Regardless, the decision wasn't going to drastically impact the Pirates' chances either way.

In the end, the Pirates opted to put their best horse on the track and hope for the best. It didn't work out so far, but everything comes down to Wednesday's matchup with the Giants. If Volquez is able to pull out a win, an added bonus is that Cole can start game 1 in Washington, scheduled for Friday, on normal rest. The decision Sunday was clearly a tough one, but given Hurdle's excellent track record and status as reigning manager of the year, he definitely deserves the benefit of the doubt.

. . .

Statistics courtesy of FanGraphs and SaberSim.

Steven Silverman is a featured writer at Beyond the Box Score and a student at Carnegie Mellon University. He also writes for Batting Leadoff. You can follow him on Twitter at @Silver_Stats or email him at Steven@SilverStats.com.