Should Gerrit Cole have started Sunday?

I was somewhat out of pocket over the weekend, so missed the semi-controversy about the Pirates' starting pitcher on the last day of the season. But this inspired me to get caught up:
In 1940, the Detroit Tigers, with three games left, needed just one more win to clinch the American League pennant. Those three games were against the second-place Indians, two games behind. Bob Feller, the best pitcher in the American League, would start the opener for Cleveland. Which left Del Baker with a big decision: Should he throw one of his good veteran starters against Feller? Or instead pitch one of his green youngsters and hope for the best, with the veterans available for the next two games?
The night before the game, Baker got a bunch of his veteran hitters in a room and took their counsel. It doesn't seem that a consensus was reached, but Baker did choose 30-year-old rookie Floyd Giebell, with just one major-league appearance on his résumé. And somewhat famously, Giebell pitched a 2-0 shutout ... and never won again in the majors.
I think Baker, well-known as a player's manager, just wanted to make sure he hadn't missed anything. I think Hurdle, who seems to be a player's manager -- granted, that's true of nearly every manager these days -- sees his "leadership council" as a player-relations tool ... and if someone gives him some good advice, all the better.
Hurdle's rationale? From the Post-Gazette:
Hurdle started Gerrit Cole in his regular turn in the rotation rather than holding back Cole, either for a possible tiebreaker game today or a wild-card game Wednesday night at PNC Park. The decision had two main facets: Start Cole, their best option, against Cincinnati Reds ace Johnny Cueto, and play for a division title? Or skip Cole, roll the dice with the long relievers and hope for the best?
"There's no way we're going to walk away from an opportunity to win our division," Hurdle said.
--snip--
"This is not about theory," Hurdle said. "This is not about analytics."
Hurdle quoted a piece of advice he had received regarding decision making: Choose the option that lets you sleep at night. How did he sleep Saturday night? "Like a baby."
Sounds like pretty good advice! Except I don't see any conflict between analytics and sleeping like a baby. I live in a somewhat sketchy neighborhood, but I sleep well at night because I know the odds are greatly against anyone breaking into the house. Especially with a big dog on duty.
If I were a manager, knowing the theory and the analytics would help me sleep well at night. And in this case, I think the analytics would have led to a different decision. Going against the Cueto in Cincinnati and hoping the Diamondbacks could beat Adam Wainwright ... just a quick back-of-the-envelope calculation suggests the Pirates' chance of tying the Cardinals for first place was approximately 20 percent.
If that happy combination had come about, the Pirates would then have played the Cardinals in a one-game playoff Monday. In St. Louis. They would have been blessed with maybe a 45-percent chance of winning that game. So now we're down to a 1-in-10 chance for the division title.
Hey, longer odds have been beat. But for that 10-percent chance of avoiding the Wild Card Game, the Pirates now enter that Wild Card Game with their fourth-best starting pitcher rather than their best. Oh, and I forgot something important; they didn't have a non-zero chance of winning the division without Gerrit Cole starting on Sunday. I also didn't mention that if they'd tied the Cardinals, they would have burned another pitcher in the one-game playoff. Which, again, they might actually have lost anyway.
None of which necessarily means that Hurdle did the wrong thing.
All we know about the psychology of managing a baseball team is that we don't know anything about the psychology of managing a baseball team. Let alone about the psychology of managing this baseball team.
If Hurdle started Cole because that’s what his players wanted him to do, or because he didn’t know or understand the odds involved … well, no, I can’t really defend him. But if he started Cole because he thought his team needed Cole to start … well, I still can’t really defend him. But I can’t really indict him, either. We’re talking about a guy who’s managed the Pittsburgh Pirates into the postseason for two years running.