When he stepped off the mound after a dominant seven innings last Tuesday night, Jack Flaherty surely thought he’d thrown his last pitch of the regular season. The Cardinals led the Diamondbacks 1-0 and the Brewers by 3 1/2 games in the NL Central. A win that night would all but lock up the division; three games up in the loss column with five games left to play is a tough lead to cough up.
But it wasn’t to be. Andrew Miller gave up a tying home run in the ninth inning, the Cardinals ended up losing in nineteen (!!) innings, and the Brewers started to catch up. Saturday night, after a beatdown at the hands of the Cubs was matched by a Brewers loss in Colorado, leaving the Redbirds a game ahead in the standings, the Cardinals announced that Flaherty would start Sunday afternoon.
In the real world, the game was a breeze. Flaherty put together another strong outing, going seven scoreless and allowing only two hits, and the Cardinal offense came to life en route to an easy 9-0 victory. The Brewers, meanwhile, pulled their starters when a St. Louis victory became inevitable, eventually losing 4-3 in 13 innings.
But those are the results that actually happened, not the results that could have happened, and knowing what could happen is often more interesting than seeing the actual results. To that end, I was curious: did the gambit of starting your best pitcher in the regular season rather than saving him for a potential elimination game make sense? Let’s do the math.
To work out the cost and benefit of starting Flaherty, we need to work out the potential scenarios that follow a Flaherty start. First, there’s the world that actually occurred: the Cardinals win the NL Central and move on to face the Braves in the NLDS. In that situation, the cost of starting Flaherty in the last game of the regular season is low. He’ll start Game 2 of the series, and can start a potential Game 5 on regular rest. There’s almost no cost here; if Miles Mikolas had pitched yesterday instead, Flaherty would start Game 1 and Mikolas Game 2 instead of vice versa, and Flaherty would still start Game 5.
Next, the Cardinals could end up tying the Brewers for the NL Central, which would require a Milwaukee win and a St. Louis loss. In that scenario, Mikolas would start today’s tiebreaker game. From there, the Cardinals would either win, in which case they would go to the NLDS against the Braves as before, only with a realigned pitching staff. Dakota Hudson would start Game 1, Flaherty Game 2, and Mikolas Game 3. This, again, isn’t a huge cost; the same three pitchers start the first three games of the series, with only their order shuffled.
The real problem scenario comes if the Cardinals were to lose a tiebreaker game against the Brewers. In that scenario, they head to Washington to face Max Scherzer and the rested Nationals, with a short rest Hudson or very short rest Adam Wainwright on the mound in an elimination game. That’s not ideal, to say the least.
Even if the Cardinals won that game, their rotation would still not be back to full strength. Whichever of Hudson or Wainwright didn’t go would take the ball in Game 1 against Clayton Kershaw and the Dodgers. From there, with Flaherty having been unavailable for the two highest-leverage games of the year, it would return to normal: Flaherty in Game 2, Mikolas in Game 3, and so on.
Now that we have the possible scenarios, we can work out how likely the Cardinals were to reach the World Series when Flaherty took the ball on Sunday. We simply use the method outlined here to create winning percentages for potential game. For example, the Cardinals had 64% odds to win against the Derek Holland-led Cubs, while the Brewers were 54% favorites to win on the road in Colorado. This means there was a 19.5% chance of a Cardinals loss and Brewers win; in other words, the Cardinals win the Central 80% of the time, and the other 19.5% of the time, a tiebreaker game would decide it.
From there, it’s simple math: the Cardinals beat the Braves roughly 42.5% of the time, and they beat the Dodgers/Wild Card winner around 38% of the time. We can iterate out the scenario where they play the tiebreaker game as well: the Cardinals with Mikolas opposing Brandon Woodruff have 57% odds to win that game. Win the game, and they have the same 42.5% odds of beating the Braves and 38% odds of winning the NLCS should they reach it.
The worst-case scenario happens only 8.6% of the time: the Cardinals lose on Sunday while the Brewers win, and then lose on Monday in Game 163 as well. That sends them to D.C., where they have a dismal 35% chance (per the odds ratio method) to beat a rested Scherzer. That only sends them to the NLDS to face the buzzsaw of the Dodgers, where they win only 33% of the time. Put it all together, and they project to make the World Series only 4.5% of the time if they are forced to play in the Wild Card game.
So basically, the Cardinals stood a 14.9% chance of making the World Series by sending Flaherty out to start on Sunday. It’s easy to run the other hypothetical: what would happen if the team ran Mikolas out Sunday and saved Flaherty for a potential tiebreaker matchup? I’ll save you the math walkthrough, but while the Cardinals still usually win the Central on Sunday, things get dire for them if they don’t.
In that scenario, Flaherty can’t start twice in any potential NLDS, leaving Mikolas as the designated pitcher who gets two turns. That doesn’t sting as much as you might think, but it still stings. All in all, the Cards make the World Series 14.4% of the time. They picked up 0.5% by starting Flaherty, which doesn’t sound like a huge deal but is still the correct decision. If you found a 0.5% chance of reaching the World Series on the ground, you would surely pick it up.
But why stop there? We can run one more interesting hypothetical. It wasn’t preordained that the Cardinals would be up a game going into the last game of the season. The Brewers had a one run lead with two outs in the ninth inning on Saturday night before Sam Hilliard hit a home run off of Josh Hader to tie the game. The Rockies went on to win in extra innings. If Hader had finished the game, the Cardinals and Brewers would be tied heading into Sunday.
Using our same odds calculations, the Cardinals would be 11.5% to reach the World Series by starting Flaherty if they went into Sunday’s games tied. That’s worse, naturally — they end up losing the division much more often when they can lose it without the need for a tiebreaker game.
What’s really interesting is that in this scenario, they’d be 11.7% to reach the World Series by starting Mikolas. Instead of picking up 0.5% by starting Flaherty, they’re dropping 0.2%. What gives?
Basically, it comes down to avoiding the Wild Card game. If Flaherty started on Sunday and the Cardinals and Brewers had the same result, the team has essentially spent their best pitcher without getting anything back for it. The odds of needing a tiebreaker game are quite high, with or without Flaherty starting against the Cubs. The best way to avoid the Wild Card, then, is to have Flaherty face the Brewers in a potential (and likely!) tiebreaker game.
With the Cardinals up a game, however, the name of the game is avoiding a tiebreaker. The Cardinals had an 8.3% chance to end up in the Wild Card game whether Flaherty or Mikolas started on Sunday — starting Flaherty, though, decreased the chances of a tiebreaker game, meaning that Mikolas can pitch more often in the postseason.
That’s the main difference. In a situation where a tiebreaker is likely, having your best pitcher in that tiebreaker is paramount. When it becomes less likely, however, using your best pitcher sooner rather than later is the play.
Of course, none of these hypothetical situations happened. Flaherty shut the Cubs down, and that’s that. He might even garner some additional Cy Young consideration — his 0.91 ERA in the second half is preposterous. Still, there’s a rule of thumb to be learned here, even if the total edges are small. Up a game going into the last game of the year? Start your ace if you can. Tied? Save him for a likely tiebreaker game, when the leverage will be highest. We’ll never know if the Cardinals would have started Flaherty if they were tied, but the math says they made the right decision in the world we have.
Ben is a contributor to FanGraphs. A lifelong Cardinals fan, he got his start writing for Viva El Birdos. He can be found on Twitter @_Ben_Clemens.