On Saturday, the Cardinals battled back from deficits of 6-1 and 8-3 to find themselves trailing by just one run with two outs in the bottom of the ninth. Yadier Molina had just singled off Mets closer Edwin Diaz. Cardinals pitcher Jack Flaherty came in off the bench to pinch run. Kolten Wong hit a high blooper that found its way in between second baseman Jeff McNeil and a diving Michael Conforto. Flaherty, showing some of his inexperience on the basepaths, twice looked back at the play instead of focusing on third base coach Pop Warner as he was heading toward third base when the ball hit the ground. He then ran for home.

This is how the play moved forward from there.

We can see Flaherty stumble a bit at third, though that stumble doesn’t look like it made a huge difference as the throw beat Flaherty by about 10 feet. With the benefit of hindsight, we know that the decision to send Flaherty ended the baseball game and handed the Mets a victory. As for the decision-making at the time of Warner’s choice to send Flaherty home, that deserves a closer examination.

The first step in looking at the decision to try and tie the game is establishing how much benefit the Cardinals would receive if Flaherty was safe and compare that to the loss if Flaherty was thrown out. We know that getting thrown out ends the game, so the Cardinals win expectancy in that scenario is of course zero. There are two other scenarios, with the first being if Flaherty stays. The Cardinals would then still be down by one run, but they would have runners on second and third base with two outs and Paul Goldschmidt stepping up to the plate. The second scenario is if Flaherty scores the tying run and Paul Goldschmidt steps up to the plate with a runner on second base.

We can plug those two scenarios into our WPA Inquirer tool and determine the Cardinals chances of winning the game. The scenario on the left is not sending Flaherty and the scenario on the right is Flaherty scoring.

If Flaherty stays at third base, the Cardinals win probability at that time was 20.1%. It’s possible that the win probability might have felt larger than a one-in-five shot with Goldschmidt stepping up to the plate, but keep in mind that Goldschmidt has made an out in 65% of his plate appearances this season and 60% in his career. Also keep in mind that the Mets’ pitcher, Edwin Diaz, is a good reliever, even if he had pitched three days in a row. Even if Goldschmidt delivers a single and a one-run lead, the Cardinals still have to navigate the bottom of the ninth inning, in which the Mets would still have a 20% chance of coming back and winning. The most Goldschmidt could do is a home run, which he’s done in just 4% of his plate appearances in his career, which would give the Cardinals a 92% chance and the Mets an 8% chance of coming back.

If Flaherty had safely made it home, we see the Cardinals would have increased their chances of winning to 46.6%. Goldschmidt still would have been up to the plate with the winning run at second, but now if he made an out, the Cardinals would still have had a decent chance of winning the game instead of the game being over. The calculus of the decision then weighs the 26.5-point increase in win probability if Flaherty is safe against the 20.1-point decrease if Flaherty is out. Because 20.1 is the risk of loss and 46.6 is the difference between the loss and the gain, Flaherty only needs a 43% chance of being safe to make the risk worth it. That’s a pretty low bar, but Flaherty looked to be out by a mile. Were his chances really that high?

When you consider the decision Warner made to send Flaherty, this is what the play looked like as it was unfolding.

Warner sees an outfielder sliding and missing the ball while the second baseman overruns the play. The ball is still on the ground as Warner has to make his decision. We know Flaherty isn’t the fastest player in the world, but his average sprint speed is 25.8 feet per second. For 90 feet, that would be about 3.5 seconds. We also have 90-feet splits showing Flaherty moving that distance in 4.03 seconds, but that includes half a second in the first five feet which is likely a little slower than Flaherty would be moving rounding third. Knowing it would take Flaherty around 3.5-4 seconds to make it home, and knowing the ball is on the ground, we next have to factor in the defense and arm of Jeff McNeil.

The Mets’ second baseman doesn’t have the best arm. He was moved off shortstop early in his career due to concerns about that arm, and when the Mets play McNeil in the outfield, he plays in left field, where shorter throws are required. To get a sense of what McNeil’s throws from the outfield are like, I watched a lot of them. Here’s a good one:

On that play, McNeil is charging and throws the ball on a bounce to home to get Maikel Franco easily. That .gif above is 3.7 seconds. Here’s another throw McNeil made from left field.

For the Cardinals’ purposes, here’s the result of a throw he made against St. Louis earlier in the season.

None of this is meant to disparage McNeil. He simply doesn’t have that strong of an arm. On a similar play in which he did well to get Franco, the play took longer than Flaherty’s likely run home. Now here’s what McNeil did against St. Louis.

McNeil wasted no effort in grabbing the ball off the ground and immediately threw a strike to home. While the 10 feet Flaherty was out by looks like a healthy distance, we are only talking about three-tenths of a second or so before Flaherty would’ve had been sliding into home. That’s a slight hesitation in getting to the ball, a wide throw, or a weaker throw due to Conforto being on the ground in front of him. If Flaherty hadn’t stumbled, the play would have been very close. If McNeil hadn’t made the exact play he did, which was a very good play for him given his past history, Flaherty would have been safe. We can argue about how much leeway we need to give, but when the break-even point on the play is at 43%, sending Flaherty was probably the right call.