With a little help from the Kansas City Royals’ aggressive brand of opportunism, the New York Mets committed a variety of blunders en route to losing the World Series. But the one that might haunt the team most in the wake of its season-ending 7-2 loss Sunday was the acquiescence of manager Terry Collins to the demand of starting pitcher Matt Harvey to remain on the mound for the ninth inning with a 2-0 lead.Up to that point, Harvey had spun a gem of a game — eight innings of shutout ball with nine strikeouts — under pressure-packed circumstances. But he’d also thrown 101 pitches and was navigating his way through the heart of the Royals’ lineup for a dangerous fourth time. Meanwhile, Mets closer Jeurys Familia had been warming up and was about to enter the game… before Collins changed his mind after Harvey lobbied to stay in. (Harvey could be seen in the dugout shouting “no way” at the idea of being replaced.)Three batters later, Harvey had already given up one run and put the eventual tying run on base, effectively giving New York its own version of Grady Little leaving Pedro Martinez on the hill in the 2003 ALCS. But how much did it really cost the Mets at each step of the way?Under normal circumstances,1As per wOBA, computed using Baseball-Reference’s Marcel projections and using the MLB average to determine the expected runs per plate appearance in a theoretical matchup between Harvey and hitters No. 3-7 in KC’s lineup. the heart of the Kansas City order would score about 0.36 runs per inning against Harvey, giving the team a corresponding 9 percent probability of scoring at least the two runs required to tie the game. But all else being equal, pitchers going through the order a fourth time see about a 7.5 percent increase to their runs allowed per inning — meaning there was more like a 10 percent chance that the Royals would score two or more runs against Harvey at that stage of the game.Meanwhile, the same Royals batters would have been expected to score about 0.35 runs per inning against a fresh Familia, which corresponds to a 9 percent probability of plating two or more runs. A difference of 1 percentage point may not sound like much, but the start of the ninth inning is already a medium-leverage situation before a pitch is thrown, so even small changes to the probability of getting out of the inning without relinquishing the lead (and therefore winning the game) are amplified.Of course, Collins arguably made a bigger mistake when he declined to pull Harvey even after Harvey allowed a leadoff walk to Lorenzo Cain. With a tired Harvey in the game, the odds of allowing two or more runs in the inning climbed to 19 percent, as opposed to the 17 percent it would have been against Familia in the same situation. (And after Cain stole second base, those numbers became 20 percent and 18 percent.)Again, the odds were still good that the Mets would be able to record three outs before the Royals scored two runs. Eric Hosmer’s subsequent double would have been an unexpected event whether he hit it off Harvey or Familia — it was the game’s most important play in terms of win probability added — and even after that, the Royals still needed Hosmer’s remarkable heads-up baserunning (and a bad throw by Lucas Duda) to tie the ballgame and force extra innings.So it’s unfair to criticize Collins too much for leaving Harvey on the mound to start the ninth inning. But in a must-win game where every small edge matters, that fateful decision definitely shaved a few percentage points off of New York’s chances of sending the Series back to Kansas City.CORRECTION, Nov. 2, 3:15 p.m.: An earlier version of this article referred incorrectly to the difference in the probability of the Royals scoring two runs in the ninth if Harvey had been replaced by Familia at the top of the inning. The difference is 1 percentage point, not 1 percent. In addition, the article incorrectly referred to Duda’s throw to home as an error. Although the throw was wide of its mark, it was not officially scored as an error.