How fast should a team pull the plug on a veteran pitcher with nearly 250 wins to his credit? For the Yankees and Mike Mussina, the magic number was three, as in three starts, although the more salient number is 17.69, Mussina’s ERA in those starts. Any pitcher, even a great one, can have a run of bad starts, but Mussina was so bad, so flat, that the Yankees were left with little choice given their position in the wild card race. Ian Kennedy, the Yankees’ top pick in the 2006 draft, will take Mussina’s start on Saturday.

What happens after that is an open question. Mussina won’t be disabled; rosters expand on September 1, so he’ll remain on the roster, as an active invalid, working to rediscover his youth. That may seem mean-spirited, but it’s an accurate description. Even when he was pitching well a month ago, Mussina’s strikeout rate had fallen to the league average. As a Yankee, he had averaged close to eight strikeouts per nine innings. The decline of his ability to make batters swing and miss presaged Mussina’s problems, though in this case A didn’t automatically have to be followed by B; many pitchers learn to pitch with age-diminished stuff. Certainly that’s what Mussina appeared to be doing throughout mid-summer, when he maintained an ERA of 3.54 over 12 starts. If Mussina isn’t hurt and hasn’t suffered some kind of mechanical breakdown, neither of which is indicated at this point, then the only point of his upcoming side sessions will be to figure out where his stuff went.

The problem is, we know where it went. It left with his younger self. Given that Mussina was one of the better pitchers in baseball as recently as last year, it seems shocking that a pitcher could succumb to age so quickly, but at 38, Mussina was pitching on borrowed time to begin with. We’ve become spoiled by pitchers such as Roger Clemens, Greg Maddux, and John Smoltz, who have gone on year after year, making compromises with age without surrendering completely. We forget that by 38, the vast majority of pitchers have long since hung up their guns. Mussina was born in December, 1968. Pat Hentgen, the 1996 Cy Young award winner, was born the month before. Former All-Stars like Hideo Nomo, Denny Neagle, Scott Erickson, and Shane Reynolds are all only months younger than Mussina.

We’re also misled by the neatness of the encyclopedia, conditioned to view the progress of a player’s career in seasons. We look at John Smith’s entry and see that he pitched well in 1987 but was miserable in 1988, and we wonder how things could have turned so quickly. But the truth is that they didn’t, that Smith’s career played out one day and one game at a time, and his arm’s odometer rolled over at some point not determined by the boundaries of the baseball season but because he passed some invisible point marked by too many pitches, too many birthdays, or taking too heavy a box up to the attic, and that was it. You run out of gas when the tank is empty whether you’ve reached your destination or not. Though it may seem arbitrary, the Moose gave out exactly when nature intended him to.

Nothing precludes Mussina from finding a new wrinkle, making yet another adjustment, and fulfilling the last year of his contract. He had already done so once, unveiling a new changeup last year that gave him life after back-to-back years of ERAs in the mid 4.00s. The problem is that with the Yankees in the unaccustomed position of looking up at the division and wild card leaders, they don’t have time to let Mussina take his lumps, especially not when he’s been so bad and they have better options.

Kennedy represents the best example of targeted drafting in team history. Coming out of college, he was supposed to be a case of what you see is what you get: He did not have the stuff of a Roger Clemens or Mark Prior. His fastball is low 90s at best, and he wasn’t predicted to develop dramatically with professional training. What he did have was professional-level polish and location, and, it was reasoned, if he simply maintained those qualities in the majors, the Yankees would have acquired a quick-grow fourth starter. That doesn’t sound like much, but with an aging rotation, with Jaret Wright and Carl Pavano still on the roster at the time of the draft, the team knew it would soon need reinforcements.

In today’s market, quality fourth starters are as hard to find as aces, and given what the Yankees have had at the back of their rotation, the standard of success wasn’t high: All Kennedy had to do was stay healthy and look like he could post a 4.00 ERA in the majors. Kennedy has done much more than that, posting a 1.91 ERA while climbing the ladder to Triple-A. His strikeout rate, just under nine per nine innings at Scranton, has also been higher than anyone anticipated.

On Saturday, all he’ll have to do is be better than Mike Mussina. As recently as last year, that would have sounded like an impossible feat for a rookie with less than awesome stuff. Sadly, now it’s no big deal.

Mr. Goldman is the author of “Forging Genius,” a biography of Casey Stengel.