Last Wednesday Yankee slugger Aaron Judge hit his 300th career home run. It was only his 955th game and 3,431st at bat. Both of these were records.

Before the ball even came down (it was up there a while) fans and statheads were wondering the same question: does he have a shot at the all-time record of 762?

I love using the phrase “on pace for,” but the trouble with this on pace for is that there’s no set number of games or at bats any player will reach. The only number we know is the number of home runs that would give Judge the record: 763. Everything else is an unknown.

Consider the number of games played. In a season it’s obviously 162. At most. For a career, that finish line is a variable, and you can’t solve an equation with more than one variable… except to describe it in terms of another variable. For example, I can say that x is half of y, or y is twice as big as x, but unless you tell me what one of them is I can’t tell you the other.

In the Judge example, the only thing set is that we want him to finish with 763 home runs. We could look at his “pace” for his first 955 games and see how long it would take him to get to 763, but there’s no guarantee he would play that long, nor that he would keep up this pace.

For what it’s worth it’s 2,429 games. This is the total number of games needed, about 15 full seasons (that number divided by 162). Subtract the 955 he’s already played and you have 1,474, or a little over nine full seasons. Nine full seasons playing every single game at the rate he’s hit home runs in his relative youth. Trouble is, everyone slows down towards the end of his career. The pace really does change, whether you’re looking at a full career, just a few seasons, a single year, a single week, etc. 

If we knew Judge were going to play until he was x years old or knew that he’d never be injured it would be a lot easier to say whether he could set the all-time record. The math can show us only when we’ve set a few factors in place. The human side of things makes it impossible without making a few assumptions. The thing Judge has working for him is that he’s a great hitter; the thing he has working against him is that he didn’t play his first MLB game until he was 24, and even at age 29 he had only 123 home runs. (Like this is easy.) For a little contrast, on his 29th birthday Alex Rodriguez hit his 370th career home run. It was the 1,374th game of a career that started when he was 18.

At this point we can sort of forget the “on pace for” and recognize what we all race against: Father Time. Let’s say Judge plays 10 more years from the day he hit his 300th home run. That would make him 42 years and a few months old, just about the same age Bonds and Hank Aaron played their final games. The math on this one is easy: 463 more home runs to go divided by 10 years is 46.3 homers a season.

Neither Aaron nor Bonds nor A-Rod nor Albert Pujols (the closest anyone’s come to the record since Bonds) ever averaged 46 in a 10-year stretch. Not in their youth, not in their later years, not ever.

Hmm.

It’ll be a tall order for Aaron Judge to pass Barry Bonds on the all-time home run list, given his relatively late start and realization that, well, we all age. If he does set the record and I have to eat crow in a subsequent post…

I’ll never be happier about admitting I was wrong.