I got the term Old Man Game from a Tucker Max essay about when he used to play basketball as a U. of Chicago undergrad with law school lecturer Barack Obama. The 35ish Obama was surprisingly ineffectual. He looked good, but he hadn't developed much Old Man Game cunning that would help his teams win, so team captains who used a high pick on the tall, smart-looking black guy often wound up losing.

Developing Old Man Game is a helpful explanation for Hank Aaron's career path in baseball.

It was embarrassing for Major League Baseball back in 2007 when Barry Bonds broke the sainted Hank Aaron's career home run record, which Hank had famously taken in 1973 from Babe Ruth. 

And, yet, Aaron's career path was a little strange, itself. He's was always seen in the press as second fiddle to Willie Mays, sometimes third fiddle to Willie and Frank Robinson. But he kept racking up homers as age took its toll on his rivals. 

In Milwaukee, per 162 games from age 20 to 31: 124 singles, 36 doubles, 8 triples, 36 homers. 

In Atlanta, per 162 games from age 32-40, 98 singles, 27 doubles, 3 triples, 43 homers.

The Atlanta ballpark is about 500 feet higher than Milwaukee's, and in general it was a better hitter's park. 

So, it looks like Aaron simply craftily focused upon the aging ballplayer's remaining strength: strength. You can see in golfers that drive length declines only slowly as they age, while putting often goes quickly.

On the other hand, I'm not wholly convinced by the statistical evidence from before the Dianabol Age (1958 onward) that this idea that players will be able to up their homers per game numbers after age 31 by uppercutting is wholly clear. 

Okay, Stan Musial went up from 25 to 29 per 162 games over those ages, so that supports it, but some of Musial's early seasons were played with the WWII ball that didn't go as far so he'd have a ton of doubles.

Babe Ruth went up from 43 to 51, but there were big changes in the ball; the 1918 ball was made out of old newspapers or something to Help the War Effort; after Roy Chapman got killed by a dirty ball he didn't see in 1920, they used newer cleaner balls and banned the spitter. Then they switched to a lively ball around 1925.

Lou Gehrig went from 37 up to 38 but died before he hit 40. Gehrig had some Old Man Game — in 1927, Gehrig was like Aaron in 1959 or Musial in 1948, ripping huge line drives for a ton of extra bases (but not quite as many homers).  But in the 1930s, Gehrig learned to pull the ball right down the short Yankee Stadium right field line for cheap homers. (Bill Dickey did, too.)

Johnny Mize from 30 to 32. Billie Williams from 28 to 29. Willie Stargell 33 to 36 when moving to a more homer friendly park. Hank Greenberg from 39 to 39, but retired young. Frank Howard 32 (mostly in cavernous Dodger Stadium) to 34. Joe Adcock 27 to 31. Jim Thome 40 and 40. Harold Baines 22 to 24. Frank Thomas 36 to 38. Barry Bonds from 35 to 53. Rafael Palmeiro from 26 to 40.  Mark McGwire from 41 to 64. Sammy Sosa from 41 to 46. Luis Gonzales from 17 to 28 (with a peak of 57 at age 33). Gary Sheffield 32 to 34.

Ted Williams declined from 38 to 36.  Mel Ott declined from 34 to 28. Frank Robinson declined from 37 to 30. Willie Mays declined from 40 to 35. Joe Dimaggio from 36 to 31. Willie Horton from 30 to 22. Ken Griffey Jr. from 42 to 32. Mike Schmidt from 38 to 36. Harmon Killibrew from 44 to 32. Ron Santo 27 to 18. Duke Snider from 36 to 21. Chuck Klein from 35 to 13. Al Kaline 27 to 21. Ernie Banks 40 to 25. Dick Allen from 35 to 27. Willie McCovey 37 to 30. Mickey Mantle 41 to 29. Eddie Matthews 38 to 25. Eddie Murray 30 to 25. Carl Yastrzemski 25 to 21. Reggie Jackson from 34 to 32. Alex Rodriguez 46 to 34. Manny Ramirez 41 to 37. Al Simmons 26 to 18. Brooks Robinson 17 to 14.

So, it looks like there are some legit examples of Old Man Game leading to more homers per game played, although it's hard to come up with anything completely trustworthy that's analogous to Aaron's trajectory. Overall, I'm inclined toward the Old Man Game explanation. But, still ...