First, here's the list of most home runs in an age-20 season:
1. Mel Ott, 1929 Giants, 42
2. Frank Robinson, 1956 Reds, 38
3. Alex Rodriguez, 1996 Mariners, 36
4. Tony Conigliaro, 1965 Red Sox, 32
5. Ted Williams, 1939 Red Sox, 31
6. Mike Trout, 2012 Angels, 30
And that's it for the guys who hit at least 30. Only nine more hit at least 20, a group that includes Hall of Famers Al Kaline, Orlando Cepeda, Eddie Mathews, Mickey Mantle, Ken Griffey Jr. and Willie Mays. (The other three were Bob Horner, Giancarlo Stanton and Vada Pinson.)
As a 19-year-old rookie, Harper hit 22 home runs in 139 games. Over his final 44 games (41 starts) and 179 plate appearances, however, he hit .327/.384/.660, including 12 home runs. That prorates to 43 home runs over 650 PAs. I wouldn't be surprised if Harper hit 43 home runs, but the various projection systems are understandably a little more conservative. Dan Szymborski's ZiPS projects 26 home runs; others are similar.
I'm a little more bullish and will put the over/under at 29.5. Can he become the seventh 20-year-old to hit 30 home runs?