From ages 32 to 34, David Ortiz hit .257/.356/.498. From ages 35 to 37, Ortiz hit .311/.401/.572. As offense went down in recent years, Ortiz went up.
How good has Ortiz been? Here are the top 10 players in OPS+ over those ages according to Baseball-Reference.com (minimum 1500 plate appearances):
1. Barry Bonds, 237
2. Babe Ruth, 210
3. Hank Aaron, 173
4. Nap Lajoie, 167
5. Tris Speaker, 164
6. David Ortiz, 161
7. Edgar Martinez, 156
8. Honus Wagner, 154
9. Stan Musial, 153
10. Chipper Jones, 152
Non-Red Sox fans will, of course, explain that away to some special pharmaceuticals that Ortiz must be taking. But isn't it possible Ortiz just made some adjustments? The biggest improvement in his game has been strikeouts. He struck out 145 times in 2010 but struck out just 88 times last in year in the same number of PAs. His BABIP last season was .321, compared to .313 in 2010, but he hit .309 as opposed to .270 merely because he was putting the ball in play more often. He's not the only recent player to hit for a higher average later in his career. Chipper Jones, for example, hit .248 at 32 and .296 at 33, but then hit .337 at 35 and won a batting title at 36 when he hit .364.
Anyway, so Ortiz has become one of the best old hitters in the game's history. By signing him through 2015 and possibly beyond, the Red Sox are banking on more seasons of big production from their designated hitter. In 2013, Ortiz hit .309 with 30 home runs. How many players have hit .300 with at least 25 home runs in their age-38 season? Three. Guys named Williams, Bonds and Ruth. OK, maybe .300 is expecting too much. Even if we lower that to .285 with at least 25 home runs, we added just one more player, Willie Stargell.
So the historical odds would suggest Ortiz fades a bit this year. The projection systems, however, are actually rather optimistic. ZiPS has him at .296 with 25 home runs (although playing just 110 games) while Steamer has him at .284 with 24 home runs.
Let's put the over/unders at a .290 average and 25.5 home runs.