They're coming fast, too, because teams understand that the really special ones can hold their own.
Having said all that, let's take a moment to appreciate that plenty of older players are still performing at a high level.
Speaking of Shields, who is 33, some of the many reasons the Padres wanted him is because of his experience and his presence and his leadership. He'll give them 220 innings and 200 strikeouts, but he'll also be an example for every other player on the team.
And so today, we salute the guys who've been around a while, the guys who are still playing at a high level, the guys who are absolute treasures.
So let's count down the 20 best members of the 35-and-older club …
1. David Ortiz, 39
To quote Robert Earl Keen, and the road goes on forever. He was a joy to watch and to be around then. He's a joy to watch and be around now. Big Papi hit 35 home runs in his 18th season, and in six seasons since turning 33, he has averaged 34 doubles, 30 homers, 74 walks and a .909 OPS.
2. Victor Martinez, 36
He was an eyelash shy of a batting title in his 12th season. Led the American League in OBP and OPS. Huge clubhouse presence. Winner.
3. Torii Hunter, 39
Here's to the youngest 39-year-old on the planet. No sign of slowing down. Joy to watch play. Joy to be around.
4. Chase Utley, 36
His career has been resurrected the past two seasons with OPSs of .823 and .746. Tough. No-nonsense. Relentless competitor. In a tough town, he deserves legendary status.
5. Adrian Beltre, 35
Consummate pro. Great defensive third baseman. Solid offensive performer. Here's hoping he plays forever, and he just might.
6. Jayson Werth, 35
Hit .292 in his 12th season. Great pro. His arrival in Washington signaled a new beginning for the Nationals.
7. Matt Holliday, 35
He's tough and consistent and productive. Been that for 11 seasons. Part of what makes the Cardinals special.
8. Albert Pujols, 35
Has it really been 14 seasons? His legs are healthy again and his 14th season produced 37 doubles, 28 home runs and 48 walks. And his team won more games than any other. Typical Pujols stuff.
9. Coco Crisp, 35
Still plays the game with energy and passion. Still productive. Does everything well.
10. Jimmy Rollins, 36
He will bring his energy and his joy and his attitude to Dodger Stadium. He wrote himself an amazing legacy in Philadelphia. He has a chance to help his new team play deep into October.
11. Cliff Lee, 36
Once he gets back on a mound and shows the world his left elbow is sound, he's likely to be traded to a contender. He'll produce the way he always has.
12. Marlon Byrd, 37
He seems ageless. Career rebirth past two seasons. Reds fans will appreciate the totality of his game.
13. John Lackey, 36
Still tough, resilient and productive. Brings a touch of ornery to the office. Fresh off a 198-inning, 164-strikeout season that showed he still has it.
14. Mark Buehrle, 35
Has never thrown fewer than 201 innings during 14 full seasons in the big leagues. That number alone speaks volumes about his accountability and smarts and toughness.
15. Juan Uribe, 35
His 14th season was his best. Not only did he hit .311, his defense at third base was among the best in the game. He gets less attention than any other Dodger. He's still rock solid.
16. Carlos Beltran, 37
The Yankees are confident that if he's healthy, he can produce the way he has for most of a 17-season career in which he has methodically built a borderline Hall of Fame resume.
17. Tim Hudson, 39
He faded in the second half of his 16th big league season. His overall numbers -- 189 innings, 3.57 ERA -- still look solid. Here's to No. 17.
18. A.J. Burnett, 38
He tossed 213 2/3 innings in his 16th season, and even though some of the numbers weren't good, the Pirates are thrilled to have him back in their rotation. He, too, brings a dash of ornery, which isn't a bad thing.
19. A.J. Pierzynski, 38
His .251 batting average was a career low, but he finished his 17th season convinced that he still has plenty left in the tank. It would be a mistake to doubt him.
20. Ichiro Suzuki, 41
One of the most remarkable players of our time. Ten-time All-Star. Led the American League in hits seven times. Great defensive outfielder. The Marlins were thrilled to get him off the free-agent market.
Richard Justice is a columnist for MLB.com. Read his blog, Justice4U. This story was not subject to the approval of Major League Baseball or its clubs.