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Older players who are smaller in stature tend to struggle more than bigs after the 82-game grind. But you can get away with playing bigs as they can do a lot of things that don't show up in the box score: Set a screen, alter a shot, block out on a free throw, make the right read on a pass. And, of course, by nature of their size, they can still get 3-5 boards/game.
If the vet is PJ Brown or Robert Horry, they're still effective shooters, as well.
Yes, there are exceptions to the "big vs little" argument. Derek Fisher has been a great addition to the Lakers. On the other hand, Chris Webber didn't have much of an impact with the Warriors.