As with many a key sabermetric tenet, Bill James is responsible for introducing the idea that ballplayers, or at least hitters, reach their peak value at the age of 27. In fact, it was a serendipitous 27 years ago, in the 1982 Baseball Abstract, that James first presented his research supporting this conclusion, thus contradicting the then-prevailing wisdom that ballplayers peak between the ages of 28 and 32.
While you wouldn't know it to see the way certain front offices function when signing over-the-hill hitters, this particular bit of James' wisdom has withstood the test of time, and has even undergone some expansion. Using more advanced valuation methods, Nate Silver has found that players peak between the ages of 25 and 29, generally cresting at 26 and 27, with some understandable variations by positions. Speed-based players, like middle infielders and center fielders, tend toward the earlier side of that range.