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Milestones and the favorite toy

Posted by Doug on March 26, 2006

In the 1980s, legendary baseball author Bill James developed a quick-and-dirty method of estimating a player's chance of eclipsing a particular milestone. I'll describe it while working through LaDainian Tomlinson's chance of breaking Emmitt Smith's rushing record:

  1. Compute the "need yards." Tomlinson has 7361 yards and needs 18355 to catch Emmitt, so his need yards is 10994

  2. Compute the years remaining. James' formula for this was 24 - .6(age). Tomlinson is 27, so this would give him 7.8 remaining seasons. Clearly this part of the formula needs a tweak; running backs don't stick around as long as left fielders do. We'll investigate this further at some point, but as a first guess, let's change the .6 to a .7, which gives Tomlinson 5.1 more seasons.

  3. Compute the established yardage level. James used the usual three-year weighted average: three times last year's yards, plus twice the year before's yards, plus the previous year's yards, all divided by 6. For Tomlinson, that estimate would be 1450 yards, which seems reasonable.

  4. Compute the projected remaining yards. 5.1 times 1450 = 7395

  5. The probability of reaching the milestone is estimated at
    (ProjectedRemainingYards / NeedYards) - .5.
    For Tomlinson this is about 17%.

Does that feel right? Would you take five-to-one odds on Tomlinson breaking Emmitt's record? Would you best against it at one-to-five? Bill James called this method The Favorite Toy, which conveys both that it is fun to play around with and that it shouldn't be taken too seriously.

In subsequent posts I'll investigate some more mathematically elaborate --- but not necessarily more accurate --- methods of estimating these sorts of things. For now I'll leave you with the short list of runners who, according to The Favorite Toy, have a shot at Emmitt Smith's rushing record.

Runner Pct Chance
Clinton Portis 26.5
Edgerrin James 21.3
LaDainian Tomlinson 17.3
Shaun Alexander 11.3

If these estimates are to be believed, there is about a 57% chance that one of these four guys will break Emmitt's record.

This entry was posted on Sunday, March 26th, 2006 at 7:25 pm and is filed under Statgeekery. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.