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ShareThisMilestones and the favorite toy
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:
- Compute the "need yards." Tomlinson has 7361 yards and needs 18355 to catch Emmitt, so his need yards is 10994
- 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.
- 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.
- Compute the projected remaining yards. 5.1 times 1450 = 7395
- 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.
I'm surprised Alexander isn't higher. Is he significantly older than the others?
Interesting entry.
By the same calculation, Edgerrin has a 32.5% chance to break the Yards From Scrimmage record.
This doesn't account for toughness nor does it account for plain luck...Ken Griffey will NOT break the home run record, neither will A Rod...gotta stay healthy, gotta stay hot.
[...] As promised in this post, I’m going to create a more sohpisticated way to estimate players’ chances of reaching records or milestones. I’ll spend this post describing the mathematics behind my method. [...]
I'd bet $50 that A-Rod breaks the HR record. Not that that has anything to do with football. Excuse me, I'm going to go find a baseball blog.
[...] Awhile back I posted a few entries (I, II, III) about estimating a player’s chances at reaching a career milestone using a mathematical gadget called a Markov chain. [...]
Tomlinson has a 27.5% chance of breaking Emmitt's record.
Tomlinson has 10,650 yards and needs 18355 to catch Emmitt, so his need yards is 7,705.
Tomlinson is 29, so he has 3.7 years remaining.
Tomlinson's established yardage level is 1586.
Projected remaining yards = 5,867.
The probability of reaching the milestone is 26.1%.
Interesting that LT ran for nearly 1500 yards last season, but his odds of breaking the record decreased slightly. That seems about right though, especially since he had his first serious injury last year.
You can't use the same age factor.
It should probably be more like 35-.6 for running backs.
LT has 11760 and needs 6595 to catch Emmitt.
Years remaining: LT is 30, so this would give him 3 years left.
Established rushing level: 1349
Projected remaining yards: 4047
Probability: 11%
[...] years ago, in some of the earliest posts on the blog, Doug used an adaption of Bill James’ “Favorite Toy” to estimate the chances of several backs to reach Emmitt Smith’s rushing record. As a quick [...]
With only 289 yards eight games into his 30 year old season, I'd say his odds are fast approaching zero.
[...] likelihood of Frank Gore becoming the 49ers all time leading rusher. In that post, he referred to another post from three years ago, which looked at the probability of certain players breaking Emmitt Smith’s career rushing [...]
Yes, clearly these probabilities are way too optimistic. Emmitt played for 15 years and all but one rushed for 900+ (and most were 1000+). Longevity is what's needed more than anything and most running backs run out of gas too soon. (Especially if they catch a lot more passes than Emmitt?)
Also:
"If these estimates are to be believed, there is about a 57% chance that one of these four guys will break Emmitt's record."
should read "...that AT LEAST one of these four guys will break Emmitt's record."
(Because the unstated calculation is that there's a 43% chance that none of them break it.)