A Favorite Toy Update for Career Homersby David Marasco A few years back Bill James made up a rough-and-ready prediction system he called the "favorite toy." The idea was to predict if a player could hit a certain milestone in a given stat. Suppose that Joe Ballplayer was at 2500 hits, what were his chances at getting to 3000? James reasoned that if you could be expected to get 500 hits based upon your previous stats, then you had a 50/50 chance of getting those 500 hits. In more general terms, he set the probability of getting to a certain milestone as (expected/needed) - 0.5. In other words, if you could be expected to get 50 more home runs, and you needed 100 for the milestone, then you had a 50/100- 0.5 = 25% chance of doing so. But how many events could be expected? James realized that there were two components to this. The first was a rate, and he felt that a weighted average of (3*last year + 2* one year prior + 1* two years prior)/6 was the proper rate. In addition to this, James estimated remaining career by assuming that a 20-year-old had 12 years left, and subtracted .6 years for each year actually used. In other words, a 30-year-old has used 10 years, so subtract 6 from 12 to get an additional 6 years expected in the career. You never have fewer than 1.5 years left, no matter what your age. As a limiter to extreme cases (both due to young players and players very close to the milestones), James included a .97^n ceiling where n is the number of years the player would need to play at the established rate. Here we've taken the home run numbers for a selection of players and projected them through the end of the 2001 season. From there we've used Favorite Toy to estimate their odds for various homerun milestones from the start of 2002.
Favorite Toy's projections on McGwire are pessimistic due to two factors: Mac's age and his drop in recent production due to injury.
Barry has benefitted from his late-career power surge. He has stated in the past his intention of catching his God Father Willie Mays at 660.
Despite recent troubles, Junior still has an excellent shot at climbing into some impressive company.
On one hand, seeing that a formula predicts that Sammy has a 20% chance of hitting 800 home runs makes you want to hit the side of the monitor to fix the computer. On the other hand, in past years Sammy has blossomed into an incredible player.
It looks like playing that year in large Comerica Park has put a dent in Juan's established rate. Perhaps after a few years in the Jake the Toy will predict better numbers for Gonzalez.
Manny is helped in this category by his young age. Still, with Manny and the rest of the players from this point on, it is a little hard to trust an algorithm where the player is expected to hit more homers in the balance of his career than he has already hit.
One of the things that Boras said was that A-Rod had a chance at 756. Right now that looks like a one-in-four chance.
Again, the 10% chance at 800 should be taken with a grain of salt, after all, he has fewer than 200 at this point.
While five men have better than a 50% chance of joining the 600 club, and two have a better than 50% chance of passing Mays, only Sammy and A-Rod are given a better than 25% chance of passing 700.
Leave feedback on our message board. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||