THE BOOK--Playing The Percentages In Baseball

Tango, thanks for the link.

The equation that I used was weight = 5.62*exp(-6.6x10-4(days ago)).  You can ignore the prefactor if you want, it all normalizes out in the equations that I use.  If you evaluate that equation, you get:

Days Ago Weight
1/2 year 4.98
1.5 year 3.91
2.5 year 3.08

Which is essentially Marcel’s 5/4/3 weighting, with the numbers jiggled to get the right weighting at the half year.

Also it turns out that, exp(-6.6x10-4*days_ago) = 0.99934^(days_ago) (uh...by design, I guess.  I used your equation as a jumping off point!)

In other words, it all comes out in the wash.

Also, I should mention that, in order to mimic Marcel most closely, I set the weight = 0 for anything more than 3 years ago.  That’s easily turn-offable, though.

Ah, well nevermind then!

Though, I think having the equation with fewer terms would be more palatable.

Tango, I see your point of view, and it’s probably one shared by...well, everybody.  But personally, I find exponentials to be highly intuitive.

I forgot to mention something here.

When you look at the running Marcels, the true talent estimate at a particular point in time presumes that the rest of career will follow the standard distribution.  So, a guy’s true talent level on Jun 1, 1999 knows nothing of his performance after that, if you follow the day-to-day Marcels.

However, given that you do know what happens after that point, your true talent ESTIMATE (as opposed to FORECAST) changes. 

Think of Ryan Howard.  After his rookie year, your forecast for him on Apr 1, 2006, was still quite tempered.  But, now that we know what he did in 2006 (MVP) and 2007 (great year), we have a new true talent estimate on Apr 1, 2006, an estimate higher than his forecast (at that point in time).