Mahler Flashcards
Tests for changing risk parameters over time
Chi-squared
Compare correlations between years
Correlation between years test
1) For each separation in time, calculate correlation between given year value and the value t years prior
2) Take straight average of correlations for each separation in time t
3) Examine how average correlation depends on t: if correlation is greater between years closer together, risk parameters are shifting over time.
6 methods for estimating X for credibility
3 methods to evaluate quality of estimate X
Least Squared Error
Limited Fluctuation
Meyers/Dorweiler – focuses on pattern of errors vs. minimization of errors
Least Squared Error
SSE = Σ (Xest,team - Xact,team)2
MSE = SSE / # of teams
Limited Fluctuation
Small Chance of Large Errors
Meyers/Dorweiler
Confirms no evidence that large predictions lead to large errors and small predictions lead to small errors
Mahler final points
If risk parameters shift over time, older data should be given less or no credibility
Not having the most recent year of historical data significantly increases the squared error of the estimate
Simplifications of baseball data
- Constant set of risks
- Readily available, accurate, and not subject to development
- Each team of equal size with equal games played
Xest = µ
Every risk is average; give past data 0% credibility
Xest = Y1
Last year repeats (100% credibility to last year)
Xest = ZY1 + (1 - Z)µ
Credibility weight last year and the grand mean
Xest = Z/n ΣYi + (1 - Z)µ
Given the last n years equal weight (Z/n)
Xest, i + 1 = ZYi + (1 - Z)Xest, i
Exponential smoothing
Weighted least squares regression - weights geometrically decreasing for older data
