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APPENDIX B. Moving Average Smoothing of Data

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Baseball’s All-Time Best Sluggers
This chapter is in the book Baseball’s All-Time Best Sluggers
226APPENDIX BMoving Average Smoothing of DataA moving averageis used in this book to smooth the seasonal standard deviations (SDs)for each offensive event. For the National League, we have 128 standard deviations,one for each year from 1876 to 2003. The numbers form a time series.The moving average is the second of three methods presented in this book for mod-eling time series data. It differs from the other two (piecewise linear regression and mul-tiple changepoint regression) in that the number of years included in each average isconstant, except for end effectsthat apply to the first and last years of the time series.Many financial reports on stock market prices use moving averages to provide sim-pler summary views of trends over time. The moving averageestimate of the SD fora given year is the average of a certain fixed number of years just below and abovethe given year plus the year itself.The critical question is: how many years? If the number of years is too small, therandom component will not get smoothed out. If the number is too large, the realtrend will get partly smoothed away. Moreover, no single number is likely to perfectlyseparate the random and true components of variation from each other.In this book, a 5-year moving average is used. Why use 5 years? Given the defini-tion of a moving average given earlier, an odd number of years is needed. Dramaticchanges such as league expansion, a shift in the style of play, or rule alterations canaffect the spread of performance fairly quickly, pushing the choice toward a small number of years. Although some baseball analysts use three years, I believe thata 5-year moving average, which produces SD estimates that shift direction much lessoften (as explained further later), is a better choice.How to Calculate Moving AveragesTable B.1 gives the raw standard deviations (first row) of the mean-adjusted regularplayers’ home run averages for the National League for 1993–2000, on square root
© 2016 Princeton University Press, Princeton

226APPENDIX BMoving Average Smoothing of DataA moving averageis used in this book to smooth the seasonal standard deviations (SDs)for each offensive event. For the National League, we have 128 standard deviations,one for each year from 1876 to 2003. The numbers form a time series.The moving average is the second of three methods presented in this book for mod-eling time series data. It differs from the other two (piecewise linear regression and mul-tiple changepoint regression) in that the number of years included in each average isconstant, except for end effectsthat apply to the first and last years of the time series.Many financial reports on stock market prices use moving averages to provide sim-pler summary views of trends over time. The moving averageestimate of the SD fora given year is the average of a certain fixed number of years just below and abovethe given year plus the year itself.The critical question is: how many years? If the number of years is too small, therandom component will not get smoothed out. If the number is too large, the realtrend will get partly smoothed away. Moreover, no single number is likely to perfectlyseparate the random and true components of variation from each other.In this book, a 5-year moving average is used. Why use 5 years? Given the defini-tion of a moving average given earlier, an odd number of years is needed. Dramaticchanges such as league expansion, a shift in the style of play, or rule alterations canaffect the spread of performance fairly quickly, pushing the choice toward a small number of years. Although some baseball analysts use three years, I believe thata 5-year moving average, which produces SD estimates that shift direction much lessoften (as explained further later), is a better choice.How to Calculate Moving AveragesTable B.1 gives the raw standard deviations (first row) of the mean-adjusted regularplayers’ home run averages for the National League for 1993–2000, on square root
© 2016 Princeton University Press, Princeton
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