Trends in Baseball Scoring & Strikeouts, Geoffrey Holland ECON 5341 Advanced Data Analysis 16 November 2015

Transcription

1 Trends in Baseball Scoring & Strikeouts, Geoffrey Holland ECON 5341 Advanced Data Analysis 16 November 2015

2 Background Statistics are intrinsic part of Baseball Series under study are Runs Scored and Strikeouts Data from Lahman Baseball Database Contains individual player records back to 1871 Nearly 100,000 player-seasons available Time period: Year of the Pitcher, 1968 Steroid Era, 1990s-2000s Second Year of the Pitcher, 2010 Data points normalized to team average for a season Work stoppages (1972, 1981, 1994) Changing number of teams (18 in 1961, 30 in 2014) 162-game season (adopted by AL 1961, NL in 1962) Examine both league-wide and individual teams

3 1,400 Runs & Strikeouts League Average 1,200 1, , Year of the Pitcher R SO

4 1,400 1,200 Runs & Strikeouts League Average Steroid Era 1, R SO

5 1,400 1,200 Runs & Strikeouts League Average 2010, Second Year of the Pitcher 1, R SO

6 Hypothesis Runs and Strikeouts will demonstrate Autocorrelation Good players tend to stay in the league, so positive performance begets positive performance Both series will be stationary Baseball seasons are finite Runs and Strikeouts are count variables, not continuous Individual Teams will have higher order Autocorrelation due to persistence of exceptional players

7 1,400 Runs & Strikeouts League Average 1,200 1, R SO Runs appears stationary, but SO may not be

8 ACF & PACF Autocorrelations of so Lag Bartlett's formula for MA(q) 95% confidence bands Partial autocorrelations of so Lag 95% Confidence bands [se = 1/sqrt(n)] Autocorrelations of r Lag Bartlett's formula for MA(q) 95% confidence bands Partial autocorrelations of r Lag 95% Confidence bands [se = 1/sqrt(n)] Underlying Process appears to be AR(1)

9 OLS Results - Runs T-stat 6.93 > % critical value β <1, so Runs is stationary

10 OLS Results - Strikeouts T-stat > % critical value But β >1, so Strikeouts is non-stationary

11 First Difference of Strikeouts -50 SO, D yearid Autocorrelations of D.so Lag Bartlett's formula for MA(q) 95% confidence bands Partial autocorrelations of D.so Lag 95% Confidence bands [se = 1/sqrt(n)]

12 VAR Model

13 Conclusions Runs and Strikeouts will demonstrate Autocorrelation First lag only High turnover Difficult to sustain performance Too many structural breaks X Both series will be stationary Runs is stationary because β <1 Strikeouts is non-stationary I(1) KPSS rejects null, ADF and PP fail to reject at α = 0.01 Probably a coincidence due to late-year outliers, but interesting nonetheless

14 Forecasting Method 1. Normalize Runs and Strikeouts for full 162 game season 2. Regress Runs and Strikeouts on Trend term 1. Save detrended Runs and Strikeouts 2. Save constants & coefficients from OLS trend regression 3. Calculate straight-line 2015 Runs and Strikeouts from trend regression coefficient & constant 4. Create VAR model from detrended Runs and Strikeouts 1. Lag selection using AIC, HQIC, and SBIC. Lag length varies by team. 5. Use VAR model to predict Runs and Strikeouts above or below trend in Add the straight-line regression to VAR-predicted delta for final adjusted forecast

15 1,400 Runs & Strikeouts League Average 1,200 1, R SO

16 League Avg Forecast 1 Lag yearid R (detrended) SO (detrended) frstat, dyn(2015) fsostat, dyn(2015) 95% LB for frstat 95% UB for frstat 95% LB for fsostat 95% UB for fsostat 2015 Forecast Strikeouts Runs OLS Straight Line Forecast 1, VAR Delta 126 (82) Adjusted Forecast 1, Actual 1, Delta from Forecast 1 (1) Delta % from Forecast 0.1% -0.2%

17 Runs and SO by Team Los Angeles Angels Baltimore Orioles Pittsburgh Pirates Texas Rangers Graphs by Team Dummy Year Runs Scored per 162 Strikeouts per 162

18 Rangers Forecast 1 Lag Year R (detrended) frstat, dyn(2015) SO (detrended) fsostat, dyn(2015) 2015 Forecast Strikeouts Runs OLS Straight Trend Forecast 1, VAR Delta 49 (79) Adjusted Forecast 1, Actual 1, Delta from Forecast 100 (43) Delta % from Forecast 8.8% -5.4%

19 Angels Forecast 2 Lags Year R (detrended) SO (detrended) frstat, dyn(2015) fsostat, dyn(2015) 95% LB for frstat 95% UB for frstat 95% LB for fsostat 95% UB for fsostat 2015 Forecast Strikeouts Runs OLS Straight Trend Forecast 1, VAR Delta 58 (69) Adjusted Forecast 1, Actual 1, Delta from Forecast 85 (81) Delta % from Forecast 8.0% -10.9%

20 Pirates Forecast 3 Lags Year R (detrended) frstat, dyn(2015) SO (detrended) fsostat, dyn(2015) 2015 Forecast Strikeouts Runs OLS Straight Trend Forecast 1, VAR Delta 186 (69) Adjusted Forecast 1, Actual 1, Delta from Forecast (34) 95 Delta % from Forecast -2.5% 15.8%

21 Orioles Forecast 4 Lags Year R (detrended) frstat, dyn(2015) SO (detrended) fsostat, dyn(2015) 2015 Forecast Strikeouts Runs OLS Straight Trend Forecast 1, VAR Delta - (9) Adjusted Forecast 1, Actual 1, Delta from Forecast 321 (36) Delta % from Forecast 31.8% -4.8%

22 Acknowledgements Lahman Baseball Database copyright Sean Lahman. Used with permission under Creative Common License This presentation was created with design template from SmileTemplates.com.

23 Questions?