Module 6

Statistics

Sample Size

• Descriptive Statistics – discussed in Module 1, characterize data, dispersion, central tendency (baseball analytics)
• Inferential Statistics – use a sample of the population and draw inferences about the whole population (projections)
• Law of Large Numbers – as sample size goes up, the sample estimate gets closer to the population estimate
• Calculating sample size is more of a statistical focus than this course.  Factors are z score, standard deviation of the population, and margin of error
  • If z score goes up, sample size goes up
  • If SD goes up, sample size goes up
  • If margin of error goes up, sample size goes down
• Russell Carleton (pizzacutter) study in 2007 todetermine how long baseball stats take to normalize (stay consistent with each other)
  • Plotted Batting Average in odd at bats vs. Batting Average in even at bats
  • Wanted R^2 of at least 0.50

Sabermetrics

WAR

• Wins Above Replacement
• Statistical framework for total offense and defense contributions that reflects performance and playing time
• Variations
  • WARP (Baseball Prospectus)
  • fWAR (fangraphs)
  • bWAR / rWAR (Baseball Reference)
  • oWAR (Open source WAR)
• Components:
  • Replacement level
  • Runs to Wins
  • Runs Estimators
• Morris Greenberg has studied the three main variations of WAR
  • Cannot predict any WAR measure just by knowing another alternative WAR calculation
  • The three variations do not have a relationship to each other
  • The three methods are probably assigning different values of wins for hitter production
  • Increased playing time leads to a greater variance between the three measures (amplifies the differences)
  • Hitters who play 2B, SS, CF have more variant outcomes than other positions, meaning these positions have different variations in fielding calculations
  • There are also more variation for pitchers in the extremes (the top and the bottom pitchers).  Probably due to how the systems attribute pitcher outcomes to pitchers versus defense.
• Basis framework of calculating WAR is to use the pythagorean calculations and extending out the calculation to become:  W/L = (R/RA)^2
• Instead of squaring this calculation, you can try todetermine the best exponent to use (instead of 2)
  • For 1901 to current, the best fit exponent is 1.863

Technology

• Park Factor = 100 * ((homeRS+homeRA)/homeG) / ((roadRS+roadRA)/roadG)
• Anything over 100 is above average, below 100 is below average
• Can use this same formula for any batting statistic
• This SQL query on the retrosheet game log can help you calculate it for teams (this one is doing a HR park factor)

R Studio

• lm() – fitting linear models
• function(arglist) expr
  return(value)
• Build functions to create automated method of recalculating things you would commonly like to reperform

SQL

• CASE
  WHEN (expression)
  ELSE
  END

History

George Lindsey

• Canadian, University of Toronto, WWII, PhD from Cambridge, Nuclear Scientist
• First work, in 1959, was a look at batting average and if it could be used to predict future performance.
  • Concludes there were too many variables at play (differing pitchers, parks, situations, leagues, etc.).
  • Conducted a study of same-sided batter-pitcher matchups and found a statistically significant result that an advantage exists for opposite handed hitters
  • First published statistical study of L/R batting splits
  • Also first published look at run scoring expectancy in bases loaded situations
  • Was trying to figure out if you should try for a force out at home in bases loaded situations or if you should try for a double play
• 2nd paper, Progress of the Score During a Baseball Game
  • Isthe probability of scoring in any half inning the same?  Is run scoring by inning homogeneous?
    • 1st (high), 2nd (low), 3rd (high) are different from mean
    • Likely due to structure of batting order
  • Does the history of scoring affectsubsequent innings?  Is scoring independent?
    • Large run scoring seems to not be independent
    • Lead changes follow a model of independence, meaning there is no tendency to overcome leads
  • Studied home field advantage (54%)
• 3rd paper, An Investigation of Strategies in Baseball
  • Tries to address steal a base or not to, sacrifice bunt with less than 2 outs, IBB when 1st base is open, etc.
  • The most important runs (in terms of affecting win probability) are those that tie the score or put you 1 run ahead
  • Analyzed all base states and the probability of scoring 0, 1, 2 runs.  Also looked at the expected runs for each situation.
  • He uses these expectations to determine optimal strategy (if you bunt in this situation, what does it do to your expected runs?).
  • If you are in a specific situation and then you hit a triple, what happens?  What happens to your expected runs in the new situation?  How much does it increase from before?
  • The beginning of linear weights
  • A value added approach of measuring a player
  • Concludes IBB is not useful except for winning by one run and runners on 2 and 3 (the likelihood of scoring 0 runs increases by actually loading the bases, but the overall expected run value of this goes up too)
  • Concludes to always play double play depth with a runner on 1st, except with a runner on third that would tie the game/take the lead
  • Concludes sacrifice play does not improve scoring chances.
  • Concludes stolen bases value is dependent upon an individual’s success rate