September 11, 2018

When Does Something "New" Happen in Baseball?

  • Never? Always? Both justifiable answers.

"New" will only be interesting if it is …

  • … a relatively rare event, and
  • … inexhaustible, so that new will always be possible.

Outline of Talk

  • Review rules of the game.
  • Define a concept of "new" in baseball that will be rare and inexhaustible.
  • Ask interesting questions about the game.
  • Sound a call to action.

Batting Starts the Play

The Batter Becomes A Runner Who Can Stop On 1 of 3 Bases

Runners Want to Avoid Outs

There are 8 Possible Situations With the Bases

  • 0 – Bases empty
  • 1 – Runner on first
  • 2 – Runner on second
  • 3 – Runner on third
  • 12 – Runners on first and second
  • 13 – Runners on first and third
  • 23 – Runners on second and third
  • 123 – Bases loaded

There are 4 Possible Situations with the Outs

  • (Blank) – No outs
  • X – One out
  • XX – Two outs
  • XXX – Three outs; half inning over

There are 25 Possible Game "States"

  • 24 Transient States
    • 0, 1, 2, 3, 12, 13, 23, 123
    • 0X, 1X, 2X, 3X, 12X, 13X, 23X, 123X
    • 0XX, 1XX, 2XX, 3XX, 12XX, 13XX, 23XX, 123XX
  • 1 Absorbing State
    • XXX

The 2 Most Frequent States

The 25 states of baseball, arranged randomly, and sized according to frequency of appearance during 2011 Major League play.

Most and Least Frequent States

The 5 Possible "Transitions" from the 0 State (Bases Empty, No Outs)

  • 0:0X – Out
  • 0:1 – Single
  • 0:2 – Double
  • 0:3 – Triple
  • 0:0 – Home Run

The 20 remaining final states cannot be reached from 0 in one play.

(E.g. 0:XXX is illegal, based on the rules of the game.)

24 Transitions Are Possible From the 123 State (Bases Loaded, No Outs)

  • All final states can be reached from 123, except 123XX

304 Transitions (Of 600 Conceivable) Are Impossible

E.g.:

  • 123X:123
  • 0:123
  • 0:0XX

The remaining 296 transitions are possible.

272 Transitions Occurred in 2011

272 transitions sized by frequency of occurrence in the 2011 Major League Season. Additionally, there were 24 legal transitions that never occurred that season (not shown).

The Most Frequent Second State

Transition Probabilities Allow Simulations, Calculations

sim.baseball(5, BAL, seed=1)
## [1] "0:0X:0XX:XXX"           "0:1:1X:23X:3X:0XX:XXX" 
## [3] "0:0X:0XX:XXX"           "0:1:1X:2XX:XXX"        
## [5] "0:1:2:2X:2X:1X:1XX:XXX"

"New" Half-innings are 2% frequent

9 most frequent half innings sized by probability. Also shown and sized by collective probability: "Rarely seen" (each < 1% frequent) and "Never seen" ("New" after 3.8 M simulations).

How Rare Are "New" Half-Innings?

New half-innings are inexhaustible

  • With no cap on score, there are infinitely-many half-innings possible.
  • "New" half-innings are getting rarer, but apparently slowly.

Questions About Baseball History

  • What is the shortest half-inning that has never been played in Major League history?
  • What never-played half-inning has the highest likelihood of occurring in the future?
  • What is the least likely half-inning that has in fact been played in major league history?

Recap of Talk

I have:

  • Defined "new" in Baseball to be a new sequence of transitions between game states.
  • Shown these events in Baseball are relatively rare and always possible.
  • Asked questions that I think Baseball fans would be curious to have answered.
  • Finally …

Call to Action

  • If you interested in answering these or similar questions,…
  • I'm looking for student collaborators.
  • Contact me, if interested.
  • Requires: experience coding, and love of Baseball.