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Is football just luck?


Gary_Yngve

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graph.gif

 

The above bargraph is the result of a million trials of twelve simulated drives.

 

A drive of 80 yds or more earned 7 points, a drive of 60-79 yards earned 3 points, and anything less earned 0 points. A drive was assumed finished on a turnover, a score, or a 4th down (mandatory FG or Punt).

 

Each play was (incorrectly) assumed to be independent of any other play, the down, or yards needed for a first.

 

The distribution of yardage was assigned relatively arbitrarily as follows:

 

2%: turnover

3%: loss of 2 to loss of 15

15%: loss of 2 to gain of 1

20%: gain of 1 to gain of 4

20%: gain of 4 to gain of 8

15%: gain of 8 to gain of 16

5%: gain of 16 to gain of 32

2%: touchdown

 

Note the wide spread in total scores.

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There's actually a lot of interest in psychology and probability:

 

http://www-stat.stanford.edu/~cgates/PERSI/courses/stat_121/lectures/psychofprob/

 

One thing I find interesting is if you take what's his name who had 3000+ hits in baseball, a .300+ average, and a hit-in-a-game streak of 40+ days, and work out the math assuming each swing has identical independent probability, the expected streak over his career agrees what actually happened.

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