26674 regular season professional football games have played

26,674 regular season professional football games have played from 1940 through 2015. 118 of these games ended in a tie from 1940 through 1973. the national football league (NFL) instituted overtime (OT) during the 1974 regular season. 527 regular season NFL games went into OT from 1974 through 2015. 32 of the 526 NFL playoff games played from 1940 through Super Bowl 50 (2016) have gone into OT. (please show work)

A) what percentage of NFL regular season games since 1940 have ( or could have) gone into OT?

B) what percentage of NFL playoff games since 1940 have gone into OT?

C) what is the probability of finding 32 OT games in a random selection of 527 NFL regular season games? what does this result suggest about the true percentage of OT games in the regular season versus the playoff? support your claim with statistical analysis

D) if 50 playoff games are randomly selected, how many do we expect to go into OT?

E) what is the probability that 50 randomly selected playoff games all end in regulation? is this a rare event? explain. how many of the 50 super bowls have gone into OT?

Solution

A) 527 regular season NFL games went into OT from 1974 through 2015.Also, 26,674 regular season professional football games have been played from 1940 through 2015.Therefore, the percentage of NFL regular season games since 1940 which have gone into OT is 527/26674 = 1.976 % ( on rounding off to 3 decimal places).

B) 32 of the 526 NFL playoff games played from 1940 through Super Bowl 50 (2016) have gone into OT. Therefore, the percentage of NFL playoff games since 1940 which have gone into OT is 32/526 = 6.084 %  ( on rounding off to 3 decimal places).

C) The probability of finding 32 OT games in a random selection of 527 NFL regular season games is 32/527 = 0.0607( approximately). The true percentage of OT games in the regular season is 1.976 % whereas the true percentage of OT games in the playoff is 6.084 % which is much higher than the true percentage of OT games in the regular season.

D) If 50 playoff games are randomly selected, we can expect 50 *0.0607 = 3.035 or, 3 games ( on rounding off to a whole number) to go into OT.

E) The probability that 50 randomly selected playoff games all end in regulation is 1 - 0.0607 = 0.9393. This number is pretty large, so that it cannot be called a rare event.32 of the 526 NFL playoff games played from 1940 through Super Bowl 50 (2016) have gone into OT.