Successful NFL running plays. In his article “American Football” (Statistics in Sport, 1998), Iowa State University statistician Hal Stern evaluates winning strategies of teams in the National Football League (NFL). In a section on estimating the probability of winning a game, Stern used actual NFL play-by-play data to approximate the probabilities associated with certain outcomes (e.g., running plays, short pass plays, and long pass plays). The fop lowing table gives the probability distribution for the yardage gained, x, on a running play (a negative gain represents a loss of yards on the play):
x, Yards | Probability | x, Yards | Probability |
−4 | .020 | 6 | .090 |
−2 | .060 | 8 | .060 |
−1 | .070 | 10 | .050 |
0 | .150 | 15 | .085 |
1 | .130 | 30 | .010 |
2 | .110 | 50 | .004 |
3 | .090 | 99 | .001 |
4 | .070 |
a. Find the probability of gaining 10 yards or more on a running play.
b. Find the probability of losing yardage on a running play.
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