For 30 years, the National Football League (NFL) has mandated sudden-death overtime to decide games that are tied after 60 minutes of play. The first team to score in overtime wins the game. If neither team scores at the end of 15 minutes of overtime, the game ends in a tie.
A coin flip determines which team gets the ball first. The winner of the toss can choose whether the team wants to receive the ball and begin an offensive series or pick a goal to defend.
Many people have the perception that whichever team wins the coin toss and chooses to receive the ball typically goes on to score and win the game, often on the first possession. This perception has led to calls for changes in the overtime rule. In fact, the NFL has suggested an alternative: The first team to score six points in overtime wins the game.
| Total no. of overtime games (1974–2003) |
365 |
| Both teams had at least one possession |
261 (72 %) |
| Team won toss and won game |
189 (52 %) |
| Team lost toss and won game |
160 (44 %) |
| Team won toss and drove for winning score |
102 (28 %) |
| Games ending in a tie | 15 (5 %) |
| Overtime games in 2002 |
26 |
| Both teams had at least one possession |
15 (58 %) |
| Team won toss and won game |
16 (62 %) |
| Team lost toss and won game |
9 (35 %) |
| Team won toss and drove for winning score |
10 (38 %) |
| Games ending in a tie | 1 (3 %) |
| Overtime games in 2003 |
23 |
| Both teams had at least one possession |
16 (70 %) |
| Team won toss and won game |
12 (52 %) |
| Team lost toss and won game |
11 (48 %) |
| Team won toss and drove for winning score |
6 (26 %) |
| Games ending in a tie | 0 (0 %) |
The data appear to support the notion that the football team scoring first in sudden-death overtime is usually the one that had won the coin toss and received the ball.
Interestingly, the cumulative data hide the effect of a rule change that occurred in 1994, when kickoffs were moved back 5 yards to the 30-yard line. Since 1994, nearly one-third of overtime games have been won on the first possession by the team that received the ball first. In the first 20 seasons, under the old rule, slightly more than one-quarter of the games were won in this fashion.
A recent analysis by economist Richard E. Hawkins of Pennsylvania State University in DuBois confirms that these differences are statistically significant.
“The analysis finds with 99.99 % certainty that the [coin] flip has made a difference in the outcome of the game over the last 10 years,” he concludes. “But for the period prior to those 10 years, the coin flip cannot be shown to be important.”
Would a first-to-six overtime rule do any better?
In the current issue of the College Mathematics Journal, Michael A. Jones of Montclair State University in New Jersey uses a probability model and data from the 2002 NFL regular season to compare the current overtime rule with the suggested first-to-six rule. His analysis looks at the impact of the coin toss on both the outcome of the game and the efficiency of eliminating ties.
Using a so-called Markov chain model, Jones examines the consequences of sudden-death overtime on two fairly matched teams, assuming that both teams have equal probabilities of scoring a touchdown and kicking a field goal. He does the same for the first-to-six proposal.
“The first-to-six proposal does decrease the probabilities that the receiving team wins the game on the first possession and that they win the game eventually,” Jones concludes. However, “although the first-to-six rule reduces the impact of the coin toss on the outcome of the game, it is less efficient at eliminating ties.”
Applied to 2002 data, the model developed by Jones suggests that the team winning the coin toss and receiving the ball would win with a probability of 49 percent under the first-to-six rule (versus 60 percent for sudden-death overtime). The probability of games ending in a tie would rise to 12 percent (versus 9 percent).
Is the suggested rule worth implementing?
“This reduction in the impact of the coin toss on the outcome of the game is a trade-off because of the increase in the number of tie games,” Jones writes. “Although fans would be happy that the outcome of the game is decided less by luck and more by play on the field, coaches may regret Monday morning quarterbacks second-guessing their decisions of whether or not to attempt field goals in overtime. Scoring three points still gives the other team an opportunity to score a touchdown and win the game.”
“One thing is certain,” he adds. “The first-to-six proposal increases the probability that fans will discuss the National Football League in the off-season.”
Puzzle of the Week
Without letting your pencil leave the paper, draw six straight lines to connect the 16 dots shown above.
Bonus: What is the minimum number of lines you would need to solve the puzzle if it consisted of 9 dots? 25 dots? n2 dots?
For the answer, go to http://www.sciencenewsforkids.org/articles/20041027/PuzzleZone.asp.
