After scoring a touchdown in football, a coach must make a decision on whether the team should kick for one extra point or attempt a two-point conversion. A coach argues that the team should always kick the extra point because it is the safer play to guarantee a point.
He argues further that in one National Football League (NFL) season, teams were successful kicking the extra point 94% of the time while they were only successful on the two-point conversion 49% of the time.
Write an argument to support the fact that a team should choose the two-point conversion based on the expected values you found in Questions 2 and 3. Be sure to include standard deviation in your answer as well.
Lets say you score 100 touch downs
kicking you get 0.94 * 100 * 1 = 94 points
running you get 0.49* 100 * 2 = 98 points
To support the decision to choose the two-point conversion over kicking the extra point in football, we need to analyze the expected values and standard deviations of both options. This will help us understand the potential outcomes and risks associated with each decision.
Expected value is a statistical concept that measures the average outcome of a random event. It is the probability-weighted sum of all possible outcomes. To calculate the expected value of each option, we need to consider the success rates provided.
For the extra point kick, the success rate is 94%. This means that, on average, the team will score 0.94 points per attempt. Therefore, the expected value of the extra point kick is 0.94.
For the two-point conversion, the success rate is 49%. This means that, on average, the team will score 1.98 points per attempt (0.49 x 2). Therefore, the expected value of the two-point conversion is 1.98.
Comparing the expected values, we can clearly see that the two-point conversion has a higher expected value (1.98) compared to the extra point kick (0.94). This means that choosing the two-point conversion will, on average, result in more points for the team.
However, it's also crucial to consider the standard deviation, which measures the variability or risk associated with each option. A higher standard deviation implies a greater range of potential outcomes.
Unfortunately, the standard deviation values for the extra point kick and two-point conversion are not provided in the question. Therefore, we don't have the complete information to assess the level of risk associated with either option accurately. However, in general, two-point conversions tend to have a higher variance, meaning there is greater uncertainty in the outcome compared to extra point kicks.
So, based on the given success rates and expected values, it is statistically advantageous to choose the two-point conversion over the extra point kick. However, the decision also depends on other factors, such as the team's overall strategy, the specific game situation, and the coach's assessment of the team's capabilities.