This article focuses on sports analytics point distributions and expected points.
One probability distribution that is especially useful in sports statistics is the distribution of the points scored. This distribution analyzes the probability of scoring points in any given situation. In a football game, a team could be on second down at their opponent’s ten-yard line. The distribution would give the probability of the team scoring 6 points, 3 points, or no points in that situation.
The distribution of points is very detailed, which is not always required. At these times, the expected value, also known as expected points, is a more useful tool. Rather than a distribution of points, the expected points boils the chances of scoring points in a particular scenario down to one number. For example, a baseball team has a runner on third base, with one out. The expected runs in this scenario would be seen as a single probability such as 0.415. Expected points are a single number summary of a point distribution. It can be useful on its own but you must be careful, as it does not contain all of the information often required in an analysis. Relating it back to the distribution can prove to be very eye opening in looking at the expected points of scenarios that are very similar to each other.
There are two basic methods used to determine the probability distribution of points. The first approach sifts through all of the historical data available combining similar scenarios together to determine the probability distribution. This approach assumes the current scenario will follow a pattern similar to previous scenarios. The second approach is to use a probability model based on the probability of certain outcomes occurring and creates the probability distribution from that information. The type of approach used depends on the type of game being analyzed. Neither method is able to guarantee the expected points in a given situation, as it is unable to take into account the intangibles of the individual players on that specific day.
Analysts can use the probability distribution to look at the probability of the impact different plays can have on the outcome of the game. This helps in ranking which type of play in a given scenario is most likely to gain the outcome desired. They can use expected points to analyze a coach’s choice in which play to call and how effective it will be in that situation or whether a different play would be more likely to have a positive outcome.
Coaches can use the probability distribution to evaluate strategies in different situations giving them information to adjust their playbook to better fit specific scenarios when facing different opponents. Looking at expected points helps them decide which play is most likely to result in a score.
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