Variation can be determined using different sources of data. Three typical sources that are often compared are overall variation, between-team variation and within-team variation.
You can use all three types of variation when analyzing points scored in the National Football League. Overall variation is determined using all of the points scored by all of the teams during one season. This overall variation is comprised of both between-team and within-team variations. Each team has its own unique make-up of players and scoring ability, which creates a variation between teams. However, teams themselves are not always consistent. They play better in one game than they do in another, which can be due to either their own offensive ability or the defensive ability of their opponent, or, most likely, a combination of the two. This is the within-team variation.
When the standard deviations of all three measurements are determined for a single season it is evident that the three measurements are related. Adding together the between-team standard deviation and the within-team standard deviation equals approximately the overall standard deviation.
With these three stats, the effect of the between-team and within-team variations on the overall variation can be analyzed. This allows analysts to focus on whether the difference in scoring ability is more predominant between different teams or between different games played by the same team. This gives the ability to discuss the consistency across the league as well as the consistency of each team. Are the rules of the league fair to all teams or does there seem to be a bias towards certain types of teams? If there is a bias, how can this be alleviated, either by the league or by coaches reconfiguring their teams. On the other hand, is the variance based on the player talent on each team, coaching talent, team cohesiveness, or any other of a myriad of factors? Looking at these numbers helps analysts determine which trades or draft picks might best be able to help improve the consistency of the team in their scoring ability from game to game.
Coaches can determine whether their standings in the league are caused more by between-team or within-team differences. Do they need to improve the overall ability of their team in order to compete more effectively with the competition? Alternatively, is the problem not with the players they currently have, but with the consistency of the team? Does their own inconsistency have a larger effect on the standings than how they compare to other teams? If so, decisions must be made regarding how to improve the team’s consistency, as well as the consistency of the individual players. Is it due to a lack of training, difficulty carrying out the plays or some other factor? Strategies can then be put into place to help alleviate these issues.
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