By Patrick Pierce

Math is beneficial across many fields. With all of the numbers in sports, stats become a crucial way to determine the effectiveness of any given player on the field or court. To understand how all of these numbers make sense in the realm of sports, Homeworkdoer has assembled information related to sports efficiency ratings below.

**The NBA’s PER**

The Player Efficiency Rating (PER) considers all of the player’s statistics measured by the NBA, whilst also considering the number of minutes they played and how many possessions their team had throughout each game.

It calculates both positive and negative statistics. For example, assists and field goals are weighed and contrasted to missed field goals and turnovers. Each of these stats is given a number related to how important it is for the overall PER.

Assists are important, but not more so than made shots. Also, the minutes the player is on the court allows a team or a fan to understand how productive any given athlete is on a per-minute basis. For example, a player who scored 20 points in 22 minutes per game is more productive than one who scored 25 points in 38 minutes per game.

Lastly, the PER is also weighed against any given team’s pace of play. Some teams have a faster pace, giving their players more opportunities to score baskets or rack up assists. However, teams that run a slower pace could still have players who are more productive, even if they are taking, and making, less shots.

**NCAA’s Team Efficiencies**

College football also considers an efficiency rating, albeit for the teams. Although less in-depth than the NBA example above, it is crucial to the sport because it results to the rankings, which give way to championship opportunities.

It is measured by the point contributions for each unit that relate to the scoring margin for each play. The figures are also adjusted based on the how strong the team’s schedule is, with “garbage time” (their likelihood of winning), weighing it down. There is a total of 100 possible points.

**NFL Quarterback Passer Ratings**

The official NFL passer ratings were developed in 1973 and updated in 1979. They use highly complex mathematical formulas to determine how much each quarterback of every team contributes to the team’s success. The formulas are broken down as:

- First divide completed passes by attempts, then subtract 0.3 and divide by 0.2.
- Next divide passing yards by attempts, then subtract 3 and divide by 4.
- Next divide touchdowns by attempts, after divide by 0.05.
- Last begin with 0.095 and subtract the total of interceptions divided by attempts. Divide the resulting number by 0.04.

The above relates to the passer rating of any given statistical figure. There is also a more complicated metric, the overall QBR. This figure has a maximum number of 158.3 and a minimum of 0. It is much more difficult to calculate and was developed by ESPN in 2011.

**Why Are They Important?**

Each of these mathematical formulas are extremely important to statisticians, both for the press and team personnel. They determine how effective any given player, or team, is to the ultimate goal of sports: winning. They also show that even the world of athletics would be severely lacking without a heavy dose of math.

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