Power Rankings

Each week, Phil the stat intern will produce and analyze the Sky’s power rankings. His analysis will give understanding to the team’s level of play from a statistical perspective.

There’s an old saying, “that numbers never lie.” So, let’s test that theory. There are a number of metrics that can be used to establish the overall quality of a team and their play within a season. Three such measurements are expected winning percentage (EWP), strength of schedule (SOS), and rating percentage index (RPI). Each of these tells us something different about a team, and when considered as a collection, can give us insight as to how a team is performing against the rest of the WNBA.

We will begin by explaining how each of these measurements are calculated, starting with EWP (Expected Winning Percentage). EWP is calculated using a formula called the Pythagorean expectation. It was originally invented by Bill James, famed baseball statistician, to create an estimate of how many games a team should have won and should have lost based on the number of runs scored and allowed. The formula has since been modified by a number of others to fit into basketball. For these calculations, the formula used was created by John Hollinger of ESPN,

Win = Points For ^ 16.5 / (Points For ^ 16.5 + Points Against ^ 16.5)
The result of this calculation is a team’s expected winning percentage. Taking the EWP and multiplying it by the games played will produce a teams expected wins. Subtracting the wins from games played will then result in expected losses. It is reasonable to assume that the ratio of points scored to points allowed is a measure of team’s quality. The big question here should be centered around what and why the exponent of 16.5 is doing in there. The simple answer is chance. In basketball, chance does not play as large a role in determining whether a higher quality team will beat a lower quality team. It is reasonable to assume that a team with a slightly higher quality will defeat an opponent of slightly less quality more times than not.
The usefulness of expected winning percentage comes through when comparing it to the real record of a team. It can give you an indication of whether a team is under performing, over achieving, or simply just unlucky. Again, there is an element of chance within basketball, and chance may not always be on your side.

The second measurement is SOS, strength of schedule. This is an overall measure of the difficulty of a team’s schedule based upon a team’s opponents’ winning percentage (OWP) and their opponents’ opponents winning percentage (OOWP).

SOS = (2(Opponents’ Winning Percentage) + (Opponents’ Opponents Winning Percentage))/3)
Based upon the formula it can be deduced that two-thirds of SOS is comprised of the opponents’ winning percentage, and one-third of it is the opponents’ opponents winning percentage. Obtaining these winning percentages involves a small degree of math. For example, to obtain the OWP of the Sky’s schedule, you take the record of their opponent and multiply it by the number of times the Sky play this opponent. You repeat this process with each of the Sky’s opponents. What you end up with is an overall win/loss record for all of the Sky’s opponents. The winning percentage of this record is the OWP. OOWP is calculated in a similar fashion. The first step is to calculate the OWP of each team in the league. Then to obtain the OOWP of the Sky’s opponents you would take the OWP of their opponent and multiply it by the number of times the Sky play this opponent. Repeat this process for the rest of the league. Finally, find the average of the OWP*Game Played for all of the Sky’s opponents. The resulting answer is the OOWP for the Sky. Plug the OWP and OOWP into the SOS formula stated above, and you obtain the SOS for the Sky. The higher the number, the tougher the schedule is. Below is the Sky’s table so you can get a better sense of how these numbers were achieved.


The beauty of the third measurement, RPI, is that it shares two inputs with SOS: OWP and OOWP. The third input is winning percentage (WP).

RPI = (WP*0.25) + (OWP*0.50) + (OOWP*0.25)
Based upon this equation, SOS comprises 75% of RPI. The remaining 25% is made up of the team’s winning percentage. So the RPI is a quantity based upon a team’s win/loss record and its SOS. RPI is a commonly used method for ranking team’s in the same league. The higher a team’s RPI, the better quality of a team they are.

Each of these measurements, when viewed together, can give us insight as to how a team is performing this season. They can tell us how tough of a schedule they play, how a team is performing against that schedule, what their expected record should be, and where a team ranks amongst its competition, just to name a few. At the end of this article is the complete table, take a look and see where the Sky rank in the WNBA in SOS and RPI, as well as a comparison of expected record versus real record. Check back weekly to see an updated table.