NCAA Power Index Explanation

The NCAA Division III Championship Selection Committee has implemented a new procedure
for selecting teams to the championship tournament. The method is called NCAA Power Index or NPI.
Table 1 lists the 14 team sports effected. No indivual sports are currently included.

Division III NCAA Sports

Field Hockey

Football

Men s Soccer

Women s Soccer

Women s Volley Ball

Men s Basketball

Women s Basketball

Men s Ice Hockey

Women s Ice Hockey

Baseball

Men s Lacrosse

Women s Lacrosse

Softball

Men s Volley Ball

Table 1. Division III Sports employing NPI.

The goal is to make the system completely transparent and eliminate subjectivity by eliminating a committee.
The old method was extensive and based on the Ratings Percentage Index (RPI) as shown below.
The new method is much simpler and based on two components, a team s performance and a team's strength of
schedule. Whereas the old SOS in the RPI was based on the opponents won-loss record and the opponent's
opponent's won-loss record, the new SOS is simply based on the average of the opponents NPI.

Men s Division III

Primary Criteria for Selecting At-Large Teams

[1] Win-loss percentage against Division III opponents

[-] Division III head-to-head competition

[-] Results vs. common Division III opponents [2] Results versus ranked Division III teams

[3] Division III strength of schedule.

Secondary Criteria for Selecting At-Large Teams

[4] Non-division III win-loss percentage

[-] Results vs. common non-D-III opponents

[5] Non-division III strength of schedule The actual NPI is calculated as follows:

NPI = (dial) * W-L percentage + (1-dial) * average opponent's NPI
where dial is between 0. and 1.0

The equation above has two components onn the right: (a) the team performance based on its team
record and thre average of its opponents NPI which is referred to as the strength of schedule(SOS).
Notice that the NPI for a team is calculated at iteration (i+1) and the NPI for each opponent in the SOS
is calculated at iteration (i). Why is this? The reason is the equation is recursive because in order to
calculate a team s NPI you need to know a team s SOS and in order to know a team s SOS,
you need to know all opponent s NPI.

So which comes first? The chicken or the egg? The solution
is that you simply iteratively repeat the calculations updating the NPI s of all teams until the NPI (and SOS)
for all teams stops changing or reaches convergence. The dial variable is a component that weighs the team's
performance versus the team s SOS. It can be adjusted by individua sports committee. Nw the formula contains
new wrinkles such as the home field advantage is implemented on the wins and losses such as
0.9/1.1 or 0.8/1.2 factors if the game is played at home or away. In addition, bonus points are given for
defeating top teams or teams above a team s NPI. Finally, if a team defeats a lower ranked team, it cannot
lose NPI because of the weakened SOS.