Análisis del Rating Pct. Index en Baloncesto

por Jean Louis Trezeguet, Bélgica - 11.27.04 ~
Actualizado por: Prof. Roberto Azar ~ 01.19.2010 & 01.05.2015

The RPI is usually defined as the sum of 25 percent of a basketball team's winning percentage (WP), 50 percent of the team's opponents' winning percentage (OWP), and 25 percent of the team's Opponents' Opponents' Winning Percentage (OOWP). Sometimes it is described as 25 percent winning percentage and 75 percent strength of schedule, with SOS defined as 2/3 × OWP + 1/3 × OOWP.

RPI Ratings are (approximately) those used by the NCAA to determine teams and seeding for the NCAA Tournament?. Anyone who has studied statistics knows that these rankings are extremely flawed, but for whatever reason, the NCAA uses them. eBA System doesn't condone them as a ranking system, just compute them.

Most discussion of the RPI involves the weaknesses of the system. The RPI is a tool in the tournament selection process, so it's not meant to be used until March.

We can agree that the best thing the RPI has going for it is its simple formula. For those who don't know, it's

25% x your winning percentage (WP) + 50% x your opponents' WP

+ 25% x your opponents' opponents' WP

More simply its 25% x WP + 75% x strength of schedule (SOS)

It's not something one can compute in their head. But any dork with a computer can calculate the RPI. While many fans know the formula, nobody really knows how it works. Which leads us to the first of the three main complaints about the RPI:

Complaint #1: ¾ of the RPI is out of a team's control.

While it seems like an obvious truth, that's not how it works at all. To illustrate this let's look at the range of values for both winning percentage and strength of schedule among all teams in recent end-of-season RPI's.

Year      Max WP     Min WP      Diff         Max SOS   Min SOS      Diff
2001      .9286      .0385      .8901         .6127      .4080      .2047
2002      .9286      .0385      .8901         .6099      .4064      .2035
2003      .9063      .0385      .8678         .6123      .3796      .2337
Avg.                            .8827                               .2140

So the portion in the team's control has a range of values of roughly .8827, while the portion out of a teams control only has a range of .2140. Even when one accounts for the fact the winning percentage is just 25% of the formula, it still turns out to have a bigger impact than SOS:

WP: .25 x .8827 = .2207

SOS: .75 x .2140 = .1605

SOS plays an important role, but unless your SOS is in the bottom third of college Basketball, a poor schedule can be overcome with a great record. For instance last year Weber St. had a schedule ranked 178 out of 327, but with a 25-3 record they were able to have an RPI rank of 41. This is the beauty of the RPI, you can't really schedule your way into a good rating as most people think. The more difficult your schedule, the harder it is to maintain a good record and therefore a good RPI.

The range of values in the SOS is also part of the reason the RPI is useless early in the year. SOS has a much greater range this time of year, so it does control the ratings. But as the year progresses, everybody's SOS gravitates towards .500 and winning percentage becomes more important.

Till here we related the myth that strength of schedule controls the RPI, while winning percentage is relatively insignificant. Now I'll examine the common complaint that merely playing "so and so" can lower or raise your RPI, regardless of the outcome

This is a statement that can't be refuted because it's true. And this article isn't really a defense, but a demonstration as to how the RPI works.

The effect of an RPI fluctuation merely due to whom one plays is obvious early in the year. By the end of the season this effect is reduced, but not eliminated. The RPI is only meaningful at the end of the year, so that's the perspective one should take when poking holes in it. And the RPI really only matters to a few teams at the end of the year, and those are the teams in the 35-70 range that are under consideration for the NCAA tournament. So for an example we should examine a bubble team's data at the end of the season.

Therefore let's look at the #43 team from last year, Gonzaga. They weren't really a bubble team, but their non-conference schedule provides more variety than anyone else, so they are a great team to examine. Gonzaga played #1 Kentucky, but also #308 Long Beach St. Here's how Gonzaga's RPI rank would have looked with certain games removed from their schedule:

Loss vs. #1 Kentucky............43 (no change)
Win  vs. #308 Long Beach........38 (+5)
Win  vs. #232 Washington St.....40 (+3)
Win  vs. #161 Washington........43 (no change)

As the game against Kentucky indicates, losing to a highly ranked team doesn't help a bubble team's RPI much. So Gonzaga was not helped by losing to Kentucky, yet they did suffer for beating LBSU and WSU. The RPI is a mish-mash of results, where sometimes winning hurts (but you knew this). The thing is, almost everybody has games against weak teams on their schedule and feels this effect to some degree.

And this effect might not be so bad. One point to consider is this: how would you replace the stinker teams on the schedule? One way is to schedule a non-D1 team, a game that won't even exist is the eyes of the NCAA. Supposedly the committee frowns on such tactics, but to what degree who knows. The other option is to schedule a better team.

The problem is, the better the team you play, the more likely you are to lose, and a loss will certainly hurt your RPI. Gonzaga's loss to #82 San Diego had as much negative impact as their win against LBSU. Had they scheduled anyone worse than #82 and lost, the effect would have been worse than the win against LBSU. And the risk of losing to a team ranked 101-200 is twice that of playing someone ranked 201 or higher.
Teams ranked 40-60 in the RPI - the bubble teams - were 130-13 (.909 win %) against teams ranked 201+ in the RPI, but they were 146-36 (.802) against teams 101-200.

So in exchange for playing a nearly risk-free game, why shouldn't a team be penalized? True, sometimes one can't anticipate just how bad a scheduled team will be in the upcoming year. But for the most part, I'd say a team knows when they're scheduling a win. And a few teams seem to do this better than others (I'm looking at you Georgetown, Virginia, and Pitt). A little incentive to avoid this practice isn't a bad thing.

There are some improvements that could be made to the formula to make it more fair to teams that can't help playing bad teams because of conference affiliation.
Add margin of victory, or throw out the games against the 1 or 2 (or more) worst rated teams on the schedule. But any change would make a simple formula more complicated. The best thing the RPI has going for it is its simplicity. And unlike the BCS, the RPI is only a tool that humans use to make their own decisions, so whether Gonzaga finished 43rd or 38th wasn't a big deal.

This one deals with how a lack of including home court advantage affects the formula. For the most part the effects are negligible. For one, most of a team's schedule is made up of conference games that involve an equal distribution of home and away games. So the smaller non-conference part of the schedule is where a team can be unfairly rewarded or penalized for an imbalance of home or road games.

Sure, it's easy to pick on a team like Georgetown that constantly plays a non-conference schedule of weak opponents at home. However, even if they played all of their games on the road, the competition has been so weak you might only expect one additional loss if that. Of their three losable non-conference games (Penn St., Duke, Temple), two are on the road. So they are not a good example of a team that takes advantage of this weakness in the RPI.

Pitt's schedule is similar to Georgetown, they've had a lot of no-risk wins on their schedule. Those are games that have been at home, but it didn't matter where they were played, they were Pitt wins regardless. It's hard to find any tournament worthy team where the imbalance in home (or road) games could make a significant difference in their RPI. Vanderbilt might be an example, but if they are really a top 10 team, then even the Indiana game being played at Bloomington wouldn't have made much difference.

There's always a cry from the mid-majors about the lack of "away-game disadvantage" in the system. But take a team like Toledo or Western Michigan that has tourney aspirations. Their non-conference schedules are loaded with road games. But as of 12/23 both have one loss. Even if all the games were at home, their record could only be improved by one game so far (Toledo still has to play at Louisville).
Overall the complaints about home court advantage not being factored into the RPI are a lot of bluster.

The team that does the best job, year-in year-out, of abusing the home court advantage is Hawaii. It's really no fault of theirs because they never have to schedule non-conference road games and they usually get some decent competition to come to the islands. This year, 2003, they will have to head to the mainland to play in the Bracket Buster in February. But for the other 325 teams, the distribution of game locations doesn't make enough difference to justify making a simple formula more complicated.

Considering its simplicity, the RPI is pretty good at what it's supposed to do. Winning games is good, playing a tough schedule is good. But more fundamentally, just being a good team is good. There's really no easy way to cheat the system. And even if you could, there is a bunch of humans waiting at the end of the season to try to smooth out the problems.