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Outsmarting the RPI: Gaming the System through Scheduling

3/09/2006
There was an >interesting article last Sunday about the Missouri Valley Conference and how they might be gaming the RPI through scheduling to make the conference appear better than it really is. The article includes lots of whining by Maryland coach Gary Williams, who is staring down a second consectutive NIT appearance if the Terps don't do something in the ACC tournament. Although Gary does have a legitimate argument, maybe he should've spend more time trying to squeeze one or two victories out of his schedule than lamenting about his conference getting hosed in the RPI.

Instead of looking specifically at the MVC or ACC, let's look at a hypothetical example and use it to show how the RPI can be gamed (make a team look better than they actually are) through smart scheduling. Take a hypothetical program that is the 50th-best team in the country. The program knows it's the 50th best program and its results year in and year out are consistent with that. Every year the 50th-best team will equate to being on the bubble but ending up in the NIT (think Air Force, Louisville, Creighton, or Colorado).

So as the coach or AD of this program, is there anyway of improving your chances of getting into the tournament without actually improving your team? Let's look at the scheduling decision. Assume the team has 28 games already on the schedule and is certain that the team will go 19-9 in those games (again, consistent with being the 50th-rated team). The team has the ability to add a home game against any Div I opponent. Who should they add to the schedule?

Due to the nuances of the RPI formula, there is a 'sweet spot' for scheduling if the team is concerned with maximizing its RPI. Check out the following chart (for a full-size version, click here):

The dark blue line shows the probability of the 50th ranked team beating a given opponent at home (+5.5 is equivalent to UConn, -5.5 is roughly equivalent to #334 Jacksonville, 0 is an 'average team, 2.1 would be the roughly the team in question). The pink line is the team's RPI if they win the game. The yellow line is the team's RPI if they lose the game. And the light blue line is the expected RPI of playing that opponent given the probability of winning versus losing. This is the line that this team would be interested in maximizing.

The 'sweet spot' for the 50th-ranked team is scheduling a game against the 98th-ranked opponent. Our hypothetical team would be expect to win this game at home about 84% of the time, and it provides the maximum expected lift in RPI. Do this for 2 or 3 other opponents and it can have a dramatic effect of the overall RPI without changing the underlying quality of the team. (For a real world example of potential impact, Arizona is no better than the 50th-ranked team in the country this year and their RPI is currently #24).

A few other interesting points about this analysis:

  1. Unless you're playing a team ranked between 40th and 167th, you'd be better off not playing the game at all. Scheduling above and below these cut-offs lead to a lower expected RPI than not playing at all (sticking with 28 games instead of 29). Similarly, beating the 191st-ranked team or below hurts your RPI versus not playing the game at all.
  2. Beating a team ranked 292nd or below would leave you with a lower RPI than if you lost to the 1st-ranked team.
  3. Losing to the 79th ranked team or above would leaving you with a higher RPI than beating the lowest ranked team.

I think it's clear that some programs have already begun to figure this out. The article states that the MVC "decided to withhold an annual $50,000 NCAA tournament distribution from programs that did not play a nonconference schedule consisting of opponents with a three-year average RPI of 149 or better." Arizona has an extremely inflated SOS of 7 mainly because they avoided playing any non-conference opponents above 180 in the RPI. Certainly, the incentives are in place to try to game the system, especially for a perennial bubble team. Making the tournament is significantly better than making the NIT every year. And all other things equal, having a higher RPI is better than having a low RPI. So should we really be surprised that this is going on? How long before most other major programs catch on and adjust their scheduling such that Savannah State won't be able to play anybody other than Prairie View A&M?

If the NCAA wanted to eliminate the possibility of gaming, they'd have to go with a system where the light blue line in that graph were flat. In other words, the potential increase in the ranking from winning would be consistent with the probability of victory and would be perfectly offset by the potential decrease in the ranking from losing and consistent with the probability of defeat. Additionally, a win would never hurt you (it just might not help much) and a loss would never help you (it just might not hurt much). Stay tuned to see how the JCI stacks up under this same analysis.



Note: For your average top 20 team, the same principles apply, although the incentive to try to get yourself into the tournament isn't as strong. However, a higher RPI is still preferred to a lower RPI all other things equal, and can only help with seeding and provide a larger cushion in case the season doesn't go quite as planned. With a higher quality team, the sweet spot changes due to a different shape of the probability of winning curve.

  1. The sweet spot for an average top 20 team at home is 31. For a neutral court game, it's 45, and for a road game it's 55.
  2. Unless you're playing a team ranked between 5th and 133rd (at home), you'd be better off not playing the game at all. Scheduling above and below these cut-offs lead to a lower expected RPI than not playing at all. Similarly, beating the 144th-ranked team or below hurts your RPI versus not playing the game at all.
  3. Beating a team ranked 304nd or below would leave you with a lower RPI than if you lost to the 1st-ranked team.
  4. Losing to the 49th ranked team or above would leaving you with a higher RPI than beating the lowest ranked team.
  5. The curve is more pronounced (less flat) for an average top 20 team relative to the 50th-ranked team in the example above, meaning the selection of opponent can have a larger effect on the RPI.

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