Power Rankings based on PairWise Comparisons

[Nintendude]

I know this topic has been done to death but I'd still like to shed light on this rankings system that I bet almost none of you have heard of. The PairWise comparison system is what's used by the NCAA to select college hockey teams for the NCAA tournament. It is an extremely fair rankings system that takes enough factors into account to properly rank teams against opponents, including ones they have never played against. It's really complicated though so bear with me while I explain how it works.

The PairWise comparison system uses four criteria to rank opponents:
1. Ratings Percentage Index (RPI) - basically a glorified winning percentage
2. Record against other "Teams Under Consideration" (TUCs) (explained below)
3. Record against common opponents (COp)
4. Head to Head record (H2H)

Each team is compared against every other TUC in these criteria. You get a point for each comparison criterion you win and one point for each H2H victory. If you have more points in an overall comparison you get a PWR point. Then you rank the TUCs based on PWR points.

TUCs are, simply, the top-25 teams in RPI, but how is RPI calculated? Well, it takes three factors into consideration weighted with the following percents:
1. The team's raw winning percentage (25%)
2. The average winning percentage of a team's opponents (21%)
3. The average winning percentage of a team's opponents' opponents (54%)

So, RPI is basically a winning percentage that takes into account how good your opponents are.

Here's an example, and I'll make it Smash-related by comparing M2K, HungryBox, and Mango. For the sake of the example let's say they are the only three TUCs.
(Note: I am making up the numbers)

M2K: RPI: .6800, TUC: 3-4 (.429), COp: 8-2 (.800)
HBox: RPI: .6750, TUC: 2-5 (.333), COp: 14-3 (.824)
Mango: RPI: .6900, TUC: 4-0 (1.000), COp: 12-1 (.923)

First let's compare M2k and HBox. M2k's record against HBox is 3-2.
RPI: M2K's is higher (1 point for M2K)
TUC: M2K's is higher (1 point for M2k)
COp: HBox's is higher (1 point for HBox)
H2H: M2k gets 3 points, HBox gets 2

M2K wins this comparison 5 to 3.

Rather than typing up the other comparisons, let's just assume that Mango wins his comparisons vs. M2K and HBox (it's pretty obvious).

So, now here's the final rankings based on PairWise comparisons:
1. Mango (won 2 comparisons)
2. M2K (won 1 comparison)
3. HBox (won 0 comparisons)

Hopefully some of this made sense. If it doesn't, take a look at the current hockey rankings:
http://www.uscho.com/rankings/pwr.php

It features an RPI chart and individual comparison table (with the actual comparisons) to see exactly where the rankings come from. Denver has 24 points, meaning that Denver wins comparisons against every other TUC.

What makes the PairWise system so strong is that you can compare players who have never played against each other before based on RPI, TUC, and COp comparisons. The H2H comparison would simply be 0 for each player but the other criteria can fairly determine who is better, especially if you take into account 24 comparisons. This has always been the biggest hurdle in generating power rankings (other than the fact that it's always been very arbitrary).

Obviously creating a comprehensive PairWise rankings table for Smash is an enormous task, but it is certainly doable especially if you don't take nobodies into account. A computer program to do all the calculations and organize the rankings would be a must. I'm not expecting this to ever be done, but I figured I might as well share it with the Smash Community.

Finally, it's worth mentioning that since 1v1 Smash doesn't use teams, "Teams Under Consideration" should really be called "Players Under Consideration," abbreviated PUCs.

 

[Nintendude]

Has nobody responded to this because it's too confusing? I can try to make it clearer if people bring up points of confusion.

I really don't think this is as scary a proposition as it seems. All it requires is a computer database where you can input tournament results and spit out all the numbers (AIB already has a lot of the necessary infrastructure). Just like how the hockey PWR are reset after every hockey season, Smash can utilize this for yearly rankings or for circuit events. Actually, PWR can be a great alternative to the points systems that circuits typically use, as you can properly rank players who do not attend many events. This can be fairer to those who are simply unable to travel the country attending all the events of a circuit.

 

[smashmachine]

dude...RPI is 25/50/25 not those random numbers up there

 

[Nintendude]

From USCHO:
http://www.uscho.com/rankings/rpi.php

"Factors involved are 1) the team's winning percentage; 2) the average winning percentage of the team's opponents; and 3) the average winning percentage of the team's opponents' opponents. These factors are multiplied by 25%, 21%, and 54% respectively."

edit: It looks like the NCAA uses 25/50/25 for basketball, which I was not aware of. It doesn't really matter though. If the Smash Community ever tries to adopt this then it can just come up with its own numbers.

 

[Nintendude]

What a flop of an idea this was lol

 

[Banks]

i think it would be pretty awesome

and could work..

if someone was willing to get the results of every tournament ever and compile them (wouldn't put it past some people lol)
edit - just realized you would not need results, you would need the bracket. this could never happen cuz ppl r lazy. most someone could do would be to make these rankings starting now, and then every TO must put the bracket image in results

if you even leave out one tournament where person-a beat person-b ****'d be all frucked up

 

[hungrybox]

i think me and m2k are like

4-2 or something my favor

but the idea could work

 

[TheManaLord]

Interesting but it's just too much and doesn't mean anything, sorry nintendude xD

 

[Miamisportsfan45]

I think that SSBB oughta have a system like POP had for the Pokemon Trading Card game. I'd be all for it if they could arrange it in that sort of fasion... But I highly doubt it would happen...

 

[Nintendude]

i think it would be pretty awesome

and could work..

if someone was willing to get the results of every tournament ever and compile them (wouldn't put it past some people lol)
edit - just realized you would not need results, you would need the bracket. this could never happen cuz ppl r lazy. most someone could do would be to make these rankings starting now, and then every TO must put the bracket image in results

if you even leave out one tournament where person-a beat person-b ****'d be all frucked up

You don't need to have every tournament. Making this simply from large-scale tournaments, where the bracket is often easily accessible, would produce some pretty good results probably (at the very least it'd be interesting). If the system is ever put together and well-received, people will have more of an incentive to release the bracket.

edit:
This would probably be good in conjunction with AiB. It already has a huge database of tournament results and I'm sure there'd be a way to link the brackets to a pairwise system considering all the other crazy functionality on that site.