Question on RPI calculation: How is this possible?

[Plebe]

A question for my fellow math-and-stats nerds on the BY:

As is well known, a given team's RPI consists of (a) the team's winning percentage (25%), (b) their opponents' winnning percentage (50%), and (c) the winning percentage of their opponents' opponents (25%). Components (b) and (c) constitute a team's strength of schedule within the context of the RPI.

So if two teams have the same win-loss record, the team with the higher RPI will have to be the team with the stronger SOS, right? This is why I'm puzzled whenever I see something like this in the RPI rankings:

How is it even mathematically possible for Miss St to have the same win-loss record as Oregon St (both are 27-3), a weaker SOS ranking (#26 as compared to #9), but yet a higher RPI?

 

[EricLA]

The only thing I can think of is Oregon STate had a loss to a team in the 51-100 ranking RPI which may have pushed them down...

 

[ochoopsfan]

The loss to USC, hurt OSU more than any of the 3 losses by MSU(South Carolina, UK or UT)

 

[triaddukefan]

SEC bias

 

[Vowelguy]

You describe the raw RPI formula. That's not what the committee uses - they have something that gives more weight to quality wins and bad losses. But I dont think they've ever released that formula, so I'm not sure this RPI calculation could be using that.

Also, some people consider the SOS to be just the opponents W-L. Others consider to be both opponents W-L, and also opponents opponents.

If it's the former being used here, then it could be the 3rd piece which is driving the differences.

________ W-L _OppoWL OppOpp _ RPI
MissSt 0.9000 0.5893 0.6036 0.6706
Ore St 0.9000 0.6011 0.5798 0.6705

 

[Plebe]

You describe the raw RPI formula. That's not what the committee uses - they have something that gives more weight to quality wins and bad losses. But I dont think they've ever released that formula, so I'm not sure this RPI calculation could be using that.

Also, some people consider the SOS to be just the opponents W-L. Others consider to be both opponents W-L, and also opponents opponents.

If it's the former being used here, then it could be the 3rd piece which is driving the differences.

________ W-L _OppoWL OppOpp _ RPI
MissSt 0.9000 0.5893 0.6036 0.6706
Ore St 0.9000 0.6011 0.5798 0.6705

Ah, I didn't realize that anyone considered SOS to be solely opponents' W-L. That would certainly explain it.

I also wasn't aware that the committee was using a tweaked RPI formula that differentiated among individual wins and losses. I know the men's committee has a formula (which I believe is published) that gives more weight to road wins and less weight to home wins, but I've read that this home and road weighting is not used in WCBB or in the other sports that use RPI.

 

[LO TRADER]

What's strange is that OSU was rated #4 yesterday, and Miss State was ranked lower (#6?). What changed in the last 24 hours? Perhaps there was an error in the calculation that has been corrected. No matter, it will all change again after this week(end).

 

[Plebe]

What's strange is that OSU was rated #4 yesterday, and Miss State was ranked lower (#6?). What changed in the last 24 hours? Perhaps there was an error in the calculation that has been corrected. No matter, it will all change again after this week(end).

That type of change isn't unusual because even if a team doesn't play on a given night, the results of their opponents' games and their opponents' opponents' games will still alter their RPI.

 

[stamfordhusky]

You describe the raw RPI formula. That's not what the committee uses - they have something that gives more weight to quality wins and bad losses. But I dont think they've ever released that formula, so I'm not sure this RPI calculation could be using that.

Also, some people consider the SOS to be just the opponents W-L. Others consider to be both opponents W-L, and also opponents opponents.

If it's the former being used here, then it could be the 3rd piece which is driving the differences.

________ W-L _OppoWL OppOpp _ RPI
MissSt 0.9000 0.5893 0.6036 0.6706
Ore St 0.9000 0.6011 0.5798 0.6705

No. There is only one RPI, and that is what the committee sees. However they do also use quality wins, bad losses, etc. but there is no special RPI that incorporates special elements.

 

[stamfordhusky]

Ah, I didn't realize that anyone considered SOS to be solely opponents' W-L. That would certainly explain it.

I also wasn't aware that the committee was using a tweaked RPI formula that differentiated among individual wins and losses. I know the men's committee has a formula (which I believe is published) that gives more weight to road wins and less weight to home wins, but I've read that this home and road weighting is not used in WCBB or in the other sports that use RPI.

1. they do not use a "tweaked" formula. There is no RPI that factors in good wins, bad losses, etc.

2. Starting in 2011, the women's RPI was changed to give the same weight to home/road games as the men's formula. A home win is multiplied by 0.6. A road win is multiplied by 1.4. A road loss is multiplied by 0.6. Etc


Thus there are two basic reasons that account for the differences cited in the original post: (1) Home/road multipliers for wins/losses; and (2) SOS is only the record of your direct opponents, while the RPI also looks at the records of your opponents' opponents.

 

[Vowelguy]

1. they do not use a "tweaked" formula. There is no RPI that factors in good wins, bad losses, etc.

2. Starting in 2011, the women's RPI was changed to give the same weight to home/road games as the men's formula. A home win is multiplied by 0.6. A road win is multiplied by 1.4. A road loss is multiplied by 0.6. Etc

> they do not use a "tweaked" formula.
> the women's RPI was changed

Uhhhh....

 

[Kaizen]

I don't trust RPI.
Well, if UConn is #1, it is different story ...LOL... forgive me.

 

[stamfordhusky]

> they do not use a "tweaked" formula.
> the women's RPI was changed

Uhhhh....

1. Was referring to the idea of a "tweaked" formula, as was referenced in the previous post, that somehow incorporates quality wins or bad losses. There never was any such formula.

2. As I stated, the change was simply to use the same calculation as the men, where road wins are more valuable than home wins etc.

 

[Vowelguy]

1. Was referring to the idea of a "tweaked" formula, as was referenced in the previous post, that somehow incorporates quality wins or bad losses. There never was any such formula.

2. As I stated, the change was simply to use the same calculation as the men, where road wins are more valuable than home wins etc.

"The Women's RPI was changed" . That's pretty much the definition of a tweaked formula. Yes, I got the details wrong. But the bottom line, there IS an adjusted RPI that they use.

 

[Plebe]

and (2) SOS is only the record of your direct opponents, while the RPI also looks at the records of your opponents' opponents.

From Rating Percentage Index - Wikipedia:

The opponents' winning percentage and the winning percentage of those opponents' opponents both comprise the strength of schedule (SOS). Thus, the SOS accounts for 75% of the RPI calculation and is 2/3 its opponents' winning percentage and 1/3 its opponents' opponents' winning percentages.
​

From RPI FAQ:

How do you figure the Strength of Schedule? It's 2/3 opponents' winning percentage and 1/3 opponents' opponents' winning percentage, the same ratio as in the RPI formula.
​

From Forum Code How-To - Tutorials:

Most folks generally know what Strength of Schedule means. Simply put, teams that have played better teams have a higher SOS. However, the calculation is more complicated that you might think, as explained by NationalChamps.net, "This component is calculated by determining the cumulative won/loss records of the team's opponents and the cumulative won/loss records of the teams' opponents' opponents. The formula shall be weighted two-third (66 2/3%) for the opponent's record and one-third (33 1/3%) for the opponents' opponents record.
​

Are all these sources wrong?

 

[cockhrnleghrn]

A question for my fellow math-and-stats nerds on the BY:

As is well known, a given team's RPI consists of (a) the team's winning percentage (25%), (b) their opponents' winnning percentage (50%), and (c) the winning percentage of their opponents' opponents (25%). Components (b) and (c) constitute a team's strength of schedule within the context of the RPI.

So if two teams have the same win-loss record, the team with the higher RPI will have to be the team with the stronger SOS, right? This is why I'm puzzled whenever I see something like this in the RPI rankings:

How is it even mathematically possible for Miss St to have the same win-loss record as Oregon St (both are 27-3), a weaker SOS ranking (#26 as compared to #9), but yet a higher RPI?

I think the location of the games is a consideration, too. Road wins are more heavily weighted.

 

[Tenspro2002]

A question for my fellow math-and-stats nerds on the BY:

As is well known, a given team's RPI consists of (a) the team's winning percentage (25%), (b) their opponents' winnning percentage (50%), and (c) the winning percentage of their opponents' opponents (25%). Components (b) and (c) constitute a team's strength of schedule within the context of the RPI.

So if two teams have the same win-loss record, the team with the higher RPI will have to be the team with the stronger SOS, right? This is why I'm puzzled whenever I see something like this in the RPI rankings:

How is it even mathematically possible for Miss St to have the same win-loss record as Oregon St (both are 27-3), a weaker SOS ranking (#26 as compared to #9), but yet a higher RPI?

I'm not certain, but I'm pretty sure that home/road games are weighted differently, e.g. a road win is given a 1.4x multiplier, while a home win only a 0.6x multiplier.

It looks like OSU has played 5 more home games and 5 fewer road games than MSU.

That could account for the difference, despite the difference in raw SOS.

 

[stamfordhusky]

From Rating Percentage Index - Wikipedia:

The opponents' winning percentage and the winning percentage of those opponents' opponents both comprise the strength of schedule (SOS). Thus, the SOS accounts for 75% of the RPI calculation and is 2/3 its opponents' winning percentage and 1/3 its opponents' opponents' winning percentages.
​

From RPI FAQ:

How do you figure the Strength of Schedule? It's 2/3 opponents' winning percentage and 1/3 opponents' opponents' winning percentage, the same ratio as in the RPI formula.
​

From Forum Code How-To - Tutorials:

Most folks generally know what Strength of Schedule means. Simply put, teams that have played better teams have a higher SOS. However, the calculation is more complicated that you might think, as explained by NationalChamps.net, "This component is calculated by determining the cumulative won/loss records of the team's opponents and the cumulative won/loss records of the teams' opponents' opponents. The formula shall be weighted two-third (66 2/3%) for the opponent's record and one-third (33 1/3%) for the opponents' opponents record.
​

Are all these sources wrong?

All these sources use SOS in a different way than most sites do. If you look at places like Sagain, Massey, etc, what they call SOS is only the record if your direct opponents. That is the general meaning of SOS. However some non-NCAA definitions of RPI, choose to call SOS the two factors used in the RPI. That us not the normal definition.

All of the definitions above use some third party definition. However if you look at an NCAA definition of RPI, they define SOS as only your direct opponents' record. The final 25% of the formula is called "opponents' SOS".