SOS - What it does and doesn't tell us

[Jamar Howard 4 President]

What "ranking" are you asking about? The title says SOS, but are you talking about "SOS rank" or are you talking about "poll ranking" or "statistical model ranking" or "predictive model ranking"? The SOS might be nearly equal in the example, but if Vermont, Louisiana Lafayette and Team A opponents have a ranking, what is the ranking (by whatever system you have selected for the other teams) for Team A and Team B.

If Team A was ranked #1 and beat each of the two teams at home by one point and Team B was ranked 300+ and beat two 150 ranked teams, I think the conclusion is different than if Team A is ranked #300 and beats a Top 10 by any score and a 300+ peer by 10 points and Team B is a #1 team that, qt home, beats their 150 opponents by 1 point each.

So the valid question would be, Team A beats two opponents and Team B beats two opponents, which would you rank for purposes of {insert the appropriate descriptor here} higher?

Im4wsu, a couple days ago I promised you an answer. Here it is:

I've re-read your post several times today, and I guess it just didn't occur to me that you were legitimately trying to clarify what I was saying. Many other posters at that time were wildly, and purposefully, going outside the bounds of what I said and demanding additional information because they were apparently scared to give a simple answer to a simple question. Your questions seem to be more legitimate, and I apologize for lumping you in with the others. I guess I just felt at the time like I had been abundantly clear and was shocked my simple hypothetical was causing so much confusion.

Here's the info you might have been asking for:
Team A beat a great team and a terrible team.
Team B beat two mediocre teams.
We know nothing about the SOS of these "great", "terrible", and "mediocre" teams.
As discussed earlier today, both Team A and Team B appear to have a very similar SOS based on their 2 games played, although they arrived at that SOS through very different means.

If I left you confused, I apologize. Hopefully we are now on the same page.

[Jamar Howard 4 President]

No they wouldn't be similar. SOS profile is not linear.

Can you expand on this?

I wanted to avoid using the RPI specifically just yet, but just as an example, RPI calculates SOS based on the sum of opponent's records. This would mean that playing a team who is 30-0 (great team) and then a team who is 0-30 (terrible team) nets a sum of 30-30. Playing two teams who were both 15-15 (mediocre) would net the same result.

Where does the "non-linearity" that you speak of come into play?

[im4wsu]

Im4wsu, a couple days ago I promised you an answer. Here it is:

I've re-read your post several times today, and I guess it just didn't occur to me that you were legitimately trying to clarify what I was saying. Many other posters at that time were wildly, and purposefully, going outside the bounds of what I said and demanding additional information because they were apparently scared to give a simple answer to a simple question. Your questions seem to be more legitimate, and I apologize for lumping you in with the others. I guess I just felt at the time like I had been abundantly clear and was shocked my simple hypothetical was causing so much confusion.

Here's the info you might have been asking for:
Team A beat a great team and a terrible team.
Team B beat two mediocre teams.
We know nothing about the SOS of these "great", "terrible", and "mediocre" teams.
As discussed earlier today, both Team A and Team B appear to have a very similar SOS based on their 2 games played, although they arrived at that SOS through very different means.

If I left you confused, I apologize. Hopefully we are now on the same page.

I guess part of my confusion is your use of the word "rank" in the top 10 and opponents are ranked 300+. I assumed from the title that "rank" referred to SOS rank, since no other "rating system" was mentioned.

[Jamar Howard 4 President]

I'll give away a portion of my endgame in order to clarify part of what the original post was intended to accomplish.

I want to eventually make the argument that two teams could have identical W/L records, identical SOS, and yet one could be considered the better team by a significant margin.

I am still curious to hear more about the "non-linearity" of SOS as that could affect the validity of my argument.

[SB Shock]

Can you expand on this?

I wanted to avoid using the RPI specifically just yet, but just as an example, RPI calculates SOS based on the sum of opponent's records. This would mean that playing a team who is 30-0 (great team) and then a team who is 0-30 (terrible team) nets a sum of 30-30. Playing two teams who were both 15-15 (mediocre) would net the same result.

Where does the "non-linearity" that you speak of come into play?

when I get home tonight I will expand.

[ShockerFever]

when I get home tonight I will expand.

That's what she said.

[SB Shock]

Here is the chart. Calculated the SOS for Team A and B for assuming the ranking is either SOS or RPI, Team A always comes out with a better SOS.

[Jamar Howard 4 President]

SB Shock, can you help explain how you got all that data from my simple hypothetical? I'm not quite following just yet.

[SB Shock]

SB Shock, can you help explain how you got all that data from my simple hypothetical? I'm not quite following just yet.

It historical data that show where the SOS would likely lie for your hypothetical scenario. I have attached another figure to show you this year distribution (which is not much different than last year). For your hypothetical to work, you actually need a linear SOS distribution like shown in the 2nd figure.

[Jamar Howard 4 President]

SB Shock, I appreciate the effort you put into creating those graphs. They are interesting. However, I don't think they actually imply what you think they imply. What we would really need to see is a graph of RPI Rank vs RPI. However, without even getting into the details of why that would be the right graph to use, I can show you an error in your calcs.

Yes, the graphs are indeed NOT perfectly linear. The ends (left and right sides) tend to dip up and down at a quicker rate. However, notice how they are symmetrical. That means that if as you start in the middle and move out to the left or right, the distance from the middle grows at the same rate. Your error was comparing 1/299 with 149/151. There are 351 teams in division 1, so we need to start with 175.5 as our middle point. Your error was to start with 150 as your mid point. Two mediocre teams (175 and 176, for example), can be averaged and will come out to almost the same value as the average of 1 and 351, or 11 and 341, etc.

The graph doesn't need to be linear. It just needs to be symmetrical for my argument to hold.

For those completely confused, I go back to my earlier post:

I wanted to avoid using the RPI specifically just yet, but just as an example, RPI calculates SOS based on the sum of opponent's records. This would mean that playing a team who is 30-0 (great team) and then a team who is 0-30 (terrible team) nets a sum of 30-30. Playing two teams who were both 15-15 (mediocre) would net the same result.

I will make one concession. I could have been more precise and said that the teams in the "mid-100s" were actually in the "170's", and instead of simply saying "300+", I could have stated "340s". My intention was to imply a good team and a bad team that were equally distant from the two mediocre teams. One much better. One much worse. In that regard, I too technically used 150 as the midpoint, forgetting that we have now greatly exceeded 300 teams and are actually at 351. (Yuck, too many teams IMO. Time for D1 to stop expanding, but I digress)

Fair enough? I stand by my statement that as a general rule of thumb, playing a great team and a terrible team will provide the same SOS as playing two very average teams.

[Jamar Howard 4 President]

I don't know how to graph so much data as quickly as you did SB Shock, but here are just a few data point comparisons as an example.

Using this season's current RPI values:

Rank	RPI Value	...	Rank	RPI Value	...	Average of	Good & Bad Teams Combined
1	.7097		351	.3136			.5117
11	.6371		341	.3755			.5063
21	.6159		331	.3872			.5016
31	.6003		321	.3993			.4998
41	.5880		311	.4078			.4979
51	.5770		301	.4154			.4962
61	.5708		291	.4238			.4973
71	.5663		281	.4326			.4995
81	.5570		271	.4412			.4991
175	.4996		176	.4996			.4996

An equal spread away from the midpoint (175.5) produces almost the exact same result every time. I think Kentucky being freakishly good this year helps the 1/351 average number be just a tad bit higher than the rest, but even in that case, the 1/351 average is still remarkably close to all the rest.

[SB Shock]

so are you doing your calculation based off of RPI or SOS? You say that you want to avoid using RPI and now you are using RPI?

[Jamar Howard 4 President]

Which calculation are you asking about SB Shock? I want to be sure that I understand exactly what you are asking before I try to respond.

[Jamar Howard 4 President]

I don’t know if this helps or not, but here is the original hypothetical, restated as best I can to clear up any confusion that has been expressed in the first several pages of this thread.

Team A is 2-0. They beat one of the 10 best teams in the county and one of the 10 worst teams in the country.
Team B is 2-0. They beat two of the most mediocre teams in the country.There are 351 teams in D1, so we are talking about a couple teams in the 170s.

Nothing else is known. We are assuming that all the facts presented are indisputable. Team A beating one of the 10 best teams in the country is to be treated as a fact and is not up for debate.

We are left with a very simply analysis.

1 - Which team do you think is better based on this limited info? Do you think that beating a great team and a terrible team is more impressive, less impressive, or equally impressive than beating 2 mediocre teams?

2 – I would argue that any formula that calculates SOS would say that Team A and Team B have virtually the same SOS despite arriving at it through vastly different means. Does anyone dispute this?

[Shocker-maniac]

I don’t know if this helps or not, but here is the original hypothetical, restated as best I can to clear up any confusion that has been expressed in the first several pages of this thread.

Team A is 2-0. They beat one of the 10 best teams in the county and one of the 10 worst teams in the country.
Team B is 2-0. They beat two of the most mediocre teams in the country.There are 351 teams in D1, so we are talking about a couple teams in the 170s.

Nothing else is known. We are assuming that all the facts presented are indisputable. Team A beating one of the 10 best teams in the country is to be treated as a fact and is not up for debate.

We are left with a very simply analysis.

1 - Which team do you think is better based on this limited info? Do you think that beating a great team and a terrible team is more impressive, less impressive, or equally impressive than beating 2 mediocre teams?

2 – I would argue that any formula that calculates SOS would say that Team A and Team B have virtually the same SOS despite arriving at it through vastly different means. Does anyone dispute this?

Sample size too small. There is not enough data to make a valid conclusion.