#### Michael Fox Fan

##### Footballguy

Before the 2007 season began, I recall getting into a debate about P Rivers. There were a few vocal posters who asserted that Rivers would underperform in 2007 (vs. 2006) because he had been the beneficiary of "easy strength of schedule (SOS)" in 2006, but was facing a much more difficult SOS in 2007. Now we all know how that turned out - Rivers performance dipped in 2007 - but what should we take from one such example?

At the time I asked the question "what does last year's SOS tell us about the following year's performance?" Mostly I was asking the question in the SP because I was too lazy to do analysis myself. After waiting....oh....at least a year, I decided to do some research. Had originally planned to write up this analysis before pre-season, but then the wife gave birth and life got a bit crazy. So here I am, post-draft, offering thoughts that will be almost completely useless until next year.

On the flip side, I read MOP's post about how the SP needs more discussion and less bickering, so that motivated me. Thanks for the inspiration MOP. Also a shout out to jgalligan, who kept prodding me over the past 2 weeks to write this up.

Ok, so here are the questions I'm really asking: does 2007 SOS have any predictive value for 2008? If a defense gave up minimal fantasy points in 2007, will it do so again in 2008? Will an easy defense continue to give up a ton of points?

Methodology:

Part A - regression

- I looked at team defensive stats from 2002-2007 (prior years were excluded because I was too lazy to adjust for expansion teams)

- Specifically, I looked at: 1) fantasy points given up Rushing, 2) fantasy points given up Passing / Receiving, 3) total fantasy points given up.

- Assumed standard scoring: 1 pt per 10 yds rushing / receiving, 1 pt per 25 yds passing, TDs worth 6 pts each. [no PPR]

- Then looked at fantasy points allowed - rushing, passing / receiving, total - for the years "N" and "N+1". Since I compared seasons 2002-2007, it provided 160 data points for each cut (32 teams x 5 seasons)

- Regressed fantasy points allowed in year "N" vs. fantasy points allowed in year "N+1"

- Looked at the results

Part B - quartile analysis

- Ranked all defensive teams (in season "N") from top to bottom based on fantasy points allowed (from 1 to 32)

- Grouped the defenses by quartile (1-8 together, 9-16, etc)

- Looked at how each quartile fared in season "N+1"

- Compared the results across quartiles

Results:

Part A - regression:

Rushing yards:

Expected fantasy points allowed in Year N+1 = 198.4 + 0.23 * Fantasy points allowed in Year N

--> for the worst defenses, they can be expected to give up 20 more fantasy points in Year N+1 than the average NFL team

R-squared = 5%

Passing yards:

Expected fantasy points allowed in Year N+1 = 539.2 + 0.24 * Fantasy points allowed in Year N

--> for the worst defenses, they can be expected to give up 40 more fantasy points in Year N+1 than the average NFL team

R-squared = 6%

Total yards:

Expected fantasy points allowed in Year N+1 = 683.1 + 0.3 * Fantasy points allowed in Year N

--> for the worst defenses, they can be expected to give up 90 more fantasy points in Year N+1 than the average NFL team

R-squared = 9%

I then ran the same analysis using defensive ranking (1-32), as a gut check, and found similar results as above (almost identical).

Conclusion: bad defenses should be expected to be worse than average next year, but not materially. And the statistical fit is extremely poor (R-squared < 10%), so the results shouldn't be relied on too heavily.

Part B - quartile analysis of fantasy points allowed:

Rushing:

Defensive ranking - fantasy points allowed - in year N+1 by quartile

Quartile 1: 12.5

Quartile 2: 15.8

Quartile 3: 19.0

Quartile 4: 18.7

Passing / receiving:

Defensive ranking - fantasy points allowed - in year N+1 by quartile

Quartile 1: 13.6

Quartile 2: 13.9

Quartile 3: 19.3

Quartile 4: 19.2

Total defense:

Defensive ranking - fantasy points allowed - in year N+1 by quartile

Quartile 1: 12.7

Quartile 2: 14.4

Quartile 3: 18.2

Quartile 4: 20.8

Conclusion: the quartile analysis shows a similar result as the regression analysis. Top quartile defenses continue to perform well on average, but they strongly revert to the mean and don't perform much better than 2nd quartile defenses. Bad defenses also mean revert to ~ the same degree.

What this tells me is that people who rely too much on Strength of Schedule when making fantasy projections or drafting are probably misguided. At the same time, it remains a reasonable consideration to take SOS into account as one of many factors -- provided that you don't overweight it.

Comments? Suggestions? Curious to hear what all the statistics folks have to say.

Chase - if I went wrong somewhere, I expect you to set me straight!

At the time I asked the question "what does last year's SOS tell us about the following year's performance?" Mostly I was asking the question in the SP because I was too lazy to do analysis myself. After waiting....oh....at least a year, I decided to do some research. Had originally planned to write up this analysis before pre-season, but then the wife gave birth and life got a bit crazy. So here I am, post-draft, offering thoughts that will be almost completely useless until next year.

On the flip side, I read MOP's post about how the SP needs more discussion and less bickering, so that motivated me. Thanks for the inspiration MOP. Also a shout out to jgalligan, who kept prodding me over the past 2 weeks to write this up.

Ok, so here are the questions I'm really asking: does 2007 SOS have any predictive value for 2008? If a defense gave up minimal fantasy points in 2007, will it do so again in 2008? Will an easy defense continue to give up a ton of points?

Methodology:

Part A - regression

- I looked at team defensive stats from 2002-2007 (prior years were excluded because I was too lazy to adjust for expansion teams)

- Specifically, I looked at: 1) fantasy points given up Rushing, 2) fantasy points given up Passing / Receiving, 3) total fantasy points given up.

- Assumed standard scoring: 1 pt per 10 yds rushing / receiving, 1 pt per 25 yds passing, TDs worth 6 pts each. [no PPR]

- Then looked at fantasy points allowed - rushing, passing / receiving, total - for the years "N" and "N+1". Since I compared seasons 2002-2007, it provided 160 data points for each cut (32 teams x 5 seasons)

- Regressed fantasy points allowed in year "N" vs. fantasy points allowed in year "N+1"

- Looked at the results

Part B - quartile analysis

- Ranked all defensive teams (in season "N") from top to bottom based on fantasy points allowed (from 1 to 32)

- Grouped the defenses by quartile (1-8 together, 9-16, etc)

- Looked at how each quartile fared in season "N+1"

- Compared the results across quartiles

Results:

Part A - regression:

Rushing yards:

Expected fantasy points allowed in Year N+1 = 198.4 + 0.23 * Fantasy points allowed in Year N

--> for the worst defenses, they can be expected to give up 20 more fantasy points in Year N+1 than the average NFL team

R-squared = 5%

Passing yards:

Expected fantasy points allowed in Year N+1 = 539.2 + 0.24 * Fantasy points allowed in Year N

--> for the worst defenses, they can be expected to give up 40 more fantasy points in Year N+1 than the average NFL team

R-squared = 6%

Total yards:

Expected fantasy points allowed in Year N+1 = 683.1 + 0.3 * Fantasy points allowed in Year N

--> for the worst defenses, they can be expected to give up 90 more fantasy points in Year N+1 than the average NFL team

R-squared = 9%

I then ran the same analysis using defensive ranking (1-32), as a gut check, and found similar results as above (almost identical).

Conclusion: bad defenses should be expected to be worse than average next year, but not materially. And the statistical fit is extremely poor (R-squared < 10%), so the results shouldn't be relied on too heavily.

Part B - quartile analysis of fantasy points allowed:

Rushing:

Defensive ranking - fantasy points allowed - in year N+1 by quartile

Quartile 1: 12.5

Quartile 2: 15.8

Quartile 3: 19.0

Quartile 4: 18.7

Passing / receiving:

Defensive ranking - fantasy points allowed - in year N+1 by quartile

Quartile 1: 13.6

Quartile 2: 13.9

Quartile 3: 19.3

Quartile 4: 19.2

Total defense:

Defensive ranking - fantasy points allowed - in year N+1 by quartile

Quartile 1: 12.7

Quartile 2: 14.4

Quartile 3: 18.2

Quartile 4: 20.8

Conclusion: the quartile analysis shows a similar result as the regression analysis. Top quartile defenses continue to perform well on average, but they strongly revert to the mean and don't perform much better than 2nd quartile defenses. Bad defenses also mean revert to ~ the same degree.

**What did we learn from all this?**What this tells me is that people who rely too much on Strength of Schedule when making fantasy projections or drafting are probably misguided. At the same time, it remains a reasonable consideration to take SOS into account as one of many factors -- provided that you don't overweight it.

Comments? Suggestions? Curious to hear what all the statistics folks have to say.

Chase - if I went wrong somewhere, I expect you to set me straight!

Last edited by a moderator: