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The Road to the NFL Playoffs: Strength Of Schedule

When the schedule for 2010 was originally published, the naysayers, scaremongers, doom merchants and other nattering nabobs of negativity came out in full force: The Dallas Cowboys have the third toughest schedule in the NFL. Woe be upon us!

I'm in a nice and mellow myth-debunking mood today, so let me make this post very, very simple: Strength of schedule don't mean Jack. There is no correlation whatsoever between a team's strength of schedule going into the season and the number of wins that team has at the end of the season. No, wait, let me correct that. The correlation (r²) is exactly 0.0006 over the last eight seasons.

But, but, but ... doesn't strength of schedule make or break a team's playoff chances and strongly affect division races? Again, let's keep it very simple. A strength of schedule based on 2009 records would matter - if you were playing in 2009.

Volatility and Strength of Schedule (SOS) or why past performance is not necessarily indicative of future results

At the start of last season, the Cowboys had the 11th toughest SOS with .516. By the end of the season the actual SOS had mellowed to .488, and Dallas ranked a comfortable 23rd.

In 2008, the Steelers started the season with the toughest SOS in the league, with opponents having combined for a .598 winning percentage in the year before. The Steelers went 12-4 in 2008, and their SOS at the end of the year turned out to be a much more manageable .520. Their initially projected 12 games against teams that were .500 or better in 2007 turned out to be eight in 2008. The Steelers rode what initially was considered one of the toughest schedules in three decades straight to a Super Bowl win.

Cue the 2009 Saints: They entered the 2009 season with the 8th toughest schedule in the league (.555) and the daunting task of playing against seven teams who'd finished with 11 or more wins in 2008. By the time the dust settled on the 2009 season, the Saints had faced what turned out to be the softest schedule in the league (.426), had faced only two teams with 11 or more wins, had made off with the Super Bowl and last I heard they were still off celebrating somewhere.

Stories like this are almost certain to happen again this year. The 'real' SOS at the end of the season will have next to nothing to do with the SOS published at the start of the season. The reason for this is that the volatility inherent in team performance from year to year makes it almost impossible to figure out which teams will have a soft schedule and which teams will have a tough schedule in 2010.

SOS does not take into account the yearly roster changes due to free agency and the draft. Nor does it account for injuries. Or changes in coaching staff, or redesigned schemes, or player retirements, or plain luck and so forth.

SOS don't mean Jack

I've gone back and looked at the schedules for all teams from 2002 through 2009, the period during which the league has played in the current divisional alignment. I looked at the SOS at the beginning of the season ("starting SOS") and how the SOS looked after the season ("actual SOS") and how each correlated with playoff appearances and W/L records. In total, that's two sets of SOS for 256 teams.

I sorted all the SOS percentages into five equally large classes, e.g. there were 51 teams with a starting SOS below .470, 53 teams with a starting schedule of between .479 and .489 and so on. I then looked at how many teams in each class enjoyed which degree of post-season success. The results are summarized in the table below:

Starting Strength of Schedule at start of season, 2002-2009
SOS range
#of teams
of which made
in % of which made
Divisional round
in % of which made
Conf. Championships
in % of which made
Super Bowl
in %
< .470 51 21 41% 14 27% 4 8% 3 6%
.470-.489 53 17 32% 12 23% 6 11% 3 6%
.490-.509 49 20 41% 11 22% 6 12% 2 4%
.510-.530 53 22 42% 17 32% 9 17% 5 9%
>.530 50 16 32% 10 20% 7 14% 3 6%
Total 256 96 38% 64 25% 32 13% 16 5%

What becomes clear pretty quickly as you look at this table is that the starting SOS does not appear to have any impact on post-season participation or -success. The percentages of how many teams make it beyond each post-season hurdle are virtually identical, regardless of how soft or tough the starting SOS was.

Sos_starting_medium In statistics, the relationship between two variables is measured using a "correlation coefficient", also referred to as "r²". The closer the r² number is to 1 or -1, the stronger the relationship between the two variables. The closer it is to zero, the weaker the relationship.

For the graph on the left, I looked at whether the starting SOS would change depending on the amount of wins teams were able to generate per season between 2002 and 2009. You'll notice that (barring the the outliers of 0 and 16 win teams which we'll get to later) the average SOS is basically the same regardless of how many games a team is able to win per season.

Running a correlation between the two variables from 2002 through 2009 shows that the correlation between the starting SOS and the number of wins each team had at the end of the season is 0.006. That's about as close to zero as you can get. There is absolutely no correlation between a team's starting SOS and it's eventual W/L record.

Wrap your mind around that for a second: As a predictor of how successful a team will be, the SOS is effectively worthless.


The two outliers with zero and 16 wins each in the graph above are the 2008 Lions and the 2007 Patriots, and because they are the only teams in their win class, the starting SOS naturally fluctuates more than for other win classes where I've aggregated more teams.

The graph on the right shows the distribution of the number of wins over the last eight years. The red bars show the actual number of teams that ended the season in each win class. The blue line shows what would have been statistically expected if all the wins followed a normal distribution pattern.

The win distribution in the NFL is pretty close to a normal distribution curve, with a slight blip at four and five wins which is compensated for with a dip at six and seven wins.

As you look at the win distribution on the right and contemplate the flat green starting SOS line above, you may wonder whether if you just average enough teams, the average will invariably approach .500. This is of course completely. At the same time, it is also completely false. Here's why:

Life's what you make it

Let's assume you're an 8-8 team and your SOS is exactly .500, meaning your opponents in a 16 game regular season have a combined 128-128 W/L record.


Now let's assume you're the 2008 Lions. Your own W/L record is 0-16. Everything else being equal, your opponents' W/L record would increase by eight wins and decrease by eight losses to 136-120 or .531. Same thing for the 2007 Patriots, but in reverse: Their 16-0 record would result an opponent W/L of 120-136, or .469. 

That is a significant swing in opponent winning percentage (.469 to .531) based on your own winning percentage alone, which in very simple terms means that the more games you win, the softer your SOS gets.

In the graph on the left I've plotted the actual SOS per season against the actual wins per season from 2002-2009. The blue line is the 'expected SOS' based on the Lions/Patriots example above, i.e. what you would expect the SOS to look like based only on your own win percentage.

The red line is the what the actual SOS looks like for each win class over the last eight years.

The correlation here is .886, which means that there is a very high interdependence between the number of wins in a season and how 'easy' the actual SOS turns out to be at the end of the season.

And that's not all. If we now look at post-season success by actual SOS, the numbers suddenly feel intuitively very right: The softer your actual strength of schedule, the higher the likelihood of post-season success.

Actual Strength of Schedule at the end of the season, 2002-2009
SOS range
#of teams
of which made
in % of which made
Divisional round
in % of which made
Conf. Championships
in % of which made
Super Bowl
in %
< .470 54 38 70% 23 43% 12 22% 6 11%
.470-.489 40 22 55% 15 38% 7 18% 4 10%
.490-.509 60 21 35% 14 23% 7 12% 3 5%
.510-.530 54 13 24% 11 20% 6 11% 3 6%
>.530 48 2 4% 1 2% - - - - - - - -
Total 256 96 38% 64 25% 32 13% 16 6%

Of course, as we saw earlier, your actual SOS is an almost direct result of the number of wins you get in a season. Which brings us back to square one: the more games you win in the regular season, the more likely you are to make the post-season.

Overall, it's simply how the cookie crumbles in the NFL. You can't have Miskatonic University on your schedule, nor can you play against the Academy of Visually Impaired Nuns. You play the hand you're dealt. Win more games than you lose, and more often than not you end up making the playoffs.

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