If you like math, you probably are thinking that improving by 7 wins is more impressive than improving by 4 wins. But if you love math, you are probably thinking about regression to the mean. After all, sure, Houston won only 2 games in 2013, but nobody expected them to be that bad last year. In fact, the Texans were arguably projected to be the best team in the state last year! ^[1] Just before the season, both Houston and Dallas had Vegas over/under odds of 7.5 wins, but the way the money lines were set up hinted that Vegas wanted to get more action on Dallas and the over.

But instead of using Vegas odds, I thought it would be interesting to take a quick look at the effects of regression to the mean on team wins. I looked at every team season from 2003 to 2014, and noted how many wins each team won in the prior year and in the current year. I then ran a linear regression using prior year (Year N-1) wins to create a best-fit formula for current (Year N) wins. That formula was:

5.51 + 0.31 * Year N-1 Wins

What this means is that to predict future wins, start with a constant for all teams (5.51 wins), and then add only 0.31 wins for every prior win. In other words, three additional wins in Year N-1 aren’t even enough to project one full extra win in Year N! That’s a remarkable amount of regression to the mean, even if not necessarily surprising. ^[2]Since this has been studied to death. For those curious, the R^2 was just 0.094, another sign of how not valuable it is to just know how many games a team won in the prior year.

As a basic matter, no team in 2014 exceeded prior wins like Houston did. But with 2 wins in 2013, Houston would have been expected to win 6.1 wins last year; that means the Texans “only” exceeded expectations by 2.9 wins after we account for regression to the mean. Dallas, meanwhile, was expected to win 8 games for the 33rd year in a row; by winning 12, the Cowboys exceeded expectations by 4 wins.

The table below shows each team from 2003 to 2014; for each team, I have listed their wins in the prior season (Year N-1), their expected number of wins in Year N based on the above regression formula, their actual Year N wins, the raw difference between Year N and Year N-1 wins, and the difference between Year N actual wins and Year N expected wins. The table is fully searchable and sortable, so type in “NYJ” to see all Jets seasons since ’03.

The team that was most “disappointing” by this metric was the Tennessee Titans, who fell from 7 to 2 wins. Tennessee also led the way in coming up short by the basic method, while the Panthers (4.5 fewer wins in 2014, but only 1.7 fewer expected wins) help illustrate the difference between the two methods.

One more interesting note: The ’04 Steelers topped the list. You may recall that Pittsburgh team from such things as Ben Roethlisberger’s rookie season, AFC Championship Game losses in Pittsburgh, and Quarter-by-Quarter Team Win Probability Added. That last link is to a fun Neil Paine post that is worth a read. In 2004, Pittsburgh won 7 more games than an average team; Neil determined that 4.98 of those wins were due to the team’s 4th quarter performance, the most by any team from 1978 to 2012. That’s one reason the Steelers were able to far exceed expectations that year.

I decided to take another stab at examining YPC averages today.  I looked at all running backs since 1970 who recorded at least 50 carries for the same team in consecutive years. Using yards per carry in Year N as my input, I ran a regression to determine the best-fit estimate of yards per carry in Year N+1. The R^2 was just 0.11, and the best fit equation was:

2.61 + 0.34 * Year_N_YPC

So a player who averages 4.00 yards per carry in Year N should be expected to average 3.96 YPC in Year N+1, while a 5.00 YPC runner is only projected at 4.30 the following year.

What if we increase the minimums to 100 carries in both years? Nothing really changes: the R^2 remains at 0.11, and the best-fit formula becomes:

2.63 + 0.34 * Year_N_YPC

150 carries? The R^2 is 0.13, and the best-fit formula becomes:

2.54 + 0.37 * Year_N_YPC

200 carries? The R^2 stays at 0.13, and the best-fit formula becomes:

2.61 + 0.36 * Year_N_YPC

Even at a minimum of 250 carries in both years, little changes. The R^2 is still stuck on 0.13, and the best-fit formula is:

2.68 + 0.37 * Year_N_YPC

O.J. Simpson typifies some of the issues. It’s easy to think of him as a great running back, but starting in 1972, his YPC went from 4.3 to 6.0 to 4.2 to 5.5 to 5.2 to 4.4. Barry Sanders had a similar stretch from ’93 to ’98, bouncing around from 4.6 to 5.7 to 4.8 to 5.1 to 6.1 and then finally 4.3. Kevan Barlow averaged 5.1 YPC in 2003 and then 3.4 YPC in 2004, while Christian Okoye jumped from 3.3 to 4.6 from 1990 to 1991.

This guy knows about leading the league.

That was going to be the full post, but then I wondered how sticky other metrics are.  What about our favorite basic measure of passing efficiency, Net Yards per Attempt? For purposes of this post, an Attempt is defined as either a pass attempt or a sack.

I looked at all quarterbacks since 1970 who recorded at least 100 Attempts for the same team in consecutive years. Using NY/A in Year N as my input, I ran a regression to determine the best-fit estimate of NY/A in Year N+1. The R^2 was 0.24, and the best fit equation was:

3.03 + 0.49 * Year_N_NY/A

This means that a quarterback who averages 6.00 Net Yards per Attempt in Year N should be expected to average 5.97 YPC in Year N+1, while a 7.00 NY/A QB is projected at 6.45 in Year N+1.

What if we increase the minimums to 200 attempts in both years? It has a minor effect, bringing the R^2 up to 0.27, and producing the following equation:

2.94 + 0.51 * Year_N_NY/A

300 Attempts? The R^2 becomes 0.28, and the best-fit formula is now:

2.94 + 0.53 * Year_N_NY/A

400 Attempts? An R^2 of 0.26 and a best-fit formula of:

3.18 + 0.50 * Year_N_NY/A

After that, the sample size becomes too small, but the takeaway is pretty clear: for every additional yard a quarterback produces in Year N, he should be expected to produce another half-yard in NY/A the following year.

So does this mean NY/A is sticky and YPC is not? I’m not so sure what to make of the results here. I have some more thoughts, but first, please leave your ideas and takeaways in the comments.