The Value of Things: Pythagorean Theory

“On a long enough timeline, the survival rate drops to zero.” — Tyler Durden

One of the hallmarks of the typical sports fan is what I like to call “magical thinking.” It is a trap that all of us find ourselves in at one point or another. If we consider the Houston Texans it follows us when we consider the transition from David Culley to Lovie Smith. The thinking goes that Culley was terribly incompetent, so even a move to someone with basic competence should net two or three victories on its own.

The notion is not crazy on its face. After all, we all saw the Patriots and Dolphins games last year. We saw the first half against the Browns. A competent coach would have won at least the Patriots and Dolphins games. Suddenly, a 4-13 season turns into a 6-11 season and you feel like you are that much closer to respectability. From a certain point of view, it makes perfect sense.

The problem comes when we expect any momentum from that moving forward. Yes, you may have won those two games last season given the circumstances, but the mistake comes in expecting those circumstances to repeat themselves. Serendipity is not a bankable plan moving forward.

What exactly is the Pythagorean Theory?

The Pythagorean Theory got its start in baseball. Honestly it works better when you have more data points. The simple idea is that when you take the number of runs a team scores and the number of runs they allow then you can predict their record most of the time. In a baseball season, most teams will finish within fives games either way of their projected record. When they don’t it becomes noticeable and noteworthy to consider for future performance. Obviously, we simply transfer this to the number of points a football team scores versus how many they allow.

The notion is based on a general premise that fans get wrong all the time. Conventional wisdom says that really good teams win the close ones. Maybe they do. Yet, This belief is based on bad assumptions. Really good teams blow their opponents out of the water. They may also win the close ones, but winning the close ones isn’t a bankable skill from season to season. Over a long enough time, the survival rate drops to zero.

The good folks at Pro Football Reference actually calculate this for us. If we look at the Texans this past season then we see that their expected record was 4.1 wins versus 12.9 losses. In other words, they finished with precisely the exact record they were supposed to based on number of points they scored and the number of points they gave up. A comparison with the bottom eleven teams shows us something different than the standings show us.

• Jacksonville Jaguars— 3-14, 3.4 Pythag., SRS= -11.41
• Detroit Lions— 3-13-1, 5.1 Pythag., SRS= -7.80
• Houston Texans— 4-13, 4.1 Pythag., SRS= -9.72
• New York Giants— 4-13, 4.1 Pythag., SRS= -8.30
• New York Jets— 4-13, 4.1 Pythag., SRS= -10.36
• Carolina Panthers— 5-12, 5.7 Pythag., SRS= -5.48
• Chicago Bears— 6-11, 5.9 Pythag., SRS= -5.20
• Washington Commanders— 7-10, 6.0 Pythag., SRS= -4.21
• Denver Broncos— 7-10, 8.9 Pythag., SRS= -0.53
• Atlanta Falcons— 7-10, -4.9 Pythag., SRS= -8.49
• Seattle Seahawks— 7-10, 9.3 Pythag., SRS= +1.94

The first thing we need to do is make sure everyone is on the same page on all of our terms. We have the records each team finished with followed by the number of wins their point differential would predict. The last stat was the average margin of victory (or defeat in most cases). If everything is running according to plan, those margins should increase as the records get further and further away from .500

We see that the Texans have the third pick in the draft and they had the third highest margin of defeat in the league. So, based on the number of points they scored and allowed, they finished exactly where they should have. While this may not seem like a revelation, it does poke a hole into our magical thinking that we had earlier.

Yes, David Culley could have led them to six wins had he been a reasonably competent coach. However, those six wins would have registered as a bonus given the overall level of production we saw on the field. This kind of thing becomes more pronounced when we look at the seven win teams on the list. They range wildly from five wins to nine wins in expected records. The question is what a team does with this information.

A team like the Broncos chose to go for it. If they are really a nine win team masquerading as a seven win team, then acquiring Russell Wilson makes that much more sense. Elevating a team from seven wins into the wild card range looks daunting. Going from nine wins to the wild card round or divisional round are a lot less challenging.

Conversely, a team like the Falcons might be better off embracing a rebuild. If they are really a five win team masquerading as a seven win team then they have a lot further to go to become a contender. Giving up an aging Matt Ryan makes more sense. That doesn’t explain why the Seahawks chose to give up their franchise quarterback, but sometimes offers are too good to pass up.

Where does this put the Texans?

The key here is to recognize magical thinking when we see it. We have to temper our expectations. Will the Texans be a better team in 2022? In all likelihood they will be considerably better. Will it translate into a noticeable increase in wins? It might not. A part of magical thinking is the fact that fans and analysts sometimes discount the good luck that came their way in the course of the previous season.

Yes, they blew games against the Patriots and Dolphins. Yes, they had other close games where things didn’t go their way. They also had games against the Titans and Chargers where things did go their way. They beat the Jaguars twice. Not only will those teams likely be better in 2022, but the fortunate bounces the Texans got in those games can’t be banked on again. Luck cuts both ways. Sometimes we catch ourselves dwelling on the bad luck when we shouldn’t.

In practical terms, it means that we have to be more sophisticated in how we measure success and failure. You can look at the record and ultimately that’s what most people do. It is a bottom line business and that is the bottom line. However, we can tell a whole lot more when we look at the average margin of victory and defeat. If they are playing closer games then they are making progress. We should focus more on Pythagoras than we do random luck.