Over the course of a season, teams have their share of good luck, and bad luck, and most of the time the two don't line up exactly the same, meaning some teams face more bad luck than others. Sometimes it's pretty obvious which teams experience very good luck (like the Browns from last year), and others it's tough to put an actual value to it. But that doesn't mean we can't do it.
A very common way to estimate Winning Percentage in football is to use the Pythagorean Expectation formula:
Winning % = Points Scored^2.37 / (Points Scored^2.37 + Points Allowed^2.37)
This was originally invented by Bill James for Baseball, but has been modified by several other sports, including football, to the exponents shown above. By doing this, you have an estimated Winning Percentage that you can compare against the actual Winning Percentage, and the difference becomes our "Luck" value. It tells us a little more about the teams season, showing how many wins the should have had, based on Points Scored/Allowed.
While this is a good method, I think we can do better. If you remember correctly, our Winning Stats has both an Offensive and Defensive "Score", so why not use them, as they take into account way more than just Points. Also, I found another method that spits out a Winning Percentage that takes into account the consistency of the team as well. It's called the Correlated Gaussian Method (CGM), and I got the idea from Ken Pomeroy, who runs the awesome stats site for College Basketball. I'm not going to explain the method here, but if you have questions, feel free to shoot me an email, and I'll explain what I did.
OK, enough set-up. Which team was the luckiest in 2009? And what team had the worst luck? Let's find out...
Here's the results from 2009. Numbers in Red are Bad Luck:
| Team | Win Percentage | Wins | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Actual | CGM | Diff | Pythag | Diff | Actual | CGM | Diff | Pythag | Diff | |
| 49ers | 0.5000 | 0.4051 | 0.0949 | 0.5941 | -0.0941 | 8 | 6.5 | 1.5184 | 9.5 | -1.5056 |
| Bears | 0.4375 | 0.2625 | 0.1750 | 0.4196 | 0.0179 | 7 | 4.2 | 2.8007 | 6.7 | 0.2872 |
| Bengals | 0.6250 | 0.6801 | -0.0551 | 0.5278 | 0.0972 | 10 | 10.9 | -0.8814 | 8.4 | 1.5550 |
| Bills | 0.3750 | 0.3133 | 0.0617 | 0.3648 | 0.0102 | 6 | 5.0 | 0.9871 | 5.8 | 0.1626 |
| Broncos | 0.5000 | 0.5654 | -0.0654 | 0.5036 | -0.0036 | 8 | 9.0 | -1.0459 | 8.1 | -0.0583 |
| Browns | 0.3125 | 0.1166 | 0.1959 | 0.2672 | 0.0453 | 5 | 1.9 | 3.1339 | 4.3 | 0.7247 |
| Buccaneers | 0.1875 | 0.1459 | 0.0416 | 0.2366 | -0.0491 | 3 | 2.3 | 0.6660 | 3.8 | -0.7854 |
| Cardinals | 0.6250 | 0.5824 | 0.0426 | 0.5840 | 0.0410 | 10 | 9.3 | 0.6818 | 9.3 | 0.6563 |
| Chargers | 0.8125 | 0.6290 | 0.1835 | 0.6961 | 0.1164 | 13 | 10.1 | 2.9356 | 11.1 | 1.8618 |
| Chiefs | 0.2500 | 0.1804 | 0.0696 | 0.2957 | -0.0457 | 4 | 2.9 | 1.1133 | 4.7 | -0.7314 |
| Colts | 0.8750 | 0.7409 | 0.1341 | 0.6726 | 0.2024 | 14 | 11.9 | 2.1451 | 10.8 | 3.2380 |
| Cowboys | 0.6875 | 0.7207 | -0.0332 | 0.7049 | -0.0174 | 11 | 11.5 | -0.5319 | 11.3 | -0.2785 |
| Dolphins | 0.4375 | 0.5987 | -0.1612 | 0.4527 | -0.0152 | 7 | 9.6 | -2.5787 | 7.2 | -0.2435 |
| Eagles | 0.6875 | 0.7292 | -0.0417 | 0.6392 | 0.0483 | 11 | 11.7 | -0.6669 | 10.2 | 0.7722 |
| Falcons | 0.5625 | 0.4565 | 0.1060 | 0.5651 | -0.0026 | 9 | 7.3 | 1.6963 | 9.0 | -0.0423 |
| Giants | 0.5000 | 0.6180 | -0.1180 | 0.4643 | 0.0357 | 8 | 9.9 | -1.8877 | 7.4 | 0.5710 |
| Jaguars | 0.4375 | 0.4617 | -0.0242 | 0.3451 | 0.0924 | 7 | 7.4 | -0.3865 | 5.5 | 1.4782 |
| Jets | 0.5625 | 0.5815 | -0.0190 | 0.7151 | -0.1526 | 9 | 9.3 | -0.3041 | 11.4 | -2.4421 |
| Lions | 0.1250 | 0.0798 | 0.0452 | 0.1820 | -0.0570 | 2 | 1.3 | 0.7240 | 2.9 | -0.9116 |
| Packers | 0.6875 | 0.7980 | -0.1105 | 0.7392 | -0.0517 | 11 | 12.8 | -1.7683 | 11.8 | -0.8278 |
| Panthers | 0.5000 | 0.3753 | 0.1247 | 0.5133 | -0.0133 | 8 | 6.0 | 1.9958 | 8.2 | -0.2130 |
| Patriots | 0.6250 | 0.7539 | -0.1289 | 0.7228 | -0.0978 | 10 | 12.1 | -2.0621 | 11.6 | -1.5641 |
| Raiders | 0.3125 | 0.0966 | 0.2159 | 0.1750 | 0.1375 | 5 | 1.5 | 3.4541 | 2.8 | 2.2004 |
| Rams | 0.0625 | 0.0951 | -0.0326 | 0.1031 | -0.0406 | 1 | 1.5 | -0.5209 | 1.6 | -0.6493 |
| Ravens | 0.5625 | 0.7046 | -0.1421 | 0.7227 | -0.1602 | 9 | 11.3 | -2.2729 | 11.6 | -2.5633 |
| Redskins | 0.2500 | 0.4906 | -0.2406 | 0.3650 | -0.1150 | 4 | 7.8 | -3.8491 | 5.8 | -1.8402 |
| Saints | 0.8125 | 0.8463 | -0.0338 | 0.7219 | 0.0906 | 13 | 13.5 | -0.5406 | 11.6 | 1.4493 |
| Seahawks | 0.3125 | 0.3597 | -0.0472 | 0.3132 | -0.0007 | 5 | 5.8 | -0.7547 | 5.0 | -0.0108 |
| Steelers | 0.5625 | 0.7681 | -0.2056 | 0.5749 | -0.0124 | 9 | 12.3 | -3.2903 | 9.2 | -0.1981 |
| Texans | 0.5625 | 0.6637 | -0.1012 | 0.5896 | -0.0271 | 9 | 10.6 | -1.6198 | 9.4 | -0.4335 |
| Titans | 0.5000 | 0.4357 | 0.0643 | 0.4252 | 0.0748 | 8 | 7.0 | 1.0283 | 6.8 | 1.1964 |
| Vikings | 0.7500 | 0.7878 | -0.0378 | 0.7253 | 0.0247 | 12 | 12.6 | -0.6040 | 11.6 | 0.3947 |
Some thoughts:
- The Colts were not the luckiest team in the league, but were the 5th luckiest, accounting for over 2 full games. I'm sure anyone can think of a handful of moments that factor into that, but truth be told, the Colts had some good fortune last year.
- The luckiest team? The Raiders, with almost 3.5 of their 5 wins coming from luck. The Browns were also very lucky last year to win 5 games, including their final 4. Can't really argue with this.
- The unluckiest team? The Redskins, losing almost 4 games due to bad luck. The New Orleans game clearly jumps out at me, but they outplayed their lousy record last year. The Steelers also underperformed by over 3 games.
- There are certainly some discrepancies between the CGM and the Pythagorean formula, but for the most part, they agree with each other. The 49ers seem to be the biggest difference, with a 3 game difference. They scored more points than their actual offensive efficiency, which is the reason for the difference.
Now, I've made a pretty big assumption saying that the entire difference between actual and calculated Winning Percentage is due to Luck. There are clearly other factors that lead to the differences, but it's just easier to tidy it up into one word. Some luck is based on putting yourself in good situations, which many good teams do. I wanted to make sure everyone understood my assumptions.
In my next article, I'll take a look at the luckiest/unluckiest teams since 2001, and whether luck from one year can predict how good/bad a team will be the following year.