## Who Got Lucky This Year? A Dash of Clint Eastwood, A Pinch of High-School Geometry

You've got to ask yourself one question:  do I feel lucky?

Well, do ya, punk?

Like it or not, luck is a part of sports.   The bank shot from half court to win a game.  The blooped broken-bat single. The tip for a pick-six interception.   All of these can break the heart of fans who can't come to grips with the idea that sometimes, for whatever reason, the ball doesn't bounce in their preferred direction.

You've probably heard one fan say to another, "Well, you guys got lucky."   In fact, many fans accused the Denver Broncos of this very thing in Week 1 on the last play of the game (the tipped touchdown to Brandon Stokley if you're living on planet Al Davis).  But what they are really saying is, "You didn't deserve to win."

While I disagree with this assessment, luck does happen.  But more importantly, we can approximate luck, not just on one play, not just on a few bad calls at the end of the game, but over the course of the season.  And we can do it with such little math that even a Raiders fan (with some Cliff's Notes) can grasp it.

#### Going Back to High School

Let me take you back to high school, and I don't mean the ugly dress or cummerbund you wore to your prom.  Let me take you back to high-school geometry.

Bill James, the who-is-your-daddy of baseball sabermetrics, discovered a nice little equation that does an excellent job of predicting a team's winning percentage in baseball over a 162-game schedule.  According to professor Wayne Winston, between 1980-2006, the equation was off on average by only 2% per team.  That's an average of only 3 games per year. In a schedule as long as Major League Baseball's, that's quite impressive.

The equation that James came up with is remarkably similar to the famous Pythagorean Theorem, so similar in fact, that James called the result of his equation a team's "Pythagorean Wins."  Hence the geometry reference. Here was his original equation:

Runs Scored2
_________________________
Runs Scored2 + Runs Allowed2

James later came back and said that the exponent should really be about 1.81, but at that point, no one cared too much. They had a nice little tool to determine those teams that won or lost more games than they should have.   In other words, they could now quantify luck.

It didn't take long for others to take this equation and apply it to other sports like football.  Daryl Morey, a real stats guy, and now General Manager for the Houston Rockets, developed a similar equation for the NFL to predict wins, which is currently used by The Football Outsiders today:

Points Scored2.37
___________________________
Points Scored2.37 + Points Allowed2.37

The reason I point this out is that many people associate The Football Outsiders with developing this predictive tool, but Morey and James are its creators.

Morey's equation is also very accurate.  Over a 16-game season, it predicts winning percentage within about 6%. That's less than 1 game per year.   And it does a better job of predicting future wins than current win-loss models when back tested.

Morey tested his exponent of 2.37 over a 10-year period.  I decided to do a little research myself and I back tested the equation over an even longer period of 23 years, and found that the best exponent for predicting winning percentages over that same period was actually 2.61.

Now that we've exhausted all the geometry that you'll ever need to know to watch football again, let's apply our equation to this year's teams.   We'll use our new equation based on 23 years of data:

Points Scored2.61
______________________
Points Scored2.61 + Points Allowed2.61

This equation will allow us to compare how many games a team won with how many games they "should" have won.

#### The Luckiest

Here are the results from the new equation, ranked from the unluckiest team (Baltimore Ravens) to the luckiest (Indianapolis Colts):

NFL Team Points Scored Points Against Net Points Actual Pct Predict Pct. Differential Wins Projected Wins Variance
Baltimore Ravens 391 261 130 56.30% 74.17% -17.87% 9 11.87 (2.87)
New York Jets 348 236 112 56.30% 73.37% -17.07% 9 11.74 (2.74)
New England Patriots 427 285 142 62.50% 74.18% -11.68% 10 11.87 (1.87)
San Francisco 49ers 330 281 49 50.00% 60.34% -10.34% 8 9.65 (1.65)
Washington Redskins 266 336 -70 25.00% 35.21% -10.21% 4 5.63 (1.63)
Green Bay Packers 461 297 164 68.80% 75.91% -7.11% 11 12.14 (1.14)
Houston Texans 388 333 55 56.30% 59.84% -3.54% 9 9.58 (0.58)
Detroit Lions 262 494 -232 12.50% 16.04% -3.54% 2 2.57 (0.57)
Dallas Cowboys 361 250 111 68.80% 72.29% -3.49% 11 11.57 (0.57)
Tampa Bay Buccaneers 244 400 -156 18.80% 21.58% -2.78% 3 3.45 (0.45)
Kansas City Chiefs 294 424 -130 25.00% 27.77% -2.77% 4 4.44 (0.44)
St. Louis Rams 175 436 -261 6.30% 8.45% -2.15% 1 1.35 (0.35)
Pittsburgh Steelers 368 324 44 56.30% 58.23% -1.93% 9 9.32 (0.32)
Carolina Panthers 315 308 7 50.00% 51.47% -1.47% 8 8.23 (0.23)
Miami Dolphins 360 390 -30 43.80% 44.80% -1.00% 7 7.17 (0.17)
Atlanta Falcons 363 325 38 56.30% 57.17% -0.87% 9 9.15 (0.15)
Denver Broncos 326 324 2 50.00% 50.40% -0.40% 8 8.06 (0.06)
Minnesota Vikings 470 312 158 75.00% 74.45% 0.55% 12 11.91 0.09
Seattle Seahawks 280 390 -110 31.30% 29.63% 1.67% 5 4.74 0.26
Buffalo Bills 258 326 -68 37.50% 35.19% 2.31% 6 5.63 0.37
Chicago Bears 327 375 -48 43.80% 41.16% 2.64% 7 6.59 0.41
Arizona Cardinals 375 325 50 62.50% 59.23% 3.27% 10 9.48 0.52
Philadelphia Eagles 429 337 92 68.80% 65.25% 3.55% 11 10.44 0.56
New York Giants 402 427 -25 50.00% 46.07% 3.93% 8 7.37 0.63
Cleveland Browns 245 375 -130 31.30% 24.77% 6.53% 5 3.96 1.04
New Orleans Saints 510 341 169 81.30% 74.09% 7.21% 13 11.85 1.15
Tennessee Titans 354 402 -48 50.00% 41.78% 8.22% 8 6.68 1.32
Cincinnati Bengals 305 291 14 62.50% 53.06% 9.44% 10 8.49 1.51
San Diego Chargers 454 320 134 81.30% 71.36% 9.94% 13 11.42 1.58
Jacksonville Jaguars 290 380 -90 43.80% 33.06% 10.74% 7 5.29 1.71
Oakland Raiders 197 379 -182 31.30% 15.34% 15.96% 5 2.46 2.54
Indianapolis Colts 416 307 109 87.50% 68.85% 18.65% 14 11.02 2.98

For those of you who don't want to spend a lot of time looking at this table, the most important columns are the last 3. These are the actual wins, the predicted wins from the equation, and the variance, which is essentially how many more games a teams should have won or lost.

#### Denver & The Turning Point

Our own Denver Broncos are a good example.  They scored 326 points and gave up 324.  Their actual record was 8-8, or 50%.  The equation projected their wins at 8.06 and their winning percentage at 50.40%.  So one would have to say the Broncos were neither more lucky nor unlucky than they should have been.

During the season we could have applied this equation week-by-week in order to project how many wins they were going to get.  For the 13-3 crowd, here is an approximation of how many games Denver was going to win after each of their games based on the equation:

Week Opponent  Projected-Bronco Wins
Week 1 Bengals 12.9
Week 2 Browns 15.1
Week 3 Raiders 15.5
Week 4 Cowboys 15.2
Week 5 Patriots 14.3
Week 6 Charger 13.8
Week 7 Bye 13.8
Week 8 Ravens 11.6
Week 9 Steelers 9.9
Week 10 Redskins 9
Week 11 Chargers 7.2
Week 12 Giants 8.4
Week 13 Chiefs 9.8
Week 14 Colts 9.1
Week 15 Raiders 9
Week 16 Eagles 8.8
Week 17 Chiefs 8.1

My original projection for the Broncos was 10-6, and I even wrote a piece here, called "Why History Won't Have a Way of Repeating Itself,"  after Week 9 saying the same.  You can now see why.  After the game against the Steelers they were still on pace to be a 10-win team.

Week 10 was really the turning point for this season and where our equation began to point to the Broncos as an 8- or 9-win team.   But, of course, you know this already, Broncos fans.  For the first 8 weeks, however, this team was a 12-win team.

#### Implications for Upsets

I find it interesting that both the Jets and the Ravens were in a position to lose out on the playoffs.  But according to the equation, both teams were "unlucky" this year and it could be argued that at least the Ravens should have had two more wins.  So if someone tells you that the the Texans, Steelers, or Broncos deserved to be in the playoffs more than these two teams, you can set them straight.  If anything, the Jets and Ravens should have been challenging for division titles.  I will grant you, however, the Jets' figures were slightly skewed given they played teams resting starters in the last two weeks of the season.

A few more surprises came from applying this equation.  First, the Saints, Chargers, and Colts were all "lucky" this season, getting more wins than they should have.  I would not be at all surprised if two of these teams fall in the divisional round.  And the team that should have had the most wins, the Green Bay Packers, ended up as a wild-card team.

Partly due to this equation, I picked the Jets, Cowboys, Patriots, and Packers to win this weekend.  You can also see why the Ravens-Patriots game is the most difficult to pick.  Both teams were unlucky this year and their projected wins were exactly the same.

Don't be surprised if the "unlucky" teams at the top of this list (Jets, Ravens, Patriots, and Packers) end up making noise in these playoffs.  As I finish this piece, I see that both the Jets and the Cowboys have already done so.  But for those with a little high-school geometry, it shouldn't have come as a shock.

There are no punks in geometry class.

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