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Stats 101: Pythagorean Wins

Pythagorean wins are a statistic that tells us the true performance level of a team, beyond what simple win loss records can tell us.

Richard Mackson-US PRESSWIRE

Anyone who has read some of my articles the past few months has probably figured out that I like NFL stats. I enjoy the story that they can tell, when used properly, to dive deeper into what is really going on with players and teams. Win-loss records by themselves tell us only so much - and Pro Bowls tell us even less.

However, I don't like just any stat. I like the ones that mean something to winning games. I don't care for the ones that have little bearing on winning. Some correlate better than others.

For instance, rushing attempts correlate extremely well to winning. But there's one problem — causation. In fact, we happen to know that having a lead (i.e. winning) is what causes rushing attempts, not vice versa. So whenever you see that annoying graphic on a broadcast about how "when Ray Rice gets 25 carries, the Ravens are 23-1!" just remember that its meaningless. Ray Rice gets 25 carries because the team is winning in the fourth quarter and killing clock.

Passing yards is another that we know does not correlate to well to winning. I wrote about this before but you can find plenty of analysis out there that supports this.

Let's put it this way: the NFL's passing yardage leader is 0-48 in Super Bowls. Just think about that for a second. In all of the 48 Super Bowls we've had since Vince Lombardi won the first, never once has the NFL's leader in passing yardage for the season gone on to win the big game.

So, it may not surprise you that points is the best correlating stat to victory. Score more often than the other guy, and you win. Simple, right?

In the 1980s, a guy named Bill James, made famous by the Moneyball exposé (a great read by the way), started the modern statistical revolution in sports. Until that point, sports, and especially baseball, used unusually crude methods of player evaluation. One of the more infamous of these methods was the baseball player's "good face". Scouts actually judged a player's face in order to predict his future ability to be a professional hitter. When the number crunchers gained traction, a major revolution occurred with the old guard feeling threatened by the new guard. Baseball eventually adjusted and now Analytics is a key component of nearly every team.

In any event, Bill James realized you could accurately predict a team's expected win loss record by calculating their runs scored and runs allowed in a certain way. Essentially, the formula was this.

When that number was multiplied by the games in a season, you had an estimate of how many games a team SHOULD have won. This calculation came to be known as Pythagorean Expectation due to its obvious similarities to the Pythagorean theorem.

Smart people have since modified it to improve its accuracy over the years and adapted it to the various sports.

I encourage you to try it out on a few teams at random and see how it holds up. The 1997 Orioles for instance, won 98 games. They played like a 93-win team, eventually losing in the ALCS to the Indians, which were an inferior team (85 expected wins). In fact, the Indians skated 3-2 by the AL's best team, the New York Yankees, which were expected to win 100 but won 96 games instead.

The 1997 Bulls won 62 games. They had a Pythagorean expectation of 61 wins (best in the NBA), eventually winning the NBA Finals.

More recently, the 2012 Orioles famously won a ton of extra inning games in order to qualify for the playoffs, winning a total of 93.  In fact, they performed like an 82 win team but thanks to that late inning magic (luck, too) they greatly outperformed their expectation.

In fact, this is one of the great purposes of Pythagorean wins: finding the teams that either underperformed or overperformed their expectation in order to determine outliers.

Another way to describe that would be to say that you can find out the "lucky" teams and the "unlucky" teams based on how far off their expectation they were. When we know who these teams are, we get a picture of who is likely to be worse next year just because they may not get the same good bounces, and who is likely to be better if their luck improves.

Two examples I'm fond of citing to make this point are in the AFC South: The 2012 Colts and 2012 Texans.

The Colts were 11-5 in 2012 fresh off a disaster season in 2011, earning a wild card berth and praise all around for Chuck Pagano, Andrew Luck, and Ryan Grigson for the work they did.

But it just so happens they had a point differential of  negative 30 (357 scored, 387 allowed). When we calculate their Pythagorean wins in 2012, we get this: (357^2.37)/(357^2.37+387^2.37) = 0.452337. Multiply that by 16 games and we get 7.23 wins.

The Colts played like a 7 win team in 2012. A fourth place schedule, soft division, a #1 overall draft pick quarterback who performed very well by rookie standards, and a number of downright fortunate comebacks helped that record (for instance, the Packers blowing an 18 point halftime lead). Still, they were exposed in the wild card round, failing to score a touchdown, as often happens in the playoffs with overmatched teams..

The Texans were famously 11-1 going into Week 14 but by then the cracks had started to appear. They needed a gift from the NFL gods to beat Detroit on a preposterous illegal challenge by Jim Schwartz that enabled a touchdown to stand, were blown out by New England, and with the #1 seed on the line, were defeated by the Colts in Week 17 to drop to the #3 seed. Their 12-4 record started to look awfully flimsy going into the playoffs where they narrowly limped past Cincinnati and then promptly were smoked again by New England in the Divisional playoffs.

When we do their Pythagorean Expectation we get this: (416^2.37)/(416^2.37+331^2.37) = 0.632209 x 16 games = 10.11. The Texans were basically a 10 win team in 2012 masquerading as a 12 win team - good, but hardly the #1 seed they looked like at one point.

Not only were these AFC south playoff teams exposed at Baltimore and New England respectively, but we had strong evidence that both the Colts and Texans would regress in 2013. When a team exceeds its Pythagorean Expectation by more than one win, this signifies probable regression.

The Texans went 2-14, a regression of epic proportions. In fact, it's fair to say they're not a two win team and wildly underperformed their expectation. Unfortunately, Kubiak was fired anyway but we benefitted from that in hiring him as our OC. The Texans will almost surely be better by several wins even though they didn't address their QB situation. For instance, its unlikely that they outplay the NFL's best team for 3.5 quarters and then improbably throw a pick 6 at the worst possible time to lose.

The Colts meanwhile went 11-5 again in a soft division but produced an expectation of 9 wins this time. So, they improved technically but performed well below their actual record. It's fair to say that we can chalk that up to the continued improvement of Andrew Luck and Robert Mathis' DPOY worthy year, as well as Houston's total collapse making the division easier. Their underlying flaws were exposed against Kansas City though, until KC lost their best four players and allowed Indy to close their 28 point deficit in improbable fashion. In any event, New England made it official, dominating them by three touchdowns.

In fact, the AFC in 2013 was one big exercise in overperforming teams who were not quite as strong as they appeared.   Not surprisingly, even the best of the AFC teams was utterly dominated when put up against the NFC's best.

Now, to tie this back into the Ravens, you probably won't be surprised to learn the Ravens team with the best Pythagorean expectation in team history: the 2000 Ravens. That team produced an expectation of 13.45 wins - fully one and a half above its actual 12 wins. In other words, it played like the best team in the NFL (the Tennessee Titans were just behind them).

This improvement was largely forecasted by the 1999 team. That team produced like a 10 win team despite only winning 8. It was statistically bound to get a little luckier the following year, which it did by producing an absolutely preposterous 49 fumbles, recovering 26 of them.  Al del Greco missing three field goals in the Divisional playoff comes to mind as well.

One of the most underperforming (or perhaps unlucky) teams in Ravens history was the 2009 team. That team had an expectation of 12 wins. It was a very underrated team, with the fourth best defense, and ninth best offense. But it only won nine, losing several tough comebacks, such as their missed field goal at Minnesota. So, that team was viewed as something of a dark horse going into the playoffs but hardly a favorite. They promptly annihilated the Patriots like no one has ever done to them before in a playoff game on their own field. Their 12 Pythagorean wins indicated that the Ravens would be much better in 2010 (or at least, a little luckier). They would win 12 games the next two seasons each, validating that prediction.

For 2013, here are the teams who overperformed expectations by more than one win and thus might regress in 2014:

  • New England
  • Denver
  • Indianapolis
  • New York (Giants)
  • New York (Jets)

The Jets won 8 games despite playing like a 5 win team.  They are a safe bet to be worse next year.

Here are the underperformers who statistically are likely to improve to some degree in 2014:

  • Detroit
  • Atlanta
  • Minnesota
  • Washington
  • Houston
  • Cleveland
  • Tampa Bay

The Texans were the most glaring underperformers, playing like a five-win team. They will be better for sure although probably never come close to winning 12 again until they draft a QB. Atlanta also should be much better even though they play in a tough division currently.

As for the Ravens, they played like a 7.1-win team. So they are what we thought they were: a fairly underwhelming 0.500 team that will probably not have the 10th worst run game in NFL history next year. As a result, I expect them to be better.