Denver Broncos scoring at 3.13 standard deviations above the NFL average

Bill Barnwell puts the scoring of the 2013 Denver Broncos in statistical perspective:

That brings us to z-score (or standard score), the measure that analyzes a figure’s distance from the rest of the data set using the mean and standard deviation from the set. By comparing each team’s points scored to the league average (and calculating the standard deviation) for the points scored of each team from that given season, we can get a measure of how much better or worse it was than the average team from that season. Fortuitously, that measure also allows us to compare teams across different years and eras. It’s not perfect, since it can’t account for things like strength of schedule or whether a team let up late in games or not, but it’s a much better measure than raw points scored.

As it turns out, even after we make these adjustments, the 2013 Denver Broncos have still scored points at a higher rate through four games than anybody else since the merger. The Broncos are scoring points on a per-game basis at a rate of 3.13 standard deviations over the mean, which is unmatched over that 43-year run. No team has ever scored more frequently, relative to its peers, than the Broncos have done relative to the rest of the league in 2013.

Because these are standardized figures, it’s possible to translate each team’s scoring rate in 2013 figures and see how close it is to Denver. In this case, after we account for the different populations, a bunch of teams move closer to Denver’s throne. Chief among them is the 1991 Super Bowl–winning team from Washington, which scored 146 points through four games in a league whose teams averaged a mere 72 points through their first four tilts. Washington’s figure placed it 2.85 standard deviations above the mean and translates to 170.9 points scored in 2013, just 8.1 points behind the Broncos. Other famous teams follow: the 2000 Rams, 1992 Bills, 1996 Packers, 1981 Chargers, 2005 Giants …

And you thought standard deviations were good only for statisticians. If you know your normal distribution, that’s way above the league average. I can only imagine how Sportscenter anchors might try to present this information…

Actually, this is quite useful for two reasons: (1) it allows us to look at the Broncos compared to the rest of the league without having to rely on the actual points scored; (2) it allows us to standardize points scored over the years so you can compare figures over a 43 year stretch. Both advantages are part of the wave of new statistical analysis taking over sports: don’t just look at the absolute value of statistics but put them in comparison to others teams or players and also provide statistics that allow for comparisons across time periods.

Quick Review: Despicable Me

I recently saw Despicable Me – I know I’m a little late to the game as this movie was released over a month ago. But I had read some good reviews and was interested in seeing it for myself. Some quick thoughts:

1. I don’t think the film will stick in my memory for long. A lot of it felt like an extended cartoon one might see on TV. Some of the characters, like Gru and Vector, are over the top. The three children alternate between being interesting and mawkish. It was somewhat entertaining but ultimately forgettable.

2. I know there are some funny scenes but I hardly laughed during the movie. Perhaps I wasn’t in a laughing mood…or perhaps the movie isn’t really that funny. Also, we were in a theater with about 10 other people so any semblance of group laughter was missing.

3. The small minions became tiresome. Sure, they may look cute but they started wearing on me after a while. I feel like if movies have to resort to characters like this to keep people interested, the story probably isn’t that great.

4. The music in the film is interesting, alternating between orchestral music and quirky modern numbers. Pharrell Williams of The Neptunes was involved and helped the score develop into something much more varied than a typical animated film.

On the whole, I was not impressed. Not terrible and not great with what seemed like too many switches between styles and ideas, this film settles into the land of average animated films.

(Overall, the movie was well-received by critics: it is 79% fresh (112 fresh out of 142 total reviews) at