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.

A new statistic to measure chemistry in basketball

Team chemistry is an elusive concept to measure but three “quantitative traders in the financial world” have developed a new statistic they say tackles the subject:

We introduce a novel Skills Plus Minus (“SPM”) framework to measure on-court chemistry in basketball. First, we evaluate each player’s offense and defense in the SPM framework based on three basic categories of skills: scoring, rebounding, and ball-handling. We then simulate games using the skill ratings of the ten players on the court. The results of the simulations measure the effectiveness of individual players as well as the 5-player lineup, so we can then calculate the synergies of each NBA team by comparing their 5-player lineup’s effectiveness to the “sum-of-the-parts.” We find that these synergies can be large and meaningful. Because skills have different synergies with other skills, our framework predicts that a player’s value is dependent on the other nine players on the court. Therefore, the desirability of a free agent depends on the players currently on the roster. Indeed, our framework is able to generate mutually beneficial trades between teams…

The research team pored over a ton of data, ran countless simulations and looked at how many points certain combinations of skills created…

One pattern that emerged was that “rare events” (like steals/defensive ball-handling) tended to produce positive synergies, while “common events” (like defensive rebounds) produce negative synergies. How come? Because increasing a team’s rebounding rate from 70 percent of defensive rebounds (which would be lousy) to, say, 75 percent (very good) represents only a 7 percent increase. But upping offensive rebounds, which aren’t nearly as common as defensive rebounds, from a rate of 30 percent to 35 percent represents a robust 17 percent gain…

Figuring out the component parts of what we know as chemistry or synergy is one of the next great frontiers of this movement. It’s not enough to put an exceptional distributor on the floor. To maximize that point guard’s gifts, a team must surround him with the right combination of players — and that combination might not always be the sexiest free agents on the market.

Sports has so much data to pore over that researchers could be occupied with for a long time.

This particular question is fascinating because one could get a lot of answers to why certain five player units are successful from different actors such as coaches, players, commentators, and fans. Players might be easier to assess (ha – look at all the issues with drafting) but looking at units requires sharp analytical skills and an overall view of a team.

Which team(s) will be the first to utilize this statistic and really build team units rather than cobble together a number of good players and then try to squeeze the best out of them? Certain players who might be considered “busts” may simply be in the wrong systems and be the “missing piece” for another team.

How (baseball) statistics can help you earn $2.025 million

Traditional baseball statistics would say that Pittsburgh Pirates pitcher Ross Ohlendorf didn’t have a great 2010 season: the 27-year old had 1 win against 11 losses with 108 innings pitched in 21 games. Yet, in an arbitration hearing, Ohlendorf just earned a pay raise from $439,000 to $2.025 million. What happened?

Even though this might seem like a minor matter (the average MLB salary in 2010 was $3.3 million), there is plenty of talk already that Ohlendorf benefited from statistics (and a field known as sabermetrics) that have become fairly normal in the last 20 years in baseball. Ohlendorf’s WHIP ((walks + hits)/innings pitched) was decent at 1.384. His ERA+ (comparing his ERA to the league average and adjusting for the ballpark) was 100, right at the league average.

Ultimately, these statistics suggest that Ohlendorf’s performance was decent, at least average. His main problem was that he was pitching for a terrible team that finished with 57 wins and 105 losses. With a little more data beyond what typically goes on a baseball card or is flashed on a television graphic, Ohlendorf got a sizable raise.

There could be some alternative takes on this outcome:

1. Wow, even an average MLB pitcher can make big money.

2. It would be interesting to know whether Ohlendorf’s representative in the arbitration hearing used all of these advanced statistics to make his case.

3. How quickly can workers in other careers develop advanced statistics to further their pitches for raises?