A few weeks ago, Spartans Weblog did a rather complete game by game graphical analysis, including trendlines of all the Big Ten schools efficiency numbers for the past season.

I decided to take a look at his Penn State numbers in a little more detail. First some background on the graphs:

Background info

First, some notes on the graphs:

- the data only includes the regular season, the Big Ten Tournament game against Illinois is not included.
- the efficiency numbers don’t distinguish between home and away games but SW says that the trendline should smooth out the home/away differences.
- these are raw efficiency numbers that are not adjusted for the opponent so it’s possible that up or down trends are related to the quality of opposition.
- for offense, the higher the number the better, thus upward trends are good. For defense, lower numbers are better, so downward trends are good.

trendlines are used to smooth out data. - Spartan’s Weblog used a third order polynomial trendline. I’m not sure that was the most appropriate trendline to use but SW doesn’t go into his rationale for the choice. Also, some of the reader comments imply there aren’t enough data points for the analysis to be meaningful.

Still the data is interesting to look at.

**PSU Efficiency Chart**

Here’s Penn State’s chart.

When SW analyzes it, he basically says the defense was poor all year long, the offense started out ok, went downhill with Claxton’s injury, then rebounded as the freshman matured.

I wanted to take this a step further.

**Big Ten Tournament**

First, I know for reasons of consistency across all teams, Spartans Weblog chose to use only regular season data. Since I was only interested in PSU’s data, I decided to take a look at the numbers including the Big Ten Tournament game against Illinois.

Here’s that graph:

Efficiency Margins

The difference between a team’s offensive and defensive efficiency numbers is called their efficiency margin. Since, by definition, teams have the same number of possessions in any specific game, if you have a positive efficiency margin for a game, you have scored more points than your opponent and thus won the game.

Here’s a graph with Spartan’s Weblog’s choice of a 3rd order polynomial trendline of PSU’s efficiency margin for all their Big Ten games, including tournament play.

Other Trendlines:

Spartan’s Weblog never described his rationale behind choosing a 3rd order polynomial to plot his trendlines. I know little about what defines the appropriate order to choose. I do know that an N-order polynomial will plot a graph that has at most N-1 hills and valleys. So his choice of a 3rd order for the trendline means the graph will have at most one hill and one valley. We see that in the chart of the offensive efficiency. The defensive efficiency just has one hill.

As an experiment, I decided to plot the efficiency margin charts using 2nd through 6th order polynomials, thus providing a graph with at most one hill or valley, in the first case, and five hills and valleys in the last case. Here are those charts.

**Efficiency Margin 2nd Order Polynomial Trendline**

**Efficiency Margin 4th Order Polynomial Trendline**

**Efficiency Margin 5th Order Polynomial Trendline**

Efficiency Margin 6th Order Polynomial Trendline

As you can easily see, the 4th through 6th order polynomials look remarkably similar. They do differ from the 3rd order polynomial in that the 3rd order shows a season ending downturn while the 4th through 6th show a year end improvement (as does the 2nd order polynomial). Someone with a better knowledge of trendlines than I can argue which is more meaningful but my “blue and white goggles”, “glass half full”, “DeChellis lackey” viewpoint is going to choose to dismiss the 3rd order and go with one of the other views. š

Rationales for third-order polynomials:

1) They look nice.

2) Football Outsiders use them for the 16-game NFL schedule. And FO is big time!

From what I’ve read, there’s no real standard for what order to use, other than intuitive judgment as to the appropriate number of shifts in performance over the sample size. Two peaks in an 18-game schedule seemed about right.

As I noted in my post, you can’t guarantee the trends are statistically significant, but you’re never going to cross that threshold in a single college basketball season. I think they’re great for discussion purposes, though.