Originally published Jul. 2020
Nine years ago, I wrote a fan post on this topic where I used statistical process control (SPC) charts to track how well the FSU defense was doing during the 2011 season against its opponents and how it compared to other FSU defenses going back to 2007. Many things have changed since then including the explosion in the use of analytics and, in my case, more knowledge on how to analyze data. Given this, and the uncertainty regarding the 2020 season, I thought it would be good to revisit this topic and take a longer view on how the FSU offense and defense has done since the start of the dynasty era in 1987.
For part one, we’ll explain the process behind the analytics, and then dive into our first set of stats.
What is a Shewhart Chart?
Nerd Alert. Technical discussion ahead! I will try and keep this as simple as I can, but I may go into the weeds a bit as needed. Reader discretion advised.
Let’s review what a Shewhart or SPC chart is and what it does. These charts are used by quality and manufacturing professionals (and increasingly in other areas) to track the performance of a particular process. What Shewhart charts do is differentiate normal, random variations in performance(Common Cause Variation) from abnormal variations in performance (Special Cause variation). They also can give you a sense of what the normal operating range of a process is and if there are any trends in performance with time. An example of this is in Figure 1 below:
The way that Shewhart charts work is through the use of control limits which are set at +/- 3 standard deviations from the average. If a point on the chart lies beyond the 3 SD limits, then there is only a very small chance ( 3 in 1000 chance for a normal distribution) that the value in question is the result of normal process variation. Basically, this is an abnormal result and worth investigating why it occurred.
So how can we use the charts to analyze how the FSU offense and defense has done over the years? What we will do is use what is called an XmR (X-Moving Range) chart to analyze the data. This is a change from nine years ago because the Yards/Play (YPP) data are over-dispersed (Basically, it doesn’t fit a Poisson Distribution which is used for count data. The number of yards and plays in a game are counts.). XmR charts are used when you are tracking individual data points per unit time rather than groups of points (e.g. taking 5 samples every hour from your process). The center line, as seen in Figure 1, is calculated by taking the average Yards per Play per Game for each season. The “control limits” are calculated using the following steps:
- Calculate the average moving range of the yards per play per game. This is a 2 point moving range since you are accounting for 2 games at a time to calculate the range.
2. Calculate the sequential standard deviation. The 1.128 in the denominator is a proportionality constant that has to do with taking a 2 point moving range.
3. Calculate the upper and lower control limits. You are adding 3 times the sequential standard deviation to the mean YPP per game for the upper limit and subtracting 3 times the sequential standard deviation from the mean YPP per game for the lower limit.
So how did Florida State football Dynasty Era teams do in terms of Offensive Yards per Play based on the Shewhart Charts?
Applying an individual data (XmR) chart to the dynasty era teams we get the following:
The red control limit lines show what the normal YPP range for the offense and defense for each season would be. The wider the red lines, the more inconsistent the offense or the defense. The blue lines show what the average YPP for each season is. Higher is best for the offense. Some notable things to see from the charts:
- The late ‘80’s teams were very inconsistent game to game on offense. The normal range for these teams was from between 1-2 YPP to 11-12 YPP. The 1995 offense was also like this. Some of this is due to the teams on the schedule and some due to the offense itself.
- The best offenses of the era were the 2000 (7.2 YPP) and 1993 (6.84) offenses.
- The charts also show if team performance improved or deteriorated. The 1990 team improved after Casey Weldon took over during the Auburn game mid-season. You can see where the 1991 team offense nose-dived from the LSU game (game 8) until seasons end. The 1995 team also did worse as the season went on. You can also tell where the notable losses were. Overall, the teams in this era had Offensive YPP’s no less than 5.5 YPP.
Offensive Performance Using a Sharpe Chart.
Let’s look at how the offense performed another way. This time we are going to use what I call a Sharpe Chart. This is named after the Sharpe Ratio from finance. The Sharpe Ratio measures the return of an investment compared to its volatility. We are going to look at something similar comparing the offensive performance in terms of average YPP per game to the standard deviation of YPP which will measure how volatile an offense is from game to game. The higher the Sharpe ratio, the better. The Sharpe ratio is calculated as follows:
The Sharp chart will plot the mean YPP on the Y-axis vs. the standard deviation of YPP on the x-axis. Here is what we get:
What we want is an offense that gains a lot of yards per play each game but is consistent game-to-game. The darker lines on the axes show the mean and SD ranges. Where you want to be is in the upper left hand corner. From this vantage point the best teams are the 2000 and 1993 squads. The worst team in terms of a risk to reward ratio was the 1996 team.