D/STPA Update

After some discussion on /r/fantasyfootball, it was suggested that I take a closer look at the numbers to support my assertions about D/STPAs being more consistent and predictable than traditional D/STs (in case you missed it, see my last post for more info on that). I decided to take a look at the numbers comparing week-by-week scoring for D/STs and D/STPAs and seeing how consistent it really was.

For those familiar with statistics, you can go ahead and skip down the results. If not, the next two paragraphs should help you understand the numbers I'm presenting.

For each team, I found the standard deviation of the scoring, which, in nutshell, describes how far apart the numbers. For example, if a D/ST or D/STPA scored 15pts every week, its standard deviation would be 0. On other hand, a team that scores 0pts half the time and 26pts the other half would have a standard deviation of 13. It's a basic statistical tool used to measure how far apart a group are, and a smaller standard deviation indicates a group of numbers that are closer together. I also included variance, which is just another way of expressing the standard deviation. It is equal to the standard deviation squared and is useful to other statistics nerds like me.

I also used RSD, or relative standard deviation, which is just a comparison of a team's standard deviation to how much it typically scores. For example, Jacksonville's D/STPA is averaging 11.33 points per game so far this year, and the standard deviation of their scores has been 5.67, which is about half of their average. Their RSD is 50.09%. Compare this to Kansas City's D/STPA, who have scored 4.58 points per game, and have a standard deviation of 2.84. Kansas City has a much smaller standard deviation, which might suggest that they've been more consistent. It turns out that Kanas City has a higher RSD, coming in at 60.01%. This is because KC's average is so much smaller, meaning it varies more relative to the average.

I sampled the data for the top 12 performing D/STs and D/STAs, then sampled again for the top 16 and finally took a look at the overall picture, sampling all 32 teams. (the data used is 2013's ESPN Standard through week 13). Total average is the average points scored each week per team. The Standard Dev Ave is the average standard deviation for each team.

1st - 12th	D/STPA	D/ST	DIFF
Total Average	9.576388889	9.347222222	0.23
Standard Dev Ave	6.029854549	6.440849765	-0.41
Average Variance	38.45196759	43.68171296	-5.23
RSD AVE	63.95199358	70.88362818	-6.93

The data for the 12 suggests that the D/STPAs score more points, and tend to be more consistent. To put a number on it, the data is about 7% more consistent for D/STPAs than D/STs.

1st - 16th	D/STPA	D/ST	DIFF
Total Average	9	8.7499999998125	0.25
Standard Dev Ave	6.0095724855625	6.338361178	-0.33
Average Variance	37.744791665625	42.23611110875	-4.49
RSD AVE	68.49325761625	74.877400960625	-6.38

Taking a look at the deeper league numbers, D/STPAs gain on the average scoring, and only lose a bit of ground to the D/STs in consistency, about .45% RSD.

1st-32nd	D/STPA	D/ST	DIFF
Total Average	6.8619791665	6.8619791664	0.00
Standard Dev Ave	6.1213286290	6.2629449369	-0.14
Average Variance	39.4450954838	40.8527156288	-1.41
Ave RSD	98.1939681550	99.7977018800	-1.60

Looking at the whole crop, we see the difference in standard deviation and RSD decrease substantially. One thing I noticed straight away was that RSD becomes a much less effective metric when a teams scoring average gets close zero. Case and point: Denver D/STPA, who comes in at a stout 2pt total (!) on the year, averaging 0.167pts per game, which resulted in a whopping 3638% RSD. Insanity! I removed that data point from the total RSD calculation as it skewed the data tremendously. For teams with low averages, simply using the standard deviation is the most effective metric. I left Denver's data in for the calculations other than RSD, as the rest were statistically usable.

The biggest takeaway? D/STPAs have been more consistent across the board so far this year. The next step is to take a look at previous years and see if this is the real deal. I'll keep you posted.

If you enjoyed this post, hated it, or even if you thought it was completely useless, leave a comment. I'll make my best effort to respond as soon as I can. For those that want  to take a look at the date themselves, feel free to check out my spreadsheet here.