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247Sports Composite Team Rankings Formula -- An Explanation & Demonstration
c ₋₀.₅[₍ₙ₋₁₎/σ]² ∑ (Rₙ - 70)e n=1where c is a specific team's total number of commits and Rₙ is the 247Sports Composite Rating of the nth-best commit times 100.
In order to create the most comprehensive Team Recruiting Ranking without any notion of bias, 247Sports Team Recruiting Ranking is solely based on the 247Sports Composite Rating.
Each recruit is weighted in the rankings according to a GAUSSIAN DISTRIBUTION FORMULA (a bell curve), where a team's best recruit is worth the most points. You can think of a team's point score as being the sum of ratings of all the team's commits where the best recruit is worth 100% of his rating value, the second best recruit is worth nearly 100% of his rating value, down to the last recruit who is worth a small fraction of his rating value. This formula ensures that all commits contribute at least some value to the team's score without heavily rewarding teams that have several more commitments than others.
Readers familiar with the Gaussian distribution formula will note that we use a varying value for σ based on the standard deviation for the total number of commits between schools for the given sport. This STANDARD DEVIATION creates a bell curve with an inflection point near the average number of players recruited per team.
Below is a graphical representation of how our formula works. You can see that the area under the curve gets smaller both as the rating for a commit decreases and as the number of total commits for a school increases. The z-axis in this graph represents the percentage weight of the score that gets applied to an overall team ranking.
Image of 3D Gaussian Distrubution
My Procedure:NOTE: For my research I used the Top 4 247Sports recruiting classes as my guinea pigs (i.e. Georgia, Alabama, Clemson, and LSU).
- Compile and index the 247Sports Composite Ratings of all recruits within a team's recruiting class (see Columns A-E from Table 1).
- Compute the mean of each team's recruiting class (see bottom of Columns B-E from Table 1).
- Compile and index the number of recruits recognized by 247Sports' Composite Rating system within each team's recruiting class (tabulated data not included in this post).
- Compute the Sample Standard Deviation of the recruiting class sizes.
σ = 9.698 recruits ≈ 9.0 recruitsNOTE: I calculated the standard deviation for the sample of 240 recruiting classes acknowledged by 247Sports, however, this led to recruit values which did not agree with 247Sports' class calculator. After closer inspection, I noticed that after approximately 200 recruiting classes, 247Sports only recognized 1-2 recruits from each of those classes. Because these small sample sizes skewed the results, 247Sports arbitrarily decided to cut off the recognized recruiting classes after about 200 or so and set a round standard deviation of exactly 9.0 recruits.
- Compute the individual Value of each recruit in their respective class using the 247Sports formula (see Columns G-J from Table 1).
- Compute the sum of all recruit values within a class to determine the overall score and verify with 247Sports' actual class scores (see bottom of Columns G-J from Table 1).
Data & Results:Table 1: Individual Recruit Ratings and Class Values
|Index||Rᵢ (UGA)||Rᵢ (Bama)||Rᵢ (Clemson)||Rᵢ (LSU)||% Value||Value (UGA)||Value (Bama)||Value (Clemson)||Value (LSU)|
Picture 1: Heat map of each team's individual recruit ratings, value depreciation, and class values.
- At the beginning of this little experiment, I noticed a discrepancy between 247Sports' class scores and their own published formula. There also seemed to have been some confusion by those, like myself, trying to understand how they calculate their scores.
- Specifically how they define an individual recruit's maximum worth: "Rₙ is the 247Sports Composite Rating of the nth-best commit times 100."
- This suggests that recruits are graded on a 100-point scale, however, this proved very quickly to be incorrect.
- It didn't take much digging to deduce from 247Sports' Class Calculator that recruits are instead graded on a 30-point scale, which prompted me to update the formula. The formula shown in the above explanation is the corrected version.
- After correcting the formula and determining the varying standard deviation they used in their formula, I was able to accurately reproduce each team's average recruit rating, individual recruit value, and overall class score (with some minor rounding errors).
- From Column F in Table 1, I isolated the exponential from 247Sports' formula which allows me to see the multiplier that determines the percent worth of a recruit's maximum value. That is:
- The highest rated recruit is worth 100% of their maximum value, the 7th highest rated recruit is worth approx. 80% of their maximum value, the 16th highest rated recruit is worth approx. 25% of their maximum value, and so on.
- This also allows us to see 247Sports' variation of the Gaussian Distribution in action.
- If you think of a recruit's % worth as a function of the area underneath the Gaussian bell curve at the location of the variate, where 0 < %W < 1.0, you can see how the rate of change in %W for the highest and lowest rated recruits is very small, whereas the greatest rate of change in %W is in the middle of the curve where approx. 68.3% of the area resides.
- From the heat maps in Picture 1, you can see exactly how Georgia's recruiting class was rated higher than Alabama's and Clemson's despite having a significantly lower average rating.
- From the blue and green heat maps you can see that Georgia's recruiting class was more top heavy than Alabama's or Clemson's and because 247Sports' model places more value on higher rated recruits, Georgia's the first 12-14 recruits or so were able to carry the weight for the rest of the class.
- From the red heat map in you can see that Georgia's largest depreciation in value was still smaller than each of its three counterparts.
Removed comments/submissions for /u/Hoihe
Comments:flq3eyx in changemyview on 28 Mar 20 (2pts):
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Submissions:f8cbe7 in OutOfTheLoop on 23 Feb 20 (1pts):
What's going on in Ukraine?dcfrr2 in askscience on 02 Oct 19 (1pts):
For the same amount of meat produced, how fares the ecological/environmental impact of fowl, pigs and goats?db8hmt in chemistry on 30 Sep 19 (1pts):
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