Sports Academy Investigation - Article 2: Player PRS and SA Level Impact on Player OR
So, it has been awhile since I have updated you on the progress of the academy investigation. At the time of writing this article, the third instalment in the report, there are over 1,800 players submitted. I want to thank everyone who has submitted and ask that you continue to do so since the final step is the most interesting one - figuring out the impact of staff. Do not falsify data and please fill in all entries for each player otherwise my script faults out and I'm forced to remove bad data on my own. To submit players you can do so HERE. Feel free to bookmark this link for your records, it will not change.
The first instalment was an introduction while in the second instalment I reported on C/L projections. For example, what are the odds of pulling a 6/6 vs. a 5/6 player. At the time of the report there were 430 player submissions. We now have over 1,800 and the numbers still indicate a 60:40 ratio of 6/6 to 5/6 C/L from the academy. The article continues to dig deeper illustrating what this means for the odds of pulling various C/L paths, assuming that said paths are an inherent property of a player at the time of pull and not something that is dynamic and can change over his career.
The first new data I wish to report are preferred side numbers. Surprisingly, the data hasn't completely settled into nice round numbers as one would expect (like 60.07% and 39.93% which was the case for C/L) but I will report them nonetheless. Of the players submitted, 34.7% were left-sided, 33.3% were right-sided and 32.0% were universal. I would expect, eventually, these numbers to settle into thirds (33% each) as one would have expected. This means, if you combine the results from the second instalment, focusing on C/L, the odds of pulling a 6/6 universal player is roughly 20%. You can then run the numbers from said previous article to figure out the odds of a player making it to 18 6/6 and being universal as well.
As much as I'd like to leave the first of the "big news" investigations for another day, time commitments being what they are I should likely give you the first of them now: the impact of player OR with SA level. I must preface this section with saying staff was not taken into account. As mentioned before, the impact of staff is a tricky business to figure out given the number of data points required and the small distribution of staff efficiencies people are reporting. With that in mind, I shall proceed.
All of the players reported were sorted into groups of the same SA level. Each group was fit using a Gaussian distribution to obtain the mean and uncertainty in the mean. This mean was used to determine the "average" OR expected (denoted μ) for a player at a given SA level. Additionally, the sigma of the Gaussian (the width of the peak) can be used to determine the odds of pulling a player above X OR for any given SA level. I have included two examples, SA Level 8 and SA Level 14. You can clearly see the peak shifted to higher OR in SA Level 14 compared to SA Level 8. In fact, SA Level 8 had an average OR expected of 208 while SA Level 14 had an average expected OR of 293. You can also clearly see the impact of having lots of data. Level 8 has 55 submitted players compared to level 14's 448. Now, keep in mind caveat at the start of this section which is amplified here given higher-SA levels will tend to have better staff working as they're run but wealthier teams.
When comparing fit of SA Levels 7 through 15 (SA levels with less than 25 players submitted were not analyzed due to the poor statistics) you obtain the figure below.
As you can clearly see, with increasing SA Level you have a distinct linear increase in the average OR you can expect dictated by the linear relation y = (14±2)x+(91±20) where y=μ=average player OR and x=SA Level. This means, at level 0 you could expect an average pull of 91±20 OR. Each SA increase from then forward will add, on average, 14 OR to your pull. Once again, it is important to note that staff was not considered in this investigation for reasons stated earlier. As a result, I could not remove the impact of staff which should yield better agreement between the points and the linear trend. It is clearly illustrated that levels 10-15 are highly-linear while levels 7-9 tend to skew the fit. Taking staff into account and obtaining more data for the 7-9 level SAs should alleviate this discrepancy.
I should return to the work I am paid to do. If anyone knows anything about simulating the emergence of turbulence in viscous hydrodynamic quasi-Keplerian accretion discs please let me know, I am a tad over my head right now.
Thanks for reading, I will report next on the impact of staff at a point in time where there is sufficient data to support such a claim. Until then, good luck in hockey playoffs, in the new soccer season and in your handball adventures.