College football recruiting services rank incoming players on a scale of 1-star (not a highly sought-after prospect) to 5-star (considered to be the best players). Recently a service attempted to validate its rankings by assigning star ratings to players upon completion of their careers to determine the accuracy of the initial rankings. The survey averaged the post-career ratings of each player and found that 5-star players' final average was 4.46, compared with 3.98 for 4-stars and 3.11 for 3-stars. This suggests that the rankings services do not effectively judge high-end talent as well as they judge players in the middle of the range.
Which of the following identifies a problem with the service's attempt to validate its rankings?
(A) Players at certain positions might be harder to judge at a younger age than players at other positions
(B) A five-star scale does not allow the most elite players to overperform their initial ranking
(C) Players may change positions over their careers and be judged at multiple different positions
(D) Some players transfer to different schools and therefore need to change their playing styles
(E) Because of differences in strength training programs at different schools, players may develop at different rates
OA will be later.
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challenger63
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charu_mahajan
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I guess C makes sense here. I was considering B initially, but, if not 'overperform', what forbid the players from 'maintaining' their rank.
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Bill@VeritasPrep
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It's B.
The conclusion is that the services do better with 3- and 4-star players than they do with 5-star players. How do we know this? Statistics, which should always be a red flag on CR.
The 3- and 4-star players' final ratings average was extremely close to their initial average. 3.98 for 4-stars, and 3.11 for 3-stars. On the other hand, 5-stars ended up with an average of 4.46, more than half a star less than their initial rating.
Choices A (different positions), C (position changes), D (playing styles), and E (strength training) all introduce factors for which we cannot account. B, on the other hand, takes issue with exactly what we can evaluate: the star system itself.
B makes the point that, for 5-star players, there are two possibilities: either they maintain their rating or they lose stars. This means that, as soon as one of the 5-star players is evaluated at 4-stars or fewer, the overall average will be less than 5. The lower ratings can balance out underperformers (those whose ratings drop) with overperformers (those whose ratings improve). For argument's sake, let's say we have 10 players for each star rating.
5-star: if 5 of them maintain their current rating, and 5 drop to 4 stars, the group average will be 4.5 stars. Still, the rating service got half of the players exactly right.
4-star: if 5 of them go up to 5 stars, and 5 drop to 3 stars, the group average is still 4 stars. However, the rating service got none of the initial ratings correct.
3-star: if 5 of them go up to 4 stars, and 5 drop to 2 stars, the group average is still 3 stars. However, the rating service got none of the initial ratings correct.
In this situation, the rating service was actually more accurate with the elite players than they were with the middle-tier players.
The conclusion is that the services do better with 3- and 4-star players than they do with 5-star players. How do we know this? Statistics, which should always be a red flag on CR.
The 3- and 4-star players' final ratings average was extremely close to their initial average. 3.98 for 4-stars, and 3.11 for 3-stars. On the other hand, 5-stars ended up with an average of 4.46, more than half a star less than their initial rating.
Choices A (different positions), C (position changes), D (playing styles), and E (strength training) all introduce factors for which we cannot account. B, on the other hand, takes issue with exactly what we can evaluate: the star system itself.
B makes the point that, for 5-star players, there are two possibilities: either they maintain their rating or they lose stars. This means that, as soon as one of the 5-star players is evaluated at 4-stars or fewer, the overall average will be less than 5. The lower ratings can balance out underperformers (those whose ratings drop) with overperformers (those whose ratings improve). For argument's sake, let's say we have 10 players for each star rating.
5-star: if 5 of them maintain their current rating, and 5 drop to 4 stars, the group average will be 4.5 stars. Still, the rating service got half of the players exactly right.
4-star: if 5 of them go up to 5 stars, and 5 drop to 3 stars, the group average is still 4 stars. However, the rating service got none of the initial ratings correct.
3-star: if 5 of them go up to 4 stars, and 5 drop to 2 stars, the group average is still 3 stars. However, the rating service got none of the initial ratings correct.
In this situation, the rating service was actually more accurate with the elite players than they were with the middle-tier players.
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whats_in_the_store
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Thanks Bill I understand most part of it, but can you explain why A is not considered at all!
Is it because all the ratings will suffer equally because of this? Please clarify!(A) Players at certain positions might be harder to judge at a younger age than players at other positions
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The central comparison is between 5-star and 3- & 4-star players; we're trying to weaken the idea that they do better with the latter category. Information about the relative difficulty of judging different postions at a young age doesn't directly address that. We don't know if they have a tendency to give certain positions more or less stars than they actually deserve, so we have no way of knowing how that will affect their overall accuracy.whats_in_the_store wrote:Thanks Bill I understand most part of it, but can you explain why A is not considered at all!Is it because all the ratings will suffer equally because of this? Please clarify!(A) Players at certain positions might be harder to judge at a younger age than players at other positions
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I really liked the question. It basically uses an understanding of arithmetic mean in a very subtle way.
Understanding the Conclusion
Since we need to find a problem i.e. a flaw or a weakener, lets first look at the conclusion:
Conclusion: This suggests that the rankings services do not effectively judge high-end talent as well as they judge players in the middle of the range.
The first question one needs to ask on reading this conclusion is about the meaning of "effectively". One needs to put on a mathematical cap to understand the meaning of this word from the previous sentence, which says that:
"The survey averaged the post-career ratings of each player and found that 5-star players' final average was 4.46, compared with 3.98 for 4-stars and 3.11 for 3-stars"
We have the below observations:
For 5 star players - Final average was 4.46 - that means a difference of 0.54 from their initial rating
For 4 star players - Final average was 3.98 - that means a difference of 0.02 from their initial rating
For 3 star players - Final average was 3.11 - that means a difference of 0.11 from their initial rating
So, we see that the difference is the largest in the case of 5 star players. This implies that effectiveness of ranking services probably refers to the difference between initial rating and final average. Lesser the difference, better the effectiveness.
Identifying the Problem
Now comes the main part, what is the problem with this way to calculate effectiveness, which is ultimately used to validate rankings.
The problems is that if a 4-star or 3-star rated player under-performs i.e. his final rating falls below his initial rating, there could be players with the same initial rating who over-perform their initial ratings. Thus, when we take average of these players, over performing players will mitigate the effects of under-performing players on the average final rating.
However, in case of 5-star rated players, no person can over-perform since the maximum final rating is also 5-star. So, in this case, every under-performer drags down the final rating and this effect cannot be mitigated by any other player since over-performance is not possible.
Therefore, option B is the correct choice.
Hope this helps
Thanks,
Chiranjeev
Understanding the Conclusion
Since we need to find a problem i.e. a flaw or a weakener, lets first look at the conclusion:
Conclusion: This suggests that the rankings services do not effectively judge high-end talent as well as they judge players in the middle of the range.
The first question one needs to ask on reading this conclusion is about the meaning of "effectively". One needs to put on a mathematical cap to understand the meaning of this word from the previous sentence, which says that:
"The survey averaged the post-career ratings of each player and found that 5-star players' final average was 4.46, compared with 3.98 for 4-stars and 3.11 for 3-stars"
We have the below observations:
For 5 star players - Final average was 4.46 - that means a difference of 0.54 from their initial rating
For 4 star players - Final average was 3.98 - that means a difference of 0.02 from their initial rating
For 3 star players - Final average was 3.11 - that means a difference of 0.11 from their initial rating
So, we see that the difference is the largest in the case of 5 star players. This implies that effectiveness of ranking services probably refers to the difference between initial rating and final average. Lesser the difference, better the effectiveness.
Identifying the Problem
Now comes the main part, what is the problem with this way to calculate effectiveness, which is ultimately used to validate rankings.
The problems is that if a 4-star or 3-star rated player under-performs i.e. his final rating falls below his initial rating, there could be players with the same initial rating who over-perform their initial ratings. Thus, when we take average of these players, over performing players will mitigate the effects of under-performing players on the average final rating.
However, in case of 5-star rated players, no person can over-perform since the maximum final rating is also 5-star. So, in this case, every under-performer drags down the final rating and this effect cannot be mitigated by any other player since over-performance is not possible.
Therefore, option B is the correct choice.
Hope this helps
Thanks,
Chiranjeev
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