Comparison of DIV MAX OPRs

[FiMFanatic]

If I read the chart correctly, the 50% scoring indicates that the Michigan Championship has the highest average quality.

Of course top 5% at World's will be higher than the top 5% of any district championship.....so 95% level somewhat irrelevant.

[Caleb Sykes]

Originally Posted by FiMFanatic

Of course top 5% at World's will be higher than the top 5% of any district championship.....so 95% level somewhat irrelevant.

Except for New England.....so your point is somewhat irrelevant.

[Ether]

Originally Posted by rtfgnow

Did you intentionally leave out PNW, NC and Chesapeake? I know they were week 6.

This is not the same as Joe's chart, but it compares all 7 district CMPs.

[howellroy]

Ok, so I am looking things over and it is true Newton seems to be the toughest but there seems to be some balance. It doesn't mean things are completely unbalanced although there is a gap between Galileo and Newton but that is going to happen when trying to set these things up. I think the greater variable is the number of matches each team played. Those who go to Regional play less matches than those who are part of a District. Regional matches do cost more to go to and there is a bit more travel over longer distances related to it. That give district matches more practice and development of a strategy that best fits their robot. Parity is a matter of every team having exactly the same resources and access money. I'm just saying.

Galileo 35.68
Tesla 35.95
Curie 36.28
Archimedes 36.93
Carver 37.85
Carson 37.96
Hopper 38.15
Newton 40.11

[Joe Johnson]

Originally Posted by rtfgnow

Did you intentionally leave out PNW, NC and Chesapeake? I know they were week 6.

No I didn't. I was in a hurry to post this with my wife basically turning out the lights in the living room as I was crunching the data (think pits at closing time ;-) and I completely forgot about the week 6 districts.

Sorry. Maybe tonight if I get time...

Dr. Joe J.

[Jared Russell]

Another trivia question for you stat-gurus out there to chew on...

Given random assignment of teams to 8 divisions, what is the probability that any division's [mean OPR, 90th %ile OPR, 75th %ile OPR, 50th %ile OPR, etc.] is as strong as Newton's?

[Joe Johnson]

Originally Posted by Jared Russell

Another trivia question for you stat-gurus out there to chew on...

Given random assignment of teams to 8 divisions, what is the probability that any division's [mean OPR, 90th %ile OPR, 75th %ile OPR, 50th %ile OPR, etc.] is as strong as Newton's?

Zing!

I don't know but I'll try to model this tonight.

Dr. Joe J

[Ether]

FWIW

Ten million 75-team samples randomly drawn from 600-team CMP population; 2.5% had average OPR greater than Newton's.


Interestingly:

mean of max OPR of 600 CMP teams = 37.331

std dev of max OPR of 600 CMP teams = 12.287

predicted std dev of the means of the 75-team samples = 12.287/sqrt(75) = 1.4187

mean OPR of Newton = 40.1149

predicted Zscore of Newton = (40.1149-37.331)/1.4187 = 1.9623

area under normal curve between mean and 1.9623 = .4570

predicted probability = 0.5 - 0.4750 = 0.025 = 2.5%

[wjordan]

Originally Posted by Jared Russell

Another trivia question for you stat-gurus out there to chew on...

Given random assignment of teams to 8 divisions, what is the probability that any division's [mean OPR, 90th %ile OPR, 75th %ile OPR, 50th %ile OPR, etc.] is as strong as Newton's?

I ran 1000 simulations (creating 8000 divisions) of the assignment process (with rookies dealt out randomly and evenly at first, then vets), and for each real CMP division counted the percentages of the simulated divisions that had higher stats than the real division.

Division,  Mean, 50th, 75th, 90th
Newton	2.11%	9.93%	0.26%	1.13%
Hopper	25.31%	75.99%	63.89%	29.55%
Carver	33.69%	14.65%	49.40%	43.60%
Carson	38.50%	40.76%	7.49%	41.76%
Arch.	62.38%	60.72%	34.96%	89.81%
Curie	79.78%	53.46%	77.20%	98.06%
Tesla	86.04%	89.74%	68.84%	81.65%
Galileo	90.23%	76.91%	76.33%	82.76%

[SpaceBiz]

Originally Posted by wjordan

I ran 1000 simulations of the assignment process (with rookies dealt out randomly and evenly at first, then vets), and for each division counted the percentages of simulated divisions that had higher stats than the real division,

Division,  Mean, 50th, 75th, 90th
Newton	2.11%	9.93%	0.26%	1.13%
Hopper	25.31%	75.99%	63.89%	29.55%
Carver	33.69%	14.65%	49.40%	43.60%
Carson	38.50%	40.76%	7.49%	41.76%
Arch.	62.38%	60.72%	34.96%	89.81%
Curie	79.78%	53.46%	77.20%	98.06%
Tesla	86.04%	89.74%	68.84%	81.65%
Galileo	90.23%	76.91%	76.33%	82.76%

If 75th %ile is the most important one (I think it is, because the third pick wins events) the .26% figure is really scary. Odds are basically 1 in 400 you are placed in a theoretical division this good.

Sent from my SAMSUNG-SM-G930A using Tapatalk

[jlmcmchl]

Originally Posted by wjordan

I ran 1000 simulations of the assignment process (with rookies dealt out randomly and evenly at first, then vets), and for each division counted the percentages of simulated divisions that had higher stats than the real division,

Division,  Mean, 50th, 75th, 90th
Newton	2.11%	9.93%	0.26%	1.13%
Hopper	25.31%	75.99%	63.89%	29.55%
Carver	33.69%	14.65%	49.40%	43.60%
Carson	38.50%	40.76%	7.49%	41.76%
Arch.	62.38%	60.72%	34.96%	89.81%
Curie	79.78%	53.46%	77.20%	98.06%
Tesla	86.04%	89.74%	68.84%	81.65%
Galileo	90.23%	76.91%	76.33%	82.76%

How did you get .01-precision decimals in the percents, if you ran 1000 simulations? that should be accurate to .1, not .01.

[ATannahill]

Originally Posted by jlmcmchl

How did you get .01-precision decimals in the percents, if you ran 1000 simulations? that should be accurate to .1, not .01.

I imagine that 1,000 simulations created 8,000 divisions.

[jlmcmchl]

Originally Posted by rtfgnow

I imagine that 1,000 simulations created 8,000 divisions.

Then that would effectively be 8000 simulations, if you treated each group of 8 simulations as permutations of each other, not 1000.

[ATannahill]

Originally Posted by jlmcmchl

Then that would effectively be 8000 simulations, if you treated each group of 8 simulations as permutations of each other, not 1000.

I think each team was dulled out once during each simulation making 8 nameless divisions, not one Newton division, one Carver division, etc. and each real division was compared to each of the 8,000 nameless ones. I don't think it was 8,000 instances of grabbing 75 teams from the entire championship list.

I'm now going to wait for Wes to actually tell us what he did.

[wjordan]

Originally Posted by rtfgnow

I think each team was dulled out once during each simulation making 8 nameless divisions, not one Newton division, one Carver division, etc. and each real division was compared to each of the 8,000 nameless ones. I don't think it was 8,000 instances of grabbing 75 teams from the entire championship list.

I'm now going to wait for Wes to actually tell us what he did.

I assigned 8 divisions 1000 times, to create 8,000 divisions. I edited my post so it was more clear.