Chief Delphi - Comparison of DIV MAX OPRs

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- - Comparison of DIV MAX OPRs (http://www.chiefdelphi.com/forums/showthread.php?t=147628)

FiMFanatic

24-04-2016 21:57

Re: Comparison of DIV MAX OPRs

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

24-04-2016 22:09

Re: Comparison of DIV MAX OPRs

Quote:

Originally Posted by FiMFanatic (Post 1578435)

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

24-04-2016 22:57

Re: Comparison of DIV MAX OPRs

Quote:

Originally Posted by rtfgnow (Post 1578431)

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

25-04-2016 12:21

Re: Comparison of DIV MAX OPRs

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

25-04-2016 14:18

Re: Comparison of DIV MAX OPRs

Quote:

Originally Posted by rtfgnow (Post 1578431)

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

25-04-2016 14:50

Re: Comparison of DIV MAX OPRs

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

25-04-2016 17:22

Re: Comparison of DIV MAX OPRs

Quote:

Originally Posted by Jared Russell (Post 1578808)

Zing!

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

Dr. Joe J

Ether

25-04-2016 17:49

Re: Comparison of DIV MAX OPRs

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

25-04-2016 19:40

Re: Comparison of DIV MAX OPRs

Quote:

Originally Posted by Jared Russell (Post 1578808)

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.

Code:

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

25-04-2016 19:52

Quote:

Originally Posted by wjordan (Post 1578981)

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,

Code:

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.

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jlmcmchl

25-04-2016 20:07

Re: Comparison of DIV MAX OPRs

Quote:

Originally Posted by wjordan (Post 1578981)

Code:

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

25-04-2016 20:08

Re: Comparison of DIV MAX OPRs

Quote:

Originally Posted by jlmcmchl (Post 1579010)

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

25-04-2016 20:11

Re: Comparison of DIV MAX OPRs

Quote:

Originally Posted by rtfgnow (Post 1579011)

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

25-04-2016 20:15

Re: Comparison of DIV MAX OPRs

Quote:

Originally Posted by jlmcmchl (Post 1579019)

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

25-04-2016 20:16

Re: Comparison of DIV MAX OPRs

Quote:

Originally Posted by rtfgnow (Post 1579024)

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

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