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Re: Offensive Power Rankings for 2008
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Re: Offensive Power Rankings for 2008
By anticipated popular demand, OPRs by division.
Column order is Team#, # of regionals, last OPR, last regional, best OPR, best regional Stats that I found interesting: Code:
Total OPR:Code:
987 2 49.3643 lv 53.1822 sdCode:
1126 2 42.8778 buck 42.8778 buckCode:
1114 3 85.1523 gtr 85.1523 gtrCode:
2056 2 59.334 gtr 59.334 gtr |
Re: Offensive Power Rankings for 2008
Can we get an OPR for divisions based on overall performance instead of individual regionals?
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Re: Offensive Power Rankings for 2008
does the makes us the 14th highest scoring robot in Galileo (based on our last regional)?
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Re: Offensive Power Rankings for 2008
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DIVISION Archimedes Code:
DIVISION Curie Code:
DIVISION Galileo Code:
DIVISION Newton |
Re: Offensive Power Rankings for 2008
How about some statistics on the individual divisions like mean, median, standard deviation, and whatever else might be interesting. I'd like to throw some fuel on the best division debate by seeing how they stack up against each other in OPR.
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Re: Offensive Power Rankings for 2008
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A C G N |
Re: Offensive Power Rankings for 2008
This might be immpossible but our team wants to know the rankings for the best hyrid teams in the country..
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Re: Offensive Power Rankings for 2008
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Re: Offensive Power Rankings for 2008
I noticed some people were requesting DPR scores. While the meaning of a DPR number isn't as straightforward as OPR, I think we may be able to improve the OPR calculation by taking it into account. If a team tends to play heavy defense, the teams they play against shouldn't have their OPR reduced when they play below average. Plus I love linear algebra so this gave me an excuse to use it.
<complex math warning> So here's the equation: Code:
( M -N ) ( p ) = ( s_t )M = n x n matrix with M(ij) = # of times i played with j. M(ii) = # of times i played. (same as M from before) N = n x n matrix with N(ij) = # of times i played against j. N(ii) = 0. p = n x 1 column vector of OPRs. p(i) = OPR for team i. (same as p from before) d = n x 1 column vector of DPRs. d(i) = DPR for team i. s_t = n x 1 column vector of total scores. s_t(i) = Sum of all of team i's match scores. (same as s from before) s_o = n x 1 column vector of total opponent scores. s_o(i) = Sum of all of team i's opponents' match scores. In other words, the first n equations add all the offense played by team i's allies, subtracts all the defense played by team i's opponents, and equates that with team i's total score. The second n equations sums all the offense played by team i's opponents, subtracts all the defense played by team i's allies, and equates it with team i's opponents' total score. We can rewrite the equation as Ax = y where A = (M -N; N -M), x = (p; d), and y = (s_t; s_o). In the data set I used, there are 2 isolated sets of teams that played no matches with teams outside their set: the Israeli and non-Israeli teams. We can separate these sets and write an equation for each one, and I think it's easier if we do: Code:
A_1 * x_1 = y_1Code:
M(11)*p(1) + M(22)*p(2) + ... + M(nn)*p(n) = 1.25 * (sum(s_t) / 3)Code:
( E 0 ) ( p ) = 1.25 * (sum(s_t) / 3)Code:
A = ( M -N )</complex math warning> I ran this against the first csv Greg posted and here are the results (top 50, ordered by OPR): Code:
Team OPR DPR OPR + DPRPersonally, I don't think it tells you a whole lot to know a team's DPR. The two OPRs tell you slightly different things about a team. The old OPR tries to tell you how much a team actually scored each match. The new OPR tries to tell you how much a team could have scored each match if there was no defense. They are both potentially useful numbers. Finally, knowing both OPR and DPR does allow you to better predict the score of a match. If you define error as: Code:
error = actual_red_score - ( p(red1) + p(red2) + p(red3) - d(blue1) - d(blue2) - d(blue3) )Method #1 MSE = 245.0446, ME = 12.306 Method #2 MSE = 180.8867, ME = 10.514 So it's better at predicting past scores. Is it better at predicting future scores? I guess we'll see. |
Re: Offensive Power Rankings for 2008
Jay, this is some very inpressive Linear Algebra. This is pretty awesome!
Two thoughts: Would it be possible for you, at some point, to post all DPR rankings from the overall data set? Also, maybe something more interesting for the results, could you try and solve for which correction factor (in the arbitrarily chosen equation) makes for the lowest ME? Maybe that can make it even more vaulble of a tool. I'll also shoot you a PM with another idea I have to make OPR (and probably DPR) even more meaningful. |
Re: Offensive Power Rankings for 2008
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Thank You! |
Re: Offensive Power Rankings for 2008
Now that its all over, would anyone like to post OPR based on just matches at nationals (separately for each division). I am interested in observing how teams did at an individual regional compared to nationals.
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Re: Offensive Power Rankings for 2008
I would like to say -- I love numbers and data. I predicted the scores of all our qualification matches and ( other than the first match that had two of our robots quit ) the scores were within 10% most of the time -- very close !!! We also had the 15th highest OPR in Archimedes -- we ended up the 17th seed -- again very close. Based on the numbers, I said we would go 6-1 -- we were 5-2.
Team 1598 |
Re: Offensive Power Rankings for 2008
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We were 15th in Galileo in OPR, however, we dont have a hurdler. All of our points are in auto/laps/assists. We thought we would go 5-2, but our matches didnt go as planned so we went 3-4. I like the details of this and i really appreciate it, i have been looking for something this detailed. :) |
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