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Unread 24-12-2013, 13:49
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Re: paper: How Accurate is OPR?
How did you validate the accuracy of your scouting data? Why did you choose to use percent error, rather then absolute error?

A few more things that would be interesting to look at:

Do the results change if you only look at the top 24 or 30 teams at an event (the teams you would be considering when forming a pick list)?
Is there an OPR at which it becomes more accurate? Looking at chart 13, OPRs above 15 seem much better then those below 15 (obviously game dependent).
Can you quantify the percent chance that Team A is better then Team B, given a specific OPR difference (IE, Team A has an OPR that is 1 higher then Team B, and has a 55% chance of being better then Team B, but Team C has an OPR that is 10 higher then Team B, and has a 90% chance of being better then Team B.
Does the percent error histogram still look normal if you discard the outliers and put more bins between -100% and +200%?
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Unread 25-12-2013, 04:52
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Re: paper: How Accurate is OPR?
Quote:
Originally Posted by Joe Ross View Post
How did you validate the accuracy of your scouting data? Why did you choose to use percent error, rather then absolute error?

A few more things that would be interesting to look at:

Do the results change if you only look at the top 24 or 30 teams at an event (the teams you would be considering when forming a pick list)?
Is there an OPR at which it becomes more accurate? Looking at chart 13, OPRs above 15 seem much better then those below 15 (obviously game dependent).
Can you quantify the percent chance that Team A is better then Team B, given a specific OPR difference (IE, Team A has an OPR that is 1 higher then Team B, and has a 55% chance of being better then Team B, but Team C has an OPR that is 10 higher then Team B, and has a 90% chance of being better then Team B.
Does the percent error histogram still look normal if you discard the outliers and put more bins between -100% and +200%?
These are all good things to think about. Particularly, you may want to reconsider your use of percent error as opposed to absolute error. I'm estimating here, but it looks like absolute error would've been pretty consistent regardless of true scoring. Take a look at the correlation of those; I'd bet very little of the variation in absolute error is explained by variation in true scoring average.

If there were such a correlation, you would have noticed it in the residual plot for your OPR-True Average linear regression. I didn't notice a residual plot in your pdf; they are essential for determining if your model is a good fit for the data.
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Unread 25-12-2013, 10:17
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Re: paper: How Accurate is OPR?
Merry Christmas!

Quote:
Originally Posted by Joe Ross View Post
How did you validate the accuracy of your scouting data?
At our events, we scouted collaboratively with other teams. Accuracy actually became a prime concern of ours, so we had every entry into our scouting database checked over by our head scout before entry (who had been watching each match as a whole immediately before validating). Additionally, we recorded matches for further verification. There were a few instances I can recall where errors were detected in entries, and we used our footage to re-scout that robot for that match.

Quote:
Originally Posted by Joe Ross View Post
Why did you choose to use percent error, rather then absolute error?
This was an attempt to make the results of our paper more applicable to other events in the 2013 season. Archimedes, for instance, is hardly indicative of the average regional or district event, and yet it forms more than half of our data (51%, to be precise; out of 196 event/team combinations sampled, 100 were from Archimedes).

Quote:
Originally Posted by Joe Ross View Post
Do the results change if you only look at the top 24 or 30 teams at an event (the teams you would be considering when forming a pick list)?
Is there an OPR at which it becomes more accurate? Looking at chart 13, OPRs above 15 seem much better then those below 15 (obviously game dependent).
Can you quantify the percent chance that Team A is better then Team B, given a specific OPR difference (IE, Team A has an OPR that is 1 higher then Team B, and has a 55% chance of being better then Team B, but Team C has an OPR that is 10 higher then Team B, and has a 90% chance of being better then Team B.
Does the percent error histogram still look normal if you discard the outliers and put more bins between -100% and +200%?
Let me get back to you on answering your questions backed up with relevant diagrams and calculations. I'd also like to look at posting our dataset too. However, here are my suspicions:
  • If you see my response Basel A's question below, sampling only the top 30 or so teams from each of our competitions should decrease the percent error, which would change the percent/tolerance table for the better. OPR should become more accurate.
  • I have no idea. Really intriguing question, though.
  • Since we do have the averages and standard deviations for each team, you could let Team A and B be represented by a variable with mu equal to their Average Score and sigma equal to the Standard Deviation in their score. If you subtract the two means and add the two variances, you should be able to find the number you're looking for by integrating from -infinity to 0 and 0 to infinity. We used this method to predict match outcomes, but it was not very accurate. I don't know of a simple way to extend that to OPR, though.
  • I'll get back to you.

Quote:
Originally Posted by Basel A View Post
These are all good things to think about. Particularly, you may want to reconsider your use of percent error as opposed to absolute error. I'm estimating here, but it looks like absolute error would've been pretty consistent regardless of true scoring. Take a look at the correlation of those; I'd bet very little of the variation in absolute error is explained by variation in true scoring average.
If you look at the scatterplot on slide 9 and compare the least squares line to the scatterplot, you'll see that absolute error decreases as Average Points Scored increases (I did have a residuals plot in here previously, but it looks like I accidentally removed it before I posted it). The percent error decreasing as Average Points Scored is not simply a function of the denominator for the percent error calculation increasing.

Quote:
Originally Posted by Basel A View Post
If there were such a correlation, you would have noticed it in the residual plot for your OPR-True Average linear regression. I didn't notice a residual plot in your pdf; they are essential for determining if your model is a good fit for the data.
I did do a residual plot, and include it previously; it must have been accidentally removed during my revising. I'll make sure to fix that to back up my previous claim (see answer to previous question).
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Unread 25-12-2013, 14:40
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Re: paper: How Accurate is OPR?
This thread combined with watching Searching for Bobby Fischer earlier today got me wondering how to apply the Elo Rating to FRC, and I think I figured it out. This is the resulting data from the 7 weeks of the 2013 season (Sorted by rating)

Code:
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3476	1378.71704051128
3467	1379.54358188031
126	1379.84588415544
2338	1380.43126000358
2791	1382.09428901178
1100	1382.64122144869
314	1382.8554922159
829	1383.22071156896
4451	1384.11517670854
2175	1384.61874933083
56	1384.93968203593
341	1385.08158247164
2603	1385.80080979714
231	1386.17096589986
2471	1389.03263285554
3753	1389.7795386336
3528	1390.42129382422
1726	1391.34011980841
4320	1391.45977062742
180	1394.47026900317
1507	1394.64499137941
4063	1395.08467436553
1288	1395.70911133172
612	1395.85243701734
1189	1396.62170664524
2638	1396.62681692185
155	1399.22392827322
1732	1400.31444752705
1625	1402.01624571653
2443	1403.01972826776
1985	1404.12577305486
2168	1404.41889197264
1939	1405.96727989276
303	1406.16077030994
3284	1406.6318958928
193	1406.77092695414
1421	1407.41709440476
111	1408.88959428744
955	1409.03965448902
4265	1409.9440029336
2851	1413.39692792868
192	1417.5072147051
103	1417.85861528435
3173	1418.08718577889
2826	1421.62238697863
2130	1422.00380603616
967	1423.83644700277
3824	1424.4877607948
293	1424.65111902078
3847	1428.17346094668
3990	1428.71918123344
222	1429.32173263643
624	1429.93955210178
329	1433.19542652553
2000	1433.42748392377
435	1435.72257537983
573	1435.76564950198
1676	1436.66179872081
2145	1438.26225072112
1918	1438.35183688243
3414	1441.73203874618
2512	1443.91869270898
360	1444.28343940142
2052	1445.68913015397
3928	1446.03315620176
125	1448.82568950045
3015	1450.51613073011
225	1453.00217390966
379	1453.75327305984
234	1455.65184105526
3539	1455.78157632052
3245	1459.87672441115
79	1464.71268563065
3314	1465.75815012018
2959	1467.68723662095
316	1470.69220506702
525	1471.31100927972
2648	1473.77307045129
1806	1477.55496241367
1519	1481.06920018518
948	1483.54675958234
987	1484.17839583617
2485	1484.49503422745
254	1485.66484858734
973	1485.94027814882
2729	1491.57552945501
2054	1508.534964774
701	1510.12548469239
1538	1510.20015629137
610	1516.28684596015
2169	1518.27635745321
148	1519.20474272572
1717	1523.36578325197
1983	1540.37859616682
245	1541.67918480531
862	1541.69744273021
1334	1549.90012172128
20	1556.33980046564
2590	1563.59789520569
868	1565.15790036299
67	1587.83178342892
1718	1602.55543781965
11	1625.84868762694
118	1655.58062776287
1114	1659.4593538914
33	1663.08681001952
359	1693.81098547929
1986	1696.82704216305
1477	1699.43206031541
2056	1709.75985745116
469	1860.09151515805

Sorted by Team #:
Code:
1	1222.5778695651
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11	1625.84868762694
16	1245.52529618795
20	1556.33980046564
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41	1104.07730737463
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73	1090.40285198676
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88	1129.70767705192
93	1199.4419062263
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100	1249.68102745789
101	1228.69464711865
102	1151.60310041278
103	1417.85861528435
107	1211.6672787567
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116	1281.12571876167
117	1126.09098497072
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166	1126.50389158326
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319	1108.3199317638
321	1007.93578705957
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353	1292.78195757421
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369	1165.46437641944
371	1103.49120376432
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4849	1096.67558771439
4850	1214.51286765616
4851	1132.70232544743
4852	1173.6052343879
4853	1169.5893564853
4854	1126.19486187291
4855	1241.04231318184
4856	1101.63239304157
4859	1140.91825536466
Here's the Perl script I used. It takes a standard input file of a match number (just sequential is fine), red teams, blue teams, ("RED"|"BLUE"|"TIE") (referring to who won.
Code:
#!/usr/bin/perl

my %rating = ();

my @data = <STDIN>;
my $K = 32;
my $defaultElo = 1200;


# Just make sure a team number and default value of 1200 exists for each hash. 
foreach(@data) {
	my ($match, $red1, $red2, $red3, $blue1, $blue2, $blue3, $res) = split;
	
	if (! exists $rating{$red1}) {
		$rating{$red1} = $defaultElo
	}
	if (! exists $rating{$red2}) {
		$rating{$red2} = $defaultElo
	}
	if (! exists $rating{$red3}) {
		$rating{$red3} = $defaultElo
	}
	if (! exists $rating{$blue1}) {
		$rating{$blue1} = $defaultElo
	}
	if (! exists $rating{$blue2}) {
		$rating{$blue2} = $defaultElo
	}
	if (! exists $rating{$blue3}) {
		$rating{$blue3} = $defaultElo
	}
}

foreach (@data) {
	my ($match, $red1, $red2, $red3, $blue1, $blue2, $blue3, $res) = split;
	
	my $Ered = 1 / (1 + 10**((($rating{$blue1}+$rating{$blue2}+$rating{$blue3})/3-($rating{$red1}+$rating{$red2}+$rating{$red3})/3)/400));
	my $Eblue = 1 / (1 + 10**((($rating{$red1}+$rating{$red2}+$rating{$red3})/3-($rating{$blue1}+$rating{$blue2}+$rating{$blue3})/3)/400));
	
	if ($res eq 'RED') {
		$rating{$red1} = $rating{$red1} + $K*(1 - $Ered);
		$rating{$red2} = $rating{$red2} + $K*(1 - $Ered);
		$rating{$red3} = $rating{$red3} + $K*(1 - $Ered);
		
		$rating{$blue1} = $rating{$blue1} + $K*(0 - $Eblue);
		$rating{$blue2} = $rating{$blue2} + $K*(0 - $Eblue);
		$rating{$blue3} = $rating{$blue3} + $K*(0 - $Eblue);
	}
	if ($res eq 'BLUE') {
		$rating{$red1} = $rating{$red1} + $K*(0 - $Ered);
		$rating{$red2} = $rating{$red2} + $K*(0 - $Ered);
		$rating{$red3} = $rating{$red3} + $K*(0 - $Ered);
		
		$rating{$blue1} = $rating{$blue1} + $K*(1 - $Eblue);
		$rating{$blue2} = $rating{$blue2} + $K*(1 - $Eblue);
		$rating{$blue3} = $rating{$blue3} + $K*(1 - $Eblue);
	}
	if ($res eq 'TIE') {
		$rating{$red1} = $rating{$red1} + $K*(0.5 - $Ered);
		$rating{$red2} = $rating{$red2} + $K*(0.5 - $Ered);
		$rating{$red3} = $rating{$red3} + $K*(0.5 - $Ered);
		
		$rating{$blue1} = $rating{$blue1} + $K*(0.5 - $Eblue);
		$rating{$blue2} = $rating{$blue2} + $K*(0.5 - $Eblue);
		$rating{$blue3} = $rating{$blue3} + $K*(0.5 - $Eblue);
	}
}

while(($key, $value) = each(%rating)) {
	print $key . "\t" . $value . "\n";
}
Not sure how useful the Elo ratings are, but there is some statistical significance with having teams like 469, 67, 1114 and 2056 near the top. I'm nowhere near good enough with statistics to determine if this is enough data to work with (my instinct says no), but it's just another interesting way to look at wins/losses

(Edit: Had mistake in my calculation)
Last edited by Michael Hill : 25-12-2013 at 14:50.
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Unread 26-12-2013, 12:19
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Re: paper: How Accurate is OPR?
I've added the dataset used for these calculations to the paper. Feel free to use it to do any more analysis that you'd like.

Now, to answer specific questions:

Quote:
Originally Posted by Joe Ross View Post
Do the results change if you only look at the top 24 or 30 teams at an event (the teams you would be considering when forming a pick list)?
Yes. By selecting the top 30 teams (in terms of Average Score), the least squares line becomes
Code:
y = 1.0486x - 0.7729
with an R^2 of 87.32%. The model actually moves further away away from the line we're expecting (y = x) when compared with the overall combined model, though it has a much higher R^2 value (a change of 7.02%).

In terms of the percent error model, the new mu is 1.11% with a sigma of 45.10%. The new table for the probability a team will fall within a given percent error is as follows:

Code:
10%	17.543%
20%	34.248%
30%	49.396%
40%	62.475%
50%	73.230%
60%	81.649%
70%	87.927%
80%	92.383%
90%	95.396%
100%	97.336%
110%	98.525%
120%	99.219%
130%	99.605%
140%	99.809%
150%	99.912%
160%	99.961%
170%	99.984%
180%	99.993%
190%	99.997%
200%	99.999%
Quote:
Originally Posted by Joe Ross View Post
Is there an OPR at which it becomes more accurate? Looking at chart 13, OPRs above 15 seem much better then those below 15 (obviously game dependent).
Here's a table of the different averages and standard deviations for OPRs greater than or equal to the OPR listed. I see large increases in standard deviation from 10 to 20 (as you observed), and from 30 to 40.

Code:
OPR	mu	sigma
80	6.88%	15.60%
70	13.02%	13.92%
60	12.57%	21.20%
50	18.15%	25.74%
40	20.00%	25.31%
30	23.33%	55.35%
20	20.56%	51.77%
10	24.36%	92.58%
0	20.76%	100.66%
-10	3.08%	131.97%
Quote:
Originally Posted by Joe Ross View Post
Can you quantify the percent chance that Team A is better then Team B, given a specific OPR difference (IE, Team A has an OPR that is 1 higher then Team B, and has a 55% chance of being better then Team B, but Team C has an OPR that is 10 higher then Team B, and has a 90% chance of being better then Team B.
This table has the mu and sigma for all teams within the OPR bin.

Code:
OPR	mu	sigma
80	6.88%	13.51%
70	17.12%	11.27%
60	12.12%	26.05%
50	26.12%	29.06%
40	24.18%	23.79%
30	28.43%	81.58%
20	13.57%	40.66%
10	36.60%	165.01%
0	4.63%	129.47%
-10	-287.83%	216.42%
Let Team A be represented by a Normal model with mu OPR, and sigma equal to the sigma in the table above multiplied by the team's OPR. Follow the same pattern for Team B. Subtract the two normal models (subtract the two averages; A-B, and add the variances to find the new sigma). Integrate underneath this curve from 0 to infinity to find the probability A would score more than B.

This is a method to approximate a prediction strategy I detailed in this post: http://www.chiefdelphi.com/forums/sh...23&postcount=1

Quote:
Originally Posted by Joe Ross View Post
Does the percent error histogram still look normal if you discard the outliers and put more bins between -100% and +200%?
Yes. https://drive.google.com/file/d/0B4t...it?usp=sharing

Quote:
Originally Posted by Basel A View Post
If there were such a correlation, you would have noticed it in the residual plot for your OPR-True Average linear regression. I didn't notice a residual plot in your pdf; they are essential for determining if your model is a good fit for the data.
We're not creating a model for the data we have, which is why I removed it; this wasn't about creating a regression that was supposed to model the data. Instead, this was about checking one of the properties of OPR: ideally, it should have a 100% correlation with True Average score, with an intercept of 0 and slope of 1.

That being said, here's links to the residual plots:

As a function of OPR:
https://drive.google.com/file/d/0B4t...it?usp=sharing

As a function of True Average Score:
https://drive.google.com/file/d/0B4t...it?usp=sharing

Quote:
Originally Posted by Michael Hill View Post
This thread combined with watching Searching for Bobby Fischer earlier today got me wondering how to apply the Elo Rating to FRC, and I think I figured it out. This is the resulting data from the 7 weeks of the 2013 season (Sorted by rating)

Not sure how useful the Elo ratings are, but there is some statistical significance with having teams like 469, 67, 1114 and 2056 near the top. I'm nowhere near good enough with statistics to determine if this is enough data to work with (my instinct says no), but it's just another interesting way to look at wins/losses
Elo predictions of matches on Saturday, based on the previous day's matches for Archimedes were around 65-80% accurate, if memory serves.

It was more accurate than the method we used where a team was represented by a normal model with mu equal to true mu and sigma equal to true sigma, and integrating underneath to find the chance for each alliance to win. See thread here: http://www.chiefdelphi.com/forums/sh...23&postcount=1
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Re: paper: How Accurate is OPR?
Quote:
Originally Posted by brennonbrimhall View Post
I've added the dataset used for these calculations to the paper. Feel free to use it to do any more analysis that you'd like.
How hard would it be to add the team number and event to the dataset?
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Re: paper: How Accurate is OPR?
Quote:
Originally Posted by Joe Ross View Post
How hard would it be to add the team number and event to the dataset?
Not hard at all.

I removed team numbers and events intentionally for team anonymity/confidentiality concerns. None of the teams used in the study granted any sort of permission for having statistics published about them on Chief Delphi, and it's not like True Average Score can be derived from other, public sources information. It was kind of like publishing the FRC equivalent of how much someone weighs without prior permission. It just didn't feel right.
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