Analysis of team ranking
 

This year's game is unusual in that there is no defense and for the most part robots work on their own in parallel to score points. As a result I figured it's reasonable (even more than usual!) to try to compute the average number of points a robot contributes to its alliance. I wrote a quick python3 script that takes as input match data (tested on the DC regional, where my former team 449 is currently playing) and outputs my ranking of teams and the number of points I think they contribute to their alliance. Apologies for the variable names, but hopefully I made up for it in with the comments.

Rankings:

1 (3419, 73.704492305515487)
2 (1731, 46.312538656273205)
3 (1418, 39.472531653896525)
4 (1895, 38.799337600450862)
5 (3490, 36.294428293019763)
6 (1599, 34.28821369481841)
7 (1885, 32.629205449774474)
8 (1033, 32.348123760832848)
9 (1421, 30.478697284154272)
10 (5338, 29.040436495747031)
11 (623, 27.745489727319374)
12 (5549, 27.121269236479719)
13 (1389, 26.60584843249497)
14 (383, 23.671855927551672)
15 (4099, 22.375266604669307)
16 (449, 21.912210928023729)
17 (116, 21.449547070425396)
18 (5243, 19.808177358212305)
19 (612, 17.344396301222865)
20 (4456, 16.61331712295609)
21 (5569, 16.37413112815706)
22 (122, 15.839607260787915)
23 (2377, 15.709065445693666)
24 (3941, 14.395635096324398)
25 (614, 13.631250573400411)
26 (2537, 11.955265914302434)
27 (686, 11.401428768949312)
28 (4541, 9.7651476520334057)
29 (4242, 8.7906915069887415)
30 (5587, 8.488917324654544)
31 (2068, 8.4789566363119739)
32 (3373, 8.3192241916003127)
33 (4821, 7.4396295708618432)
34 (2186, 6.5217325036723395)
35 (3650, 6.196980101798685)
36 (2912, 5.8563204263368132)
37 (620, 5.783804197530789)
38 (53, 5.3467216070143158)
39 (4472, 4.7981247189600955)
40 (2421, 4.7603990054157492)
41 (4464, 4.6403121971023475)
42 (2964, 4.075077317496544)
43 (1123, 3.2348248124167291)
44 (1915, -0.067152495721547467)
45 (4949, -1.8884154681926013)
46 (5520, -2.1497370184179658)
47 (3748, -2.471672298659696)
48 (611, -3.0598363988393888)

Source code:

Re: Analysis of team ranking
 

It would appear you've independently discovered what is commonly called OPR :) Although it works very well this year, it can also work well in more defense-heavy years. The main breakage for OPR is exponential scoring (2007) or piece-limited scoring (2011), or when it _really_ matters how resistant you are to scoring (2009).

As a guy that once wrote a OPR scraper way back in the day, I gotta say that's a fantasticly concise implementation

Re: Analysis of team ranking
 

Additional comments:

- obviously there variance in team performance, so this won't be a perfect predictor
- these results list a couple teams as providing negative points on average -- this is fairly clearly not true. These teams probably contribute about 0 points on average. This actually gives a pretty good rough estimate of the precision of these numbers (error of ~3 should be expected on all numbers)
- if teams have strategies that involve working together in some way, this model does not account for that.
- if teams have strategies that interfere with each other (i.e. all 3 teams need to be fed at the feeding station to reach their full potential), this model does not account for that

Re: Analysis of team ranking
 

@Bongle I was actually thinking of Moneyball as I wrote this. But I actually think this game is _even better_ than baseball for such analysis because robots aren't playing dramatically different positions in these matches --> all robots have equal opportunity to score points

Re: Analysis of team ranking
 

That's not entirely true - the way the math works out, you end up solving for "the number of points added by that team being in an alliance". If a team tends to take fouls, gets in the way, blocks visibility, or breaks their alliance partners, they may end up with a negative value.

Similarly, it is possible for a team to have a positive value without ever scoring a single piece: if the team facilitates scoring in some way (good strategy, supplying parts, bringing a ramp, etc), they may still have a positive effect on the alliance's score.

Your other points about limitations are correct.

Re: Analysis of team ranking
 

Would you please run a short experiment?

Attached is a ZIP file containing Qual Match data for all 67 events in 2015 weeks 1 through 4, in the column format described in your code (I included both tab-delimited and comma-delimited).

Please run your script on that data and tell us how long it takes the script to do the computation.

Re: Analysis of team ranking
 

Note: all the data is in one big file; you only need run the script once on that file (not 67 separate runs)

Re: Analysis of team ranking
 

It runs out of memory after a few seconds computing least squares. I guess my script was too quick and dirty to handle that much data ;)

Ok, closed out of my memory-hog browser and reran it. It finished in 68 seconds. It's single threaded --> only using 1 core. I don't know the exact specs but I'm using an old laptop. If you want it to run faster you could get a reasonable estimate running the script for each regional and averaging the results for teams that competed in multiple regionals. My script basically ran instantly on the DC regional alone, it just didn't scale well.

Results:

1 (1114, 119.53710628381191)
2 (2056, 107.52392526361433)
3 (1730, 98.937520154912633)
4 (2481, 85.411141027422389)
5 (1678, 83.604692998775761)
6 (987, 81.614933990522147)
7 (118, 80.969024034928296)
8 (4488, 80.539400149979258)
9 (254, 79.885031034931174)
10 (148, 79.432991922526838)
11 (5406, 78.607729049050903)
12 (1519, 78.606114913994432)
13 (1619, 77.525461715196158)
14 (1658, 72.769643357190205)
15 (3130, 71.271318091324432)
16 (1671, 70.02262062115436)
17 (2338, 68.377599976884255)
18 (1280, 68.31086262054076)
19 (3683, 68.046518730572274)
20 (314, 67.063058451290729)
21 (4143, 66.197146406242695)
22 (2085, 65.826088138212199)
23 (1756, 65.300090499752486)
24 (225, 64.935706448058212)
25 (1538, 64.559840785724475)
26 (330, 64.541264057923442)
27 (2852, 64.483030815000632)
28 (1986, 62.974425411332938)
29 (2451, 62.637597604073804)
30 (2974, 60.564349115146001)
31 (1023, 60.560211511217332)
32 (1983, 59.916674128430934)
33 (744, 59.594728708265407)
34 (1657, 59.279400181300687)
35 (67, 58.964359968912603)
36 (2122, 58.817777660610751)
37 (2342, 57.489327516287716)
38 (1640, 57.464812178955)
39 (2826, 56.916928984985773)
40 (234, 56.858881704686439)
41 (3339, 56.533409767618949)
42 (4655, 56.39313720643888)
43 (3230, 56.122255030023631)
44 (1574, 55.625450146975965)
45 (624, 55.340768974856552)
46 (2077, 55.213700500454443)
47 (525, 55.123176093827624)
48 (2783, 54.867531033295869)
49 (303, 54.677252325474406)
50 (2512, 54.663228166283453)
51 (1156, 53.95917064433668)
52 (701, 53.489926552157726)
53 (135, 53.310632416341505)
54 (3824, 52.981920713390842)
55 (4678, 52.90258841628895)
56 (2137, 52.82827564039772)
57 (1806, 52.545135953520244)
58 (4201, 52.100455606412289)
59 (4967, 51.976661185189229)
60 (58, 51.708557689346009)
61 (1569, 50.999721751403754)
62 (2587, 50.879055731499093)
63 (3663, 50.352150843306362)
64 (3360, 50.32364073573774)
65 (70, 50.212423608681007)
66 (456, 49.514397347218271)
67 (226, 49.421619066877071)
68 (3419, 49.291886530691805)
69 (4613, 49.182337568239383)
70 (2383, 48.952668799007341)
71 (4451, 48.461565771037783)
72 (4039, 48.428887067643302)
73 (60, 48.304027027456911)
74 (3452, 48.237009235381947)
75 (694, 48.146194119499853)
76 (2643, 47.617699872486028)
77 (85, 47.524384916070105)
78 (1403, 47.469950277471035)
79 (494, 47.374147160288466)
80 (1918, 47.291935686802972)
81 (287, 47.257974979802917)
82 (2386, 46.953430407180903)
83 (203, 46.861955923046182)
84 (1024, 46.697459369030227)
85 (876, 46.137245094936418)
86 (3646, 46.13325578237896)
87 (340, 46.084590782880028)
88 (3132, 45.713812619738299)
89 (4564, 45.704005687502573)
90 (71, 45.592449645849975)
91 (2337, 45.302005071186898)
92 (3200, 45.067571065424303)
93 (379, 44.960948960140477)
94 (2054, 44.735136796993629)
95 (1208, 44.698482053595882)
96 (78, 44.46540330346042)
97 (2767, 44.397595621836118)
98 (1676, 44.241945432579165)
99 (2231, 44.074739609953014)
100 (1876, 44.059135373758906)
101 (5188, 44.006924999206518)
102 (33, 43.991463573919681)
103 (662, 43.937410242633831)
104 (107, 43.844215107033079)
105 (2883, 43.838433292634448)
106 (126, 43.680710097846031)
107 (4522, 43.658797513513953)
108 (125, 43.554274627035511)
109 (4539, 43.541714417941485)
110 (2457, 43.313197516131233)
111 (1768, 43.202978983685014)
112 (2062, 42.91184275827608)
113 (3996, 42.878462653349217)
114 (1218, 42.221423588184592)
115 (4947, 42.21385679919382)
116 (4028, 42.184039856147834)
117 (4003, 42.058582095894693)
118 (230, 41.974917059019731)
119 (610, 41.906402824077851)
120 (2607, 41.670540732672599)
121 (4917, 41.384462943129392)
122 (3688, 41.147751248112812)
123 (3930, 41.033422854244797)
124 (1493, 40.986924808173157)
125 (4500, 40.741418876306227)
126 (4118, 40.695131685614619)
127 (971, 40.523141542947506)
128 (3238, 40.466262103026601)
129 (359, 40.422448697174524)
130 (61, 40.330053037398599)
131 (3418, 40.150604856512359)
132 (48, 40.137305510265087)
133 (2996, 40.028508239671567)
134 (2619, 39.968708976433774)
135 (5030, 39.877431370188553)
136 (263, 39.839439286180657)
137 (4048, 39.825826430840849)
138 (1296, 39.808174436676225)
139 (56, 39.662074105094518)
140 (4049, 39.655310597148734)
141 (4946, 39.601027916048579)
142 (3604, 39.539475208943301)
143 (348, 39.481859806964366)
144 (1318, 39.370452934396013)
145 (3467, 39.295360485121932)
146 (4911, 39.224358414364175)
147 (3616, 39.110279455887301)
148 (5618, 39.086526813133673)
149 (2635, 38.980266823053611)
150 (2930, 38.840601375514616)
151 (3374, 38.81788764505211)
152 (4256, 38.784719563512631)
153 (973, 38.463844062433054)
154 (51, 38.334314781676767)
155 (384, 38.201138768628411)
156 (2590, 38.147515826742477)
157 (4096, 38.116308218237869)
158 (4623, 38.092545615566564)
159 (4952, 37.86114845595975)
160 (133, 37.828067879761136)
161 (1718, 37.787600674391747)
162 (2474, 37.692730385543939)
163 (3743, 37.59312775479782)
164 (1816, 37.542280174166791)
165 (2410, 37.496877654564656)
166 (1501, 37.104342080915757)
167 (3620, 37.037606938363133)
168 (5122, 36.982541576210828)
169 (4481, 36.865262298598083)
170 (3937, 36.841636721001414)
171 (1647, 36.751313815118657)
172 (3284, 36.74635714111696)
173 (1310, 36.716915159692995)
174 (3711, 36.708942403153074)
175 (2168, 36.657044244067841)
176 (219, 36.622331677278126)
177 (4618, 36.592685886997145)
178 (4009, 36.541388801745121)
179 (179, 36.46999930280974)
180 (192, 36.428357257530422)
181 (1511, 36.412379877666389)
182 (2468, 36.411558461182182)
183 (1466, 36.410653763267597)
184 (176, 36.341368086411364)
185 (3954, 36.106465544323413)
186 (236, 36.030241466107022)
187 (1065, 35.866091693146807)
188 (217, 35.739433335936802)
189 (293, 35.714822450042767)
190 (3171, 35.700953362598391)
191 (4450, 35.675245209103132)
192 (3478, 35.497911882995631)
193 (1025, 35.33059600491984)
194 (2067, 35.302384982157086)
195 (858, 35.220534346307758)
196 (20, 35.213858881906404)
197 (3787, 35.200316831586413)
198 (3245, 35.154820267538746)
199 (3947, 34.936457120925624)
200 (5124, 34.900427199797058)
201 (1690, 34.843920361381095)
202 (2605, 34.842650608275285)
203 (469, 34.826502670309935)
204 (88, 34.781860065335088)
205 (4471, 34.776523328229906)
206 (3055, 34.772009951076569)
207 (1629, 34.734579749225233)
208 (492, 34.62041348642861)
209 (4859, 34.584359681765029)
210 (2470, 34.584346687341977)
211 (188, 34.462145048031729)
212 (5155, 34.435692705316441)
213 (2522, 34.35816391473486)
214 (34, 34.173866945917425)
215 (5415, 34.146785509913705)
216 (1502, 34.067087880802461)
217 (4001, 34.064597422588839)
218 (4055, 33.916169496312733)
219 (1094, 33.883434363608139)
220 (1523, 33.871609512708311)
221 (5479, 33.849391237999257)
222 (3528, 33.828080185259267)
223 (5069, 33.77734334023711)
224 (3574, 33.690314713091702)
225 (1572, 33.650008671190953)
226 (2170, 33.575593261620348)
227 (3015, 33.547013037090167)
228 (3959, 33.523300871264311)
229 (3044, 33.406171382153723)
230 (904, 33.342751678172135)
231 (846, 33.327700541596251)
232 (4377, 33.305432679592052)
233 (670, 33.259397175471463)
234 (3309, 33.247368517097016)
235 (5753, 33.236142903316946)
236 (2169, 33.094046510981954)
237 (5492, 33.046067910839866)
238 (4061, 33.01891123496646)
239 (280, 32.985235881445348)
240 (1937, 32.945294053227798)
241 (4330, 32.895140642192821)
242 (2959, 32.807809147273616)
243 (4381, 32.793946338233482)
244 (245, 32.711707797251968)
245 (292, 32.579249817782227)
246 (4914, 32.53912196307197)
247 (246, 32.470985984479007)
248 (2471, 32.404626971136231)
249 (4646, 32.384273327934203)
250 (1225, 32.374217436032403)
251 (1261, 32.345344589914419)
252 (3618, 32.319420811573949)
253 (706, 32.087559612208366)
254 (2489, 32.080162945238371)
255 (5674, 32.068028144346975)
256 (365, 32.063866801911502)
257 (2550, 31.968333087158392)
258 (2907, 31.963996692538135)
259 (4543, 31.937642440156992)
260 (2344, 31.883372165807916)
261 (5172, 31.746782970946477)
262 (3968, 31.738032978366853)
263 (4004, 31.660944083506916)
264 (5603, 31.656178443794023)
265 (3547, 31.624098353856535)
266 (27, 31.615954801848815)
267 (5511, 31.59945800797674)
268 (4485, 31.588001091120738)
269 (1595, 31.558596969881869)
270 (3539, 31.556723877535198)
271 (2478, 31.435819566154908)
272 (3039, 31.41599321476928)
273 (447, 31.408100879172181)
274 (3955, 31.397208810781596)
275 (2040, 31.396818339564696)
276 (4384, 31.36827170756532)
277 (5112, 31.338720289318339)
278 (1712, 31.225301368796138)
279 (1763, 31.219614687869981)
280 (1319, 31.027832060889921)
281 (5053, 31.026096768004098)
282 (316, 31.004945681413208)
283 (195, 31.002772387355328)
284 (138, 30.978073568382566)
285 (5502, 30.96655526350947)
286 (1477, 30.854716412418391)
287 (5776, 30.833279403898562)
288 (45, 30.771497026266104)
289 (3588, 30.730249883028147)
290 (222, 30.661345061396982)
291 (2081, 30.585445374235022)
292 (5554, 30.579978307945261)
293 (1720, 30.573435485801873)
294 (4624, 30.501204083289633)
295 (4498, 30.421878762510477)
296 (2526, 30.412593900599504)
297 (5758, 30.403677283741686)
298 (3003, 30.289741529784614)
299 (383, 30.274427792634622)
300 (1723, 30.218861857075929)
301 (811, 30.192776246588522)
302 (342, 30.168485860212456)
303 (4189, 30.13965943188408)
304 (171, 30.111080057728859)
305 (1885, 30.08157855417863)
306 (3501, 30.056119432123456)
307 (885, 30.042265795522237)
308 (4325, 29.978999286032156)
309 (3612, 29.972457662016737)
310 (433, 29.965135411743013)
311 (343, 29.815721870600417)
312 (4550, 29.783543177508189)
313 (5735, 29.760366282137795)
314 (3451, 29.623168415939425)
315 (193, 29.597381522938797)
316 (1665, 29.477226112588852)
317 (5038, 29.371603785511478)
318 (5013, 29.367568082295421)
319 (1577, 29.351057855544511)
320 (1522, 29.329602508326648)
321 (3623, 29.319629407542678)
322 (3944, 29.165672846015873)
323 (5254, 29.152950147461201)
324 (3570, 29.146301900278111)
325 (308, 29.108891367260316)
326 (2867, 29.07047844203802)
327 (4905, 29.050359447749955)
328 (4103, 29.008081199277097)
329 (93, 29.002439064178919)
330 (269, 28.990050531142835)
331 (3357, 28.987813199246801)
332 (4906, 28.987217737312413)
333 (1492, 28.931717575968353)
334 (1735, 28.843015541771116)
335 (5442, 28.724169408312502)
336 (3336, 28.712610544003628)
337 (5413, 28.696880079236056)
338 (4364, 28.611574275852828)
339 (1775, 28.584899036665753)
340 (3065, 28.525796636906136)
341 (2612, 28.469954244499142)
342 (2052, 28.430475381231936)
343 (157, 28.411865437907171)
344 (4586, 28.402948306541667)
345 (418, 28.385761801791819)
346 (1706, 28.370790285515668)
347 (538, 28.361433414481329)
348 (166, 28.36103280869056)
349 (2834, 28.349114945963684)
350 (862, 28.341719529492536)
351 (339, 28.312336861693979)
352 (2501, 28.291988136942045)
353 (5332, 28.221843780634114)
354 (3546, 28.219951278962149)
355 (1089, 28.179779922305691)
356 (74, 28.170630647060285)
357 (16, 28.153537909491376)
358 (3970, 28.068452679409923)
359 (2016, 28.054055944982938)
360 (4909, 28.046294197793365)
361 (1732, 28.004259847789143)
362 (5722, 28.000893562008127)
363 (5470, 27.964602396088338)
364 (4505, 27.957193742959475)
365 (1507, 27.918932823151927)
366 (2609, 27.881283715612394)
367 (3735, 27.842927062337381)
368 (1325, 27.83399855612867)
369 (2771, 27.805249600837143)
370 (3234, 27.777086187904139)
371 (364, 27.773516882454661)
372 (1287, 27.695541678956054)
373 (868, 27.686820418135625)
374 (4343, 27.674281064913401)
375 (1099, 27.628699640049589)
376 (4991, 27.614565128957356)
377 (4681, 27.606551378589774)
378 (2655, 27.585967703038538)
379 (967, 27.543757884969985)
380 (1209, 27.49029315446089)
381 (2075, 27.489002477372793)
382 (4546, 27.487066617423164)
383 (3635, 27.48356561968173)
384 (3250, 27.477190342232095)
385 (2506, 27.464706103391794)
386 (2228, 27.460322730350228)
387 (5638, 27.427765735683632)
388 (4499, 27.40789367631136)
389 (1421, 27.404206618353694)
390 (1592, 27.386817099943038)
391 (3260, 27.365005454713454)
392 (854, 27.359701627787871)
393 (488, 27.357071384709442)
394 (283, 27.340562809508832)
395 (4196, 27.251498552372244)
396 (4075, 27.247775472572336)
397 (3883, 27.212920975158571)
398 (5031, 27.198910831670158)
399 (3166, 27.196904723704534)
400 (1737, 27.169193486402385)
401 (5533, 27.158765140173511)
402 (4179, 27.121111391478998)
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67.87user 0.10system 1:08.05elapsed 99%CPU (0avgtext+0avgdata 399012maxresident)k
0inputs+0outputs (0major+53269minor)pagefaults 0swaps

Re: Analysis of team ranking
 

so is this just if all teams were at the DC regional based on their score?

It would put us in the top 30% of teams...

Re: Analysis of team ranking
 

Try this instead:

1) compute N = A^T∙A

2) compute d = A^T∙b

3) compute teamscores = scipy.linalg.cho_solve(scipy.linalg.cho_factor(N), d)

... where A is np.array(matchdata) and b is np.array(matchscores)

The computation time should be reduced from 68 seconds to about 2 seconds or less.

Re: Analysis of team ranking
 

No, not quite, this is a slightly different computation. I'm trying to answer the question "how much value does each robot contribute to its alliance?"

In most (qualification) matches robots operate reasonably independently from one another. This makes my question a lot easier to answer -- if robots don't influence each other's performance, then each robot should contribute (on average) the same score to any alliance it plays with. So I've got one variable per team -- how many points it contributes to its alliance -- and I'm trying to solve for the set of values for these variables that comes closest to predicting the actual match scores.

The listing above is my estimate of how many points each robot contributes to its alliance (given no interaction with other robots)

Re: Analysis of team ranking
 

I understand that, then this just means that the teams at the DC regional were skewed, or something else?

Re: Analysis of team ranking
 

I haven't done any in-depth analysis, but DC doesn't look too far out of line from the set of all regionals.

@MikLast I think I misinterpreted what you were saying. This would be a reasonable estimate of how well teams would do if each team played this game without an alliance. So congrats if you team is in the top 30%, you have a good robot :)

Re: Analysis of team ranking
 

Ah, i misunderstood you also then. Thank you for clarifying, and i cant wait to show my team this next week.

Re: Analysis of team ranking
 

I'd run this test myself but I have Python2.7.5 installed and your Python3 code crashes when I try to run it. Not being very fluent in Python, I'm not in a good position to try to port it.

Based on some testing I did here, I'm fairly confident that your computation time can be dramatically reduced by making the small changes shown above.