
Originally Posted by
Robert-Y
What about the densest rounds sorted by average distance in percentage?
I thought about that but didn't see an easy enough way to do that. For average absolute difference I can use the simple formula (worst-best)/(persons-1), ignoring all times between best and worst because they don't affect the average absolute difference (worthy of a proof if you have a minute). For average relative difference, that doesn't work, as the middle ones do matter (worthy of a proof if you have another minute). And I'm also not sure how to properly average it and whether this is really what I want.
So, well, let's pretend the middle ones are "evenly spaced" so that all pairs of adjacent ones are the same factor x apart, then
worst = best * x^(persons-1) and thus x = (persons-1)th root of worst/best
See below for results.
Or maybe someone with better math knowledge has a better definition of densest in relative terms? Large gaps would make the round look much less dense, but they would go unnoticed with this definition of mine. I'd like something that rewards both for small factors and for similar factors.
Code:
select competitionId, eventId, roundId, best, worst, round(power(worst/best,1/(persons-1)),4) avgFactor, persons from
(select competitionId, eventId, roundId, min(if(average>0,round(average/100,2),999999999)) best, max(if(average>0,round(average/100,2),999999999)) worst, count(*) persons
from Results
where roundId in ('f','c')
group by competitionId, eventId, roundId) helper
where persons>1 and worst<999999999
order by power(worst/best,1/(persons-1)), persons desc
limit 100;
+----------------------------+---------+---------+--------+--------+-----------+---------+
| competitionId | eventId | roundId | best | worst | avgFactor | persons |
+----------------------------+---------+---------+--------+--------+-----------+---------+
| CubeCanadaDay2011 | mmagic | f | 6.92 | 7.01 | 1.0130 | 2 |
| OGU2006 | sq1 | f | 46.45 | 47.14 | 1.0149 | 2 |
| IVBogota2012 | 444 | f | 54.97 | 57.76 | 1.0166 | 4 |
| WC2009 | 333 | f | 10.74 | 13.81 | 1.0169 | 16 |
| Euro2010 | 333 | f | 10.31 | 12.68 | 1.0174 | 13 |
| AachenSummer2012 | 333 | f | 9.68 | 18.78 | 1.0176 | 39 |
| HungarianOpen2009 | 555 | f | 91.49 | 119.00 | 1.0177 | 16 |
| TaipeiOpen2011 | 444 | f | 44.28 | 89.79 | 1.0178 | 41 |
| Euro2010 | 555 | f | 77.60 | 99.54 | 1.0179 | 15 |
| Euro2006 | 333 | f | 14.97 | 19.55 | 1.0180 | 16 |
| SuzhouOpen2011 | 333 | f | 11.97 | 14.59 | 1.0182 | 12 |
| MunichOpen2011 | 444 | f | 49.10 | 60.26 | 1.0188 | 12 |
| WC2007 | 333 | f | 12.46 | 16.51 | 1.0189 | 16 |
| BeijingSummer2011 | 333 | f | 12.60 | 15.80 | 1.0190 | 13 |
| HungarianOpen2009 | 444 | f | 51.57 | 68.99 | 1.0196 | 16 |
| Vastervik2008 | mmagic | f | 5.10 | 5.20 | 1.0196 | 2 |
| WC2003 | 333 | f | 20.00 | 22.92 | 1.0197 | 8 |
| WC2005 | 333 | f | 15.10 | 18.71 | 1.0197 | 12 |
| WC2009 | 555 | f | 78.20 | 104.80 | 1.0197 | 16 |
| Euro2010 | 333oh | f | 18.39 | 24.17 | 1.0197 | 15 |
| TaiwanSummerOpen2009 | 333 | f | 13.30 | 16.49 | 1.0197 | 12 |
| GuangdongOpen2009 | 333 | f | 11.83 | 20.57 | 1.0200 | 29 |
| RizalOpen2009 | 444 | f | 69.49 | 83.27 | 1.0203 | 10 |
| KansaiOpen2012 | 333 | f | 11.19 | 13.98 | 1.0204 | 12 |
| ThailandOpen2009 | 333 | f | 12.72 | 18.72 | 1.0205 | 20 |
| PhilippinesOpen2008 | 333 | f | 14.94 | 21.99 | 1.0206 | 20 |
| WC2009 | 444 | f | 45.18 | 61.48 | 1.0207 | 16 |
| SlovenianOpen2012 | 444 | f | 51.21 | 61.73 | 1.0210 | 10 |
| TaiwanSpring2010 | 333 | f | 12.45 | 15.65 | 1.0210 | 12 |
| HungarianOpen2010 | 333 | f | 12.39 | 15.58 | 1.0210 | 12 |
| Malang2011 | 222 | f | 6.35 | 16.29 | 1.0212 | 46 |
| USNationals2010 | 444 | f | 43.76 | 59.94 | 1.0212 | 16 |
| TaiwanSpringOpen2011 | 333 | f | 11.02 | 15.16 | 1.0215 | 16 |
| TaiwanSummerOpen2008 | 333 | f | 15.02 | 18.98 | 1.0215 | 12 |
| ThailandOpen2010 | 333 | f | 12.54 | 15.85 | 1.0215 | 12 |
| MunichOpen2010 | 444 | f | 48.82 | 67.84 | 1.0222 | 16 |
| StanfordWinter2010 | 333 | f | 12.69 | 16.20 | 1.0224 | 12 |
| GuangzhouBigCubes2010 | 555 | f | 84.76 | 92.64 | 1.0225 | 5 |
| HongKongCubeDay2010 | 444 | f | 55.60 | 66.42 | 1.0225 | 9 |
| WC2007 | 555 | f | 105.07 | 147.29 | 1.0228 | 16 |
| MNWOpen2011 | 333 | f | 11.79 | 15.11 | 1.0228 | 12 |
| Euro2008 | 333 | f | 11.71 | 16.48 | 1.0230 | 16 |
| WC2011 | 444 | f | 35.22 | 49.58 | 1.0231 | 16 |
| PolishOpen2009 | 333 | f | 11.81 | 15.20 | 1.0232 | 12 |
| GuangdongOpen2008 | 333 | f | 12.74 | 18.40 | 1.0232 | 17 |
| FinnishOpen2009 | mmagic | f | 5.56 | 5.69 | 1.0234 | 2 |
| USNationals2009 | 444 | f | 52.84 | 74.75 | 1.0234 | 16 |
| SingaporeOpen2009 | 333 | f | 12.96 | 15.96 | 1.0234 | 10 |
| EastGermanOpen2010 | 444 | f | 51.94 | 73.50 | 1.0234 | 16 |
| NewZealandChamps2009 | sq1 | f | 28.17 | 28.83 | 1.0234 | 2 |
| TorontoSpring2011 | 333 | f | 12.47 | 15.36 | 1.0234 | 10 |
| Euro2008 | 333oh | f | 21.79 | 30.85 | 1.0234 | 16 |
| TianjinOpen2011 | 333 | f | 13.56 | 15.95 | 1.0235 | 8 |
| ShenzhenSummerOpen2009 | 333 | f | 12.03 | 17.06 | 1.0236 | 16 |
| CubingKoreaJanuary2012 | 333 | f | 11.49 | 14.86 | 1.0237 | 12 |
| HumanRightsDay2011 | 444 | f | 44.30 | 66.15 | 1.0239 | 18 |
| USNationals2011 | 333 | f | 9.91 | 14.12 | 1.0239 | 16 |
| UKDWOpen2011 | 333 | f | 11.52 | 19.89 | 1.0240 | 24 |
| CubikBoxCup2011 | 333 | f | 10.26 | 14.65 | 1.0240 | 16 |
| IndonesianOpen2011 | 333 | f | 11.58 | 17.34 | 1.0240 | 18 |
| Shandong2010 | 333 | f | 15.64 | 24.62 | 1.0242 | 20 |
| Cheonan2008 | 333 | f | 13.63 | 17.74 | 1.0242 | 12 |
| AustrianOpen2011 | 333 | f | 10.83 | 14.10 | 1.0243 | 12 |
| BerkeleySummer2011 | 333 | f | 10.96 | 17.72 | 1.0243 | 21 |
| TaiwanSummer2010 | 333 | f | 10.71 | 16.14 | 1.0244 | 18 |
| MunichOpen2011 | 333 | f | 10.72 | 13.98 | 1.0244 | 12 |
| Netherlands2006 | 444 | f | 74.32 | 79.93 | 1.0246 | 4 |
| CaltechWinter2007 | 333 | f | 14.82 | 19.36 | 1.0246 | 12 |
| ShantouOpen2010 | 333oh | f | 24.95 | 37.74 | 1.0246 | 18 |
| Kuikuiltik2012 | 444 | f | 51.13 | 109.35 | 1.0248 | 32 |
| MatsudoOpen2010 | 444 | f | 48.05 | 54.34 | 1.0249 | 6 |
| SilesiaOpen2012 | 333 | f | 10.57 | 13.89 | 1.0251 | 12 |
| VCubeSpiel2011 | 333 | f | 10.58 | 24.63 | 1.0252 | 35 |
| USNationals2010 | 333 | f | 10.93 | 15.87 | 1.0252 | 16 |
| USNationals2009 | 333oh | f | 20.37 | 29.58 | 1.0252 | 16 |
| HaNoiOpen2011 | 333 | f | 12.81 | 16.85 | 1.0252 | 12 |
| SanFranciscoOpen2009 | 333 | f | 13.41 | 19.50 | 1.0253 | 16 |
| Borneo2010 | 333oh | f | 24.46 | 49.31 | 1.0254 | 29 |
| NorwegianOpen2009 | 555 | f | 132.07 | 142.42 | 1.0255 | 4 |
| CyberOpen2011 | 333 | f | 11.72 | 15.47 | 1.0256 | 12 |
| IndonesianChampionship2010 | pyram | f | 7.81 | 37.41 | 1.0256 | 63 |
| Seoul2008 | 333 | f | 13.63 | 18.00 | 1.0256 | 12 |
| JapanOpen2011 | 444 | f | 44.64 | 59.13 | 1.0259 | 12 |
| KoreanChampionship2011 | 333 | f | 11.13 | 16.34 | 1.0259 | 16 |
| GermanOpen2007 | 333 | f | 13.62 | 20.01 | 1.0260 | 16 |
| ChinaTourismDay2012 | 222 | f | 5.20 | 9.15 | 1.0260 | 23 |
| USNationals2010 | 333oh | f | 18.53 | 27.29 | 1.0261 | 16 |
| MunichOpen2010 | 555 | f | 92.72 | 136.68 | 1.0262 | 16 |
| TaiwanWinterOpen2010 | 333 | f | 12.42 | 16.51 | 1.0262 | 12 |
| GalantaOpen2009 | 333 | f | 15.20 | 20.22 | 1.0263 | 12 |
| PolishOpen2008 | 333 | f | 12.89 | 17.15 | 1.0263 | 12 |
| BWOpen2012 | 555 | f | 85.49 | 113.85 | 1.0264 | 12 |
| SpanishChampionship2011 | 333 | f | 11.73 | 15.63 | 1.0264 | 12 |
| HungarianOpen2008 | 333 | f | 13.20 | 19.56 | 1.0266 | 16 |
| Germany2009 | 444 | f | 59.53 | 71.54 | 1.0266 | 8 |
| USOpen2008 | 444 | f | 57.95 | 77.44 | 1.0267 | 12 |
| JRCAKansaiSpring2010 | 333 | f | 12.21 | 13.93 | 1.0267 | 6 |
| IndonesianOpen2011 | 555 | f | 92.81 | 124.06 | 1.0267 | 12 |
| CubingKoreaNewYears2012 | 333 | f | 10.79 | 22.05 | 1.0268 | 28 |
| WC2011 | 555 | f | 59.94 | 89.18 | 1.0268 | 16 |
+----------------------------+---------+---------+--------+--------+-----------+---------+
100 rows in set (0.69 sec)
That AachenSummer2012 round with 39 persons stands out a bit and indeed looks rather dense:
http://www.worldcubeassociation.org/...esults=1#333_f
Btw, note that I only consider rounds where the worst average was still successful (not a DNF). I might thus be missing rounds with one or more DNF average that are otherwise very dense.
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