Wednesday, November 21, 2012

Further NCS MOC XC Meet statistical breakdown by Sstoz Tes


Medians for N.C.S. state meet qualifiers from 2005 - 2011 (left column) and 2012 (right column):

d. 1 b.: 2005 - 2011: 16:06; 2012: 16:20 (race 2)
d. 2 b.: 2005 - 2011: 16:25; 2012: 16:49 (race 5)
d. 3 b.: 2005 - 2011: 16:12; 2012: 16:42 (race 9)
d. 4 b.: 2005 - 2011: 16:45; 2012: 17:21 (race 8)
d. 5 b.: 2005 - 2011: 17:19; 2012: 17:04 (race 1)

d. 1 g.: 2005 - 2011: 19:10; 2012: 19:47 (race 4)
d. 2 g.: 2005 - 2011: 19:29; 2012: 20:30 (race 7)
d. 3 g.: 2005 - 2011: 19:18; 2012: 19:51 (race 6)
d. 4 g.: 2005 - 2011: 20:27; 2012: 20:41 (race 10)
d. 5 g.: 2005 - 2011: 20:29; 2012: 20:42 (race 3)

Due to the conditions, it seems logical that the races would, relative to respective historical norms, get progressively slower as the day progressed. At first this seems to hold true -- the only race with a faster-than-typical median for 2012 was the first race of the day (d. 5 b., 1,44% faster). From there, though, the pictures becomes less clear -- race 10, for example, was the 3rd closest to historical norms (1,18% slower), race 4 was the 8th furthest (3,22%) and race 7 was furthest off (5,18%). See below for table:

1 -1.44%
3 1.06%
10 1.18%
2 1.55%
5 2.49%
6 2.85%
9 3.09%
4 3.22%
8 3.58%
7 5.18%

The typical conversion ratio from the Hayward course to Woodward Park (not applicable to earlier-season meets for obvious reasons and not applicable to non-state meet qualifiers because of the specialized population from which the below statistics are derived) has been 102,765% (that is, one multiplies one's Hayward time by 1,02765 to find the equivalent state meet time), though that has ranged from 1 in 2011 to 1,03552 in 2007. As with most non-standard distributions (running race results skew heavily to the right side of the curve), the conversion has a high amount of variability from one year to the next -- the sigma is 1,262% (of the 12 state qualifying courses used between 2005 & 2011, the N.C.S. course has the 3rd highest amount of variability). A c.i. of 1,96 (that is, 95% (alpha/2)) shows that only the 2011 ratio was statistically significant. And I have no idea why. *Shrug*

Given all of that, it is dangerous territory to find a conversion factor for the 2012 results. The obvious route is to derive the ratio from a given 2012 race's median to that divisions & genders 2005 - 2011 median (e.g. the 2012 d. 1 girls were slower than the 2005 - 2011 median by 3,22%; if one compares this to the N.C.S. d. 1 girls 2005 - 2011 state meet median (19:46), the conversion factor becomes 0,99916 (19:46/19:47)). This is dangerous territory, though, because the population is so small -- between 18 & 47 depending on the race (one cannot use an overall median from the 2012 state-meet qualifer, I think, because it seems likely that course conditions impacted each race differently). In case anyone wants to live dangerously, though, below are conversion factors for each race:

d. 1 b.: 1,02039%
d. 2 b.: 101,139%
d. 3 b.: 100,499%
d. 4 b.: 099,904%
d. 5 b.: 104,395%

d. 1 g.: 099,916%
d. 2 g.: 098,007%
d. 3 g.: 100,504%
d. 4 g.: 101,410%
d. 5 g.: 101,288%

4 comments:

Anonymous said...

You guys are so funny!!! XC is not about times? Who cares? I see a 70's movement (where every course was short) just so kids can feel good about themselves. You act like spoiled California brats. Guess what... The rest of the country runs in soggy muddy conditions. Get over it!!!

Anonymous said...

I appreciate the statistical backflips that go on to get this comparison, but imho, 2012 won't work. Hard to factor in multiple runners falling down (some multiple times) to a reasonably dry, sunny Fresno course and accurately predict that the sunny, dry course will be slower. This year, I believe that the stats are interesting, but not particularly relevant.

Peter Brewer said...

Ssos did a great job explaining that this was a statistical exercise, not an attempt to provide guidance. The phrase "if you want to live dangerously" showed up in the account. The whole purpose was to see if there could be any consistency derived from the data. Conclusion: not much that had merit as a predictor of future times, or as a comparison with other years.

Peter Brewer
Northgate High

Anonymous said...

Is this the median state qualifier time or the average of the final qualifier?

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