Thursday, November 15, 2012

NXN-MW vs. MW State meets - a statistical review

Several have been discussing how the state meet courses compared to the NXN regional courses (specifically, the Midwest and the Illiniois and Michigan state meets). I decided to contribute to the discussion by recreating the statistical analysis I do for each NXN Region meet looking at how all the athletes did compared to their state meet race.


For the Midwest, there were 632 runners in the championship races; I was able to identify 503 of those athletes as having run in state meets.


Note: For reference, I identify how fast/slow a course is by using the raw seconds of my 200.0 rating mark (e.g., if I say “200.0 ~ 15:10”, that means that my 200.0 mark is around 910 seconds). For the NXN Midwest championship races, I identified the ratings at 909.8 for boys and 917.0 for girls (I had to rate them separately because it became apparent that the girls ran notably slower than the guys).


Illinois vs. NXN-Midwest: I was able to identify 190 athletes that ran both races. By dividing their NXN-MW time by the course adjustment (909.8 for boys, 917.0 for girls) and multiplying by their state meet time, I came up with course adjustments for each athlete. The median rating for all these athletes were 821.48, their average was 820.65, but their standard deviation was 22.61 seconds (significant variance – there are outliers in the analysis that need to be removed). After taking out the outliers, I was left with 156 athletes.  The median rating was 822.26, average rating was 822.69, and standard deviation was 9.40 (MUCH better). I use the average rating, and therefore the course rating for Illinois State is marked at 822.7 (200.0 = 13:42.7).


Michigan vs. NXN-Midwest: I was able to identify only 15 runners that ran both races. Using the same process as I do for all other states, I was left with 12 runners that averaged a rating of 868.71. Ergo, Michigan’s State meet rating sits at 868.7 (200.0 = 14:28.7). That’s a difference of about 41 seconds for guys and about 48 seconds for girls. Note that with such a low sample size, the results could have easily changed if more athletes had participated, but you have to work with what happened. The standard deviation of 12.29 seconds is still solid, and the rating isn’t too far off what I’ve had Michigan at in the past (though it is faster than I had it last year for whatever reason – could very well be  that I was off, or that it ran slow last year).


Missouri vs. NXN-Midwest: 69 athletes to start with, ended up with 53 athletes in the end.  A 906.35 average and 907.04 median with a 10.53 standard deviation means that Missouri was rated at 200.0 = 906.4.


Indiana vs. NXN-Midwest: 103 athletes ended up at 76. 892.57 average and 10.11 standard deviation means 200.0 = 14:52.6.


Ohio vs. NXN-Midwest: 126 athletes ended up at 88. 875.13 average and 8.66 standard deviation means 200.0 = 14:35.1.




All of these findings matched up decently well with both what I’ve had the state meets at in previous years, and what I estimated them to be before NXN-Midwest was run. If they didn’t line up right with one, I’d probably take a closer look; if they didn’t line up with either, I’d have to take a MUCH closer look to see what it was so different… luckily, I don’t think I’ve ever had to do the latter, though there are certainly times when I have to do the former because I had notably over/underestimated a state before they were able to compete on the regional level (e.g., Montana state in the Northwest this year, NXN-Northwest showed me I had previously underrated them by a significant amount).




As for what that all means for how the times at each course compare, it depends completely on how fast the runner that you are comparing ran at these races.


For a few of quick reference charts to give an idea:


17:00.00 = IL Boys = 15:22.35

17:00.00 = MI Boys = 16:13.92

17:00.00 = MO Boys = 16:56.19

17:00.00 = IN Boys = 16:40.72

17:00.00 = OH Boys = 16:21.10

19:55.00 = IL Girls = 17:52.11

19:55.00 = MI Girls = 18:52.06

19:55.00 = MO Girls = 19:41.19

19:55.00 = IN Girls = 19:23.20

19:55.00 = OH Girls = 19:00.40



16:30.00 = IL Boys = 14:55.22

16:30.00 = MI Boys = 15:45.28

16:30.00 = MO Boys = 16:26.30

16:30.00 = IN Boys = 16:11.28

16:30.00 = OH Boys = 15:52.24


19:20.00 = IL Girls = 17:20.71

19:20.00 = MI Girls = 18:18.90

19:20.00 = MO Girls = 19:06.59

19:20.00 = IN Girls = 18:49.13

19:20.00 = OH Girls = 18:27.00


16:00.00 = IL Boys = 14:28.09

16:00.00 = MI Boys = 15:16.63

16:00.00 = MO Boys = 15:56.41

16:00.00 = IN Boys = 15:41.85

16:00.00 = OH Boys = 15:23.39


18:45.00 = IL Girls = 16:49.31

18:45.00 = MI Girls = 17:45.74

18:45.00 = MO Girls = 18:32.00

18:45.00 = IN Girls = 18:15.07

18:45.00 = OH Girls = 17:53.60


  1. I appreciate the info... but it doesn't line up with what I see for IL, at least on the girls side. Of 67 girls I've identified as running both races, only 3 ran less than 94 seconds (or 99 for that matter) slower at NXN-MW (two had obviously bad state meets, well off PRs). The average difference was 2:06. Throw out outliers it's 2:03 (because 2 of the outliers were those 2 I just referenced, whereas there were a number who were slow at NXN). I can send the data if you'd like.

    1. Well, I can't copy and paste all of the ones I found on here (replies are limited to 4096 characters apparently), but I found 77 girls that ran both NXN-MW and IL State. But the big difference between why you're getting a difference much larger than I am is because I use what amounts to a multiplier, rather than raw seconds difference.

      The girls that aren't outliers range from running 103.6 seconds slower (1:43.6) to 157.0 seconds slower (2:37.0); when talking about how big of a difference that is as a multiplier, the 200.0 rating for the courses is only a little more than 95 seconds (917.0 - 822.7 = 94.3) ... when you apply that multipler to where the girls are at, the difference fits. That's because the 200.0 mark I'm measuring a very fast level even for boys, which means there will be an even greater difference once you get down to the girls times.

    2. In terms of raw time difference for IL girls, these were the average times of the 77 girls that ran both (61 of which were not outliers):

      Without taking out the outliers: 20:09.4 @ NXN-MW, 17:51.4 @ IL State
      After removing all the outliers: 19:59.4 @ NXN-MW, 17:52.8 @ IL State

    3. Thanks again for the clarification, and for all your hard work. I understand you're converting to a general scale, because you want to compare across many meets - and I truly thank you for that! - and that affects results somewhat. But it's confusing to me (and I'm sure others) to read that the IL course was on average 94 sec faster for girls, when that was true for only a tiny fraction (for most the IL course was, as you said, 1:43 to 2:37 faster). A girl who ran 1:45 slower at NXN could read the above analysis (prior to your comment) and think she slowed down more than average, when in fact she probably ran great at NXN.

      I've also sometimes computed the course diffs as ratios, which should equalize things for boys & girls (or faster vs um, less fast, runners). Ratio of times at NXN-MW to IL state was 1.119. [I didn't reach down below 21:00 precisely because that would skew the time-difference data]. Haven't checked ratios of boys, to see if that matches.

    4. You're right, I should have explained it as I did in the comment below, comparing how at XX:XX, the comparative time at XX State was XX:XX. But if I don't list the 200.0 mark, people would just assume that the difference is, say, 2:05 for girls and 1:35 for guys, even though that's not exactly true (if will vary depending on how fast/slow the runner is).

  2. Another way to look at it, using these course differences described in my post...

    A 16:30 at NXN-MW for boys equates to:

    IL Boys = 14:55.22
    MI Boys = 15:45.28
    MO Boys = 16:26.30
    IN Boys = 16:11.28
    OH Boys = 15:52.24

    And a 19:20 at NXN-MW for girls equates to:

    IL Girls = 17:20.71
    MI Girls = 18:18.90
    MO Girls = 19:06.59
    IN Girls = 18:49.13
    OH Girls = 18:27.00

  3. I updated the post to include three general reference charts to better explain the differences, and removed the talk of how the base level compares between the courses to avoid the confusion.

  4. This is GREAT, and aligns very well with what I'd found. Basically, your "94 sec" was for the top girl (probably even faster), whereas I was reporting the "average" girl (as I noted, I left out slower ones to not skew times - and under rough conditions, the ones I saw did even worse).

    Basically this has convinced me I should at least switch over to using ratios or percent diffs instead of time time diffs - just means I have to change the format on my stupid excel spreadsheet (I should find a way to make the time format default to a better format for xc times - who cares about time of day, anyway?); or enter minutes and seconds into diff columns....

    1. or use another column to change format from whatever you start with... such as "IF(cell*60*24>500,cell*60*24,cell*60*60*24)" which would change both mm:ss and hh:mm into raw seconds (as long as all the race times are over 8:20).