Conversion Rates From HM to Marathon

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  • Last year I started to put all this data into SPSS (mainly because I was meant to be writing a thesis and anything else seemed infinitely more interesting than doing that!) yesterday I updated it, and if people are interested here are the stats as I find them (one caveat, there may be the odd error in here as I did transfer all times by hand…but hopefully this won’t unduly influence results!)

    Firstly to account for the fact some people had done many marathons and others one I did two analyses (1) only using people first listed HM and marathon time (2) in the people who had done two or more marathon, I used the average of all their times. There may be other better ways of doing this.

    FIRST MARATHON

    118 people (72 male 46 female) had provided data for at least one marathon. The graph shows HM time plotted against marathon time. Although it fans out a bit at slower HM times, I think it’s pretty amazing how consistent the relationship is. Even Choisty’s anomalous time sits right on the expect regression line! The correlation between them was 0.94

    ../members/images/459012/Gallery/Correlation_1.JPG

    MULTIPLE MARATHONS

    53 people (35 male, 18 female) provided data for two or more marathons. The correlation here was 0.96.

    /members/images/459012/Gallery/correlation_2.JPG

  • /members/images/459012/Gallery/Correlation_1_0.JPG

    Darn that didn't work completely.

    Here is the first graph:

  • Do females convert statistically better than males?

    To measure conversion I divided marathon time by HM time.

    For the first marathon, the mean conversion for men was 2.29 (95% confidence limits,  2.26 - 2.32, thus 95% of men had marathon times that were between 2.26 and 2.32 times their half marathon times) and for women it was 2.26 (95% CL 2.22 – 2.29). Although women on average converted slightly better, the difference would be less than 5 mins over the marathon, and the overlapping confidence limits show this difference is not statistically significant.

    Multiple marathons: Both males and females showed slightly better conversion if the average over multiple marathons was used (2.26 for males and 2.24 for females) but again this difference was not statistically significant.

  • Do faster runners convert better than slower runners?

    For first marathons, there was no relationship between HM time and conversion factor. However when looking only at those who had done 2+ marathons, there was a correlation, with faster runners showing a better conversion. This was particularly true for the men. This could however be because there are not many men in the dataset with half times slower than 100 mins (1:40).

    /members/images/459012/Gallery/correlation_3_1.JPG


  • I also looked at the effect of age, and found no significant relationship with conversion.

    Anyway if anyone would like a copy of the dataset either in SPSS or Excel, PM me your email and I’ll send it. I'm sure there are many more analyses that could be done with the data set.

  • Fantastic analysis thank you
  • RatzerRatzer ✭✭✭
    Fabulous, Catalin.  So, if you want to have an estimated marathon time off your HM, times by two and add a quarter, and you won't go too far wrong!
  • To Ratzer - as an estimate that would probably work (or multiply by 2.25, which is the same thing). Certainly more conservative than MacMillan.
  • MinniMinni ✭✭✭
    Very interesting Catalin.  Off to find a calculator....
  • Excellent work, Catalin.

    It will be interesting to see how adding more and more data confirms/changes the regression lines.

    Its the first real world analysis I've seen on this subject.

  • Blimy - that's really interesting, Caitlin. And puts my marathon time bang on the 2.25x HM, so maybe it wasn't anything like as bad as I thought.

    HM 2:16, FM 5:06.

  • Ooo - very interesting. Matches my plan for MK tomorrow. Thanks a bunch Caitlin
  • JoolskaJoolska ✭✭✭
    That's great, Catalin. Thanks for doing the number crunching.
  • Interesting statistics. It gets my times for Liverpool half & full about right for last year

    Male 40 half mar 1:39:57 marathon 3:48:30 (tight hamstring)

    Stats estimate 3:45 which was what I was on for bar the tight hamstring.

    Have since done 1:35:30 on same Liverpool half this year, could've gone faster if not for the sheer number of people and course, also doing Edinburgh soon which is a lot flatter... Difficult to factor that in stats people have listed, "hard" courses for either of the runs.



  • Just one question - for those that gave data for more than 1 marathon, was there evidence that you learn from the first marathon experience? ie: was the conversion better for the 2nd and later marathons than it was for the first? The very marginal shift in the average conversion of first marathons over all marathons suggests it might, if the data were cut the right way.

    I'm feeling (after having finished all of 1 marathon) that I didn't really know what I'd let myself in for until I'd finished it. Certainly I wasn't prepared for quite how far 26 miles is, despite having done 3x20 mile runs in the build up.
  • MinniMinni ✭✭✭
    Helen - I felt exactly the same after my first and the only reason I did a second was because I'd got a GFA.  I'm not sure about the data but you are definitely more mentally prepared for your second and this really helps. 
  • Very interesting stats.  Always looked at double half time and add 20 Mins.

    Male 46

    P.B  - HM 1:36 **

    P.B  - FM 3:36 **  Spot on.

    Will see tomorrow after Stratford if my full time improves.

  • I wish I had the same excuse for a second, Minni! Instead I'm dreadfully disappointed in the performance (of which time is just one indicator) and am thinking of a campaign for 2014. Suspect I'd be heading for the divorce courts if I put him through that again too soon image
  • Catalin, that analysis is great.  I love a bit of proper statistical analysis to back up conventional wisdom.

    Mind you, it does make me think that maybe I am aiming too high as I'd need a conversion of 2.17 to break 3 hrs, going off my best ever HM time....

  • Catalin Bond wrote (see)

    Do females convert statistically better than males?

    To measure conversion I divided marathon time by HM time.

    For the first marathon, the mean conversion for men was 2.29 (95% confidence limits,  2.26 - 2.32, thus 95% of men had marathon times that were between 2.26 and 2.32 times their half marathon times) and for women it was 2.26 (95% CL 2.22 – 2.29).

    In looking at Ally's comment, I realised the error in what I wrote on Friday - I was mistaking my standard error and standard deviation.

     For a first marathon

    We can be 95% confident that the mean for men falls between 2.26 and 2.32 and the mean for women falls between 2.22 and 2.29.

    68% of male runners would fall between a conversion rate of 2.14 and 2.44 (i.e. 1 standard deviation)

    68% of women would fall between having a conversion rate of 2.13 and 2.38

    For average over multiple marathons

    68% of male runners would fall between a conversion rate of 2.15 and 2.37 (i.e. 1 standard deviation)

    68% of women would fall between having a conversion rate of 2.14 and 2.30

  • To Ally Watson - Looking at all marathons run by women approximalte there were conversions of 2.17 or better in approximately 1/3 marathons, so it is possible! (Though these were all half marathons runs in the run up to the marathon, rather than HM hest times).

    For men less than 1/4 had conversions better than 2.17.

  • More grist for the stats mill

    HM Mar 2012: 1:34
    Mara Apr 2012: 3:32

    I paced it for 3:32 and was pretty comfortable with even splits. It was my third marathon.

    Cheers, Ant
  • To Helen Liz,

     Looking at the data most people have better conversions on subsequent marathons than their first. Looking only at the people who had done more than one marathon, the average conversion for first marathons was 2.29, and for other marathons excluding their first it was 2.23 - a mean improvment of 0.06. This was much the same for males and for females. 

  • Thanks, Caitlin. That's a not insignificant 8 minutes at my pace - enough to get me my sub 5, assuming all things were equal (a rather large assumption, I accept). That's encouraging image
  • RatzerRatzer ✭✭✭

    Catalin, you have a fan in me - I love these stats!  image

    But, as more of a challenge, if you were to split the HMs into pace bands, of say 5 minutes each, how would the relative pace bands convert upwards?  (I have a feeling the faster pace bands would have worse conversions on their first marathons.)  Of course I'm assuming you have something much more important to do, but the important thing you have to do is boring and you need a distraction... image

  • Interesting - does the conversion follow a normal distribution?
  • To Christopher Morgan - the conversion does not follow a normal distribution. Instead has a positive skew.

    Ratzer - I've not done what you asked (five minute bins), but can show a scatter plot of  HM time against conversion. This plot is just for first marathons. 

    /members/images/459012/Gallery/run.JPG



  • RatzerRatzer ✭✭✭

    So it does seem actually (in spite of my thoughts) that quicker HM times appear to offer a better conversion for the first marathon.  Admittedly with all sorts of caveats in the data.  Conversion drops downward at about the 90 minute HM mark (male - 120min female), although excellent conversions are still seen.  After this 90 min mark, conversions appear to taper in.  (After 120 for females there seem too few data points to be meaningful, but initial observation says conversion improves again.)

    So, if you're around the 1:30 mark (male) or 2:00 mark (female), be very cautious about your predicted marathon time for your first race, so that you don't have a poor run!

  • Makes sense - if you can do sub 90 mins for a half, chances are you know what you're doing and are likely to convert well for first marathon. Over this point, you get some people who'll have trained well and convert well, some people who didn't give it their all in a half, and hence convert well, and some who did their best effort in a half, but blew up in the marathon, whether that's becasue they went off too fast, got injured or were just undertrained for a marathon.

    I reakon if you want the best conversion - jog a half at marathon pace image but thet would be cheating! 

    Or maybe I should name (and not shame) the best converters so we can ask them for their training tips.

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