Conversion Rates From HM to Marathon

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.

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. 

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

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...

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. 

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 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.

Re: realworld research:

After some googling I managed to find a link to a couple of articles I remember from some years back:

http://www.hillrunner.com/jim2/id209.html

Unfortunately there is something up with the website but luckily archive.org helped out

http://web.archive.org/web/20090203081730/http://mysite.verizon.net/jim2wr/id70.html

and so did google cache

http://webcache.googleusercontent.com/search?q=cache:JPK_8wTfEdQJ:www.hillrunner.com/jim2/id208.html+jim2+Half+Marathon+Pace+vs.+Marathon+Pace%29&cd=1&hl=en&ct=clnk&gl=uk

Catalin Bond wrote (see)

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

I love stats.

Good job on doing this lot.

Just looked back at my times

PB for mara is 2.19 times my PB for half.

First mara is 2.28 times my first half.

My PB for mara is 85% of my first mara

My PB for half is 82% of my first.

Have you thought of publishing this....it would be an interesting study especially if you could get more data perhaps by linking official finishing times. There are some obvious   factors that would need controlling in addition to age and  gender  (eg. slower runners in larger races will be more likely to be hampered with congestion so a variable dealing with the number of runners or possibly difference between gun and chip time could be included). 

Sorry to be a stats geek, but did you transform the data to deal with the skew when calculating the CIs. Also how did you deal with runners with multiple data points I see some have contributed over 10 sets of times?

Just thought, time scale would have been good. Started running 3 1/2 years ago. My first race was Reading HM March 2009. My first mara was Stratford April 2010

Christopher Morgan wrote (see)

Sorry to be a stats geek, but did you transform the data to deal with the skew when calculating the CIs. Also how did you deal with runners with multiple data points I see some have contributed over 10 sets of times?

No worries about being a stats geek! No I didn't transform the data before calculating the intervals. Having looked at it again, using transformed data pulls down the upper limit of the interval a little, pulls down the mean but leaves the bottom limit much the same: First mara - male mean 2.29 (68% between 2.14 and 2.43) female mean 2.22 (68% between 2.11 and 2.34). Average mara - male mean 2.24 (2.15 - 2.35) - female eman 2.19 (2.14 - 2.25).

To account for different numbers of marathons, I looked firstlly only at the first marathons. Then for people with more than one marathon, I worked out their average HM time and average marathon time (excluding the first marathon). Probably are better ways of doing this.

Either way it seems a lot more accurate than other calculators I have tried for me at any rate.

Bump.

Some pointed this thread out to me.   1:41 for half and 3:51 for full.   So 2.29!