To Infinity and Beyond - Becoming a Better DopeyBadger (Comments Welcome)

One of my favorite things about running is the research behind it. I love love love to break down articles or papers to read more in-depth into what they're trying to say. @JeffW posted this article in the running thread and I couldn't resist digging into it.



Ian Williams: An updated formula for marathon-running success

This is another attempt by someone in trying to optimize the marathon race equivalency calculation portion. There's little doubt that the 5k, 10k, and HM relationships are strong. But the M sits atop the mountain with a difficulty unlike the others in properly estimating finish time from other race distances previously completed. Why is it even important to have a good race equivalency going into a race day? Well, running a marathon can literally come down to a few seconds per mile vs best performance and literal blow-up. It all comes down to the physiological difference between the M and the other races. Once you pass a certain threshold the ticking time bomb that is pace will starting counting down. And unless you pace perfectly, things can go haywire quick. So a good race equivalency or honest assessment of race day goal pace can be extremely beneficial. The classic formula used in most online calculators is Peter Rigel's formula:

M = HM x 2^1.06

Which means your M is 2.08 times slower than your HM.

I've previously reviewed a new-age calculation from Vickers (link).

So let's dive right into Ian Williams attempt at adjusting the classic marathon race equivalency calculator.

Sample size - 1071 different HM to M relationships. Good, but about half the size of Vickers data set (although Vickers used 5k, 10k, and HM performances). Williams did cut the data set to runners who had completed at least 5 HM and Ms, thus more experienced runners who knew what they were getting themselves into.

Sample collection - :crazy2: An internet "logging system" open to anyone using fetcheveryone.com to find participants. The article does not speak to potential issues of representativeness and selection bias. I'm not terribly concerned about the selection bias. There is literally no data as to whether this data set resembles a normal population set (male/female/age/training history/representative finishing times, etc.). I have reason to believe that the majority of William's data set is from runners at 2:00 half marathon or less (based on the displayed data and groups he chooses to display). The male median time in this study was UNK for the marathon versus 4:11 for NYC marathon, and 4:16 for Running in the USA. The female median time in this study was UNK, 4:38 in NYC, and 4:41 in Running in the USA. So my best guess on what I can surmise from the data set is that while the median national time is close to 4:16-4:41 in the US, very little of this data set (if at all) was based on runners around or slower than the national average.

I can't tell initially from the article whether the data is logged daily or just once at the end. That would call into question the chance for error. More measurements would reduce the chance for error. If you've got the entire data set (like a Strava history), then everything is there. But if the dataset Williams used relied solely on self-reporting, then it could make for a much higher chance for error.

Also, I can't tell if this is recent HM vs recent M. Or if it is PR HM vs recent M.

Alight, so let's dive in!

As previously stated, Rigel is:

M = HM x 2^R

where R=1.06

Williams sets out to redefine R with a new value that makes the calculator more accurate for more people.

Williams starts by using his dataset of 1071 runners to define the relationship between their HM and M performances.

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The very first thing that sticks out to me - no y-axis defined. What exactly am I looking at here? It would appear to be a histogram or distribution plot of the relationship of the 1071 runners HM to M. 1.06 represents the current Rigel. Williams proposed 1.15 is a better R value since it falls further towards the middle. I would not deny that either based on the graph. It certainly appears the 1.15 falls much closer to the middle than 1.06. And if being conservative on pacing for the marathon is an important variable (which I believe it is), then being on the slower side for predicting won't prevent a great marathon performance (because you can negative split the back half of the race). But I wasn't satisfied having no y-xais. So I made one for him:

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I actually used photoshop to measure the height of each of his bars. Then I assumed this shown data set represented the whole 1071 runners. Which may or may not be the case. I don't believe anyone is faster than 1.01, but slower than 1.30 is certainly possible. Although, I certainly don't know. I feel relatively confident because the total height of the bars added together was 49.79 or very very close to a whole number of 50. That means I could calculate the number of runners per bar:

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So when I look back at the 1.01 bar, it really represents 0.25% of the population or a guess of 2.7 runners. Makes sense. Only 3 runners out of 1071 were able to hit a 1.01 R value. So, does my data extraction work? Well Williams states in the article that less than 5% of the runners had a R of 1.06. His other linked article says 49 total runners at 1.06 or less. That jives closely with what I've got. Remember mine are in bars of 1.06. But that probably really means 1.055 to 1.064. So the numbers will be off slightly, but not terribly. So keep in mind when the data set talks about runners at exactly 1.06, it's really only talking about 29 total runners. A much much much smaller data set suddenly.

But what does that mean in actual time conversions?

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So for example, someone with a R of 1.01 with a HM time of 2:00:00 was able to run a M in 4:01:40. For someone after 5 HM/Ms to run a virtual identical pace between their HM and M is astounding. Almost too astounding... That brings up another question about the dataset. The relationship between HM and M can't be viewed under a microscope. There are variables of race day that matter so much for performance. Race crowding, elevation, and weather just to name a few. If someone is running a uphill HM in hot weather in 2:00:00 and then a downhill cold weather M in 4:01:40, then the data starts making more sense. Regardless, it's another reason to cast question on this. Vickers did a better job attempting to correct this. So since Vickers is such a great guy and released his dataset to the public we can map Vickers dataset in the same manner as Williams. Vickers has a total of 862 runners in his dataset (including what I believe is a slower median population meaning it is more representative of the US population of marathon runners) that have matching HM and M condition races (and if not matching than an adjustment was used).

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Hooray! I'd say for the most part the datasets follow a similar trend. Not the same, but similar.

So the initial conclusion was 1.15 is a better predictor R for HM to M than is 1.06. It does split the middle of the data set (with 47% on both sides). So better. Williams dataset says the midpoint is 1.15 with a 25-75% range of 1.10 to 1.19 and Vickers dataset says the midpoint is 1.13 with a 25-75% range of 1.09-1.17.

So for a 2:00 HM runner, what does that mean?

Rigel - traditional calculator (1.06) = M of 4:10:12
Williams - 1.15 = M of 4:26:18 (range of 4:17-4:33)
Vickers - 1.13 = M of 4:22:38 (range of 4:15-4:30)

Since you are likely to see a better performance in the marathon with a conservative start, this new value of around 1.13-1.15 looks good to me. Slower is better at the beginning so you can leave some room for error in the second half of the race. Go out too fast in the beginning and the risk of blowing up is much much higher.

The problems start to arise when he starts to parce the data apart to make other conclusions about training in general that leads to performance.

Does gender matter?

Matches what I've read before. Women are better pacers during a marathon (more even/negative splits and less positive splits, (or faster at the end)), hypothesized that women are better at burning fat then men, and hypothesized that women are better at dissipating heat than men. So if a woman and a man have equal HM times going into the M, the woman is more often than not going to beat the man.

So I agree with the conclusion.

Are faster runners better?

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The bottom grey line represents the top 10% of runners with that HM time in each subset of data. So Williams pieced apart the dataset into secondary pools with HM times of 1:20, 1:25, 1:30, 1:35, 1:40, etc. Given the relative smoothness of the line we can tell this is the case. Remembering back, there are only 67 total runners with a 1.06 or less in the dataset of 1071. There are only 256 with a 1.10 or less. There appear to be 9 subsets of data. As would make sense, there are likely fewer runners in the dataset at 1:20-1:30, then there is at 1:50-2:00 (if this dataset is anything like a normal population of HM runners). So the data at the beginning of the line is probably based off very few runners.

The first thing that jumps out to me is that the relationship between HM time and R (for M) is pretty equal for the top 10% across all HM times. A 1:20 10% runner is around 1.06, but so is a 1:55 runner. And the difference between the two is quite small anywhere in-between.

So the variation of the mean is not coming from the top 10% becoming worse converters, but the bottom portion of the population as the HM time slows are getting worse at being converters. So the question would follow, what are the top 10% runners doing that are all near 1.06 across all HM times that the bottom 10% are not? Seems to suggest that regardless of HM time you can be a good converter if you're doing the right things in training. And those in the slower HM times tend to have more runners doing the wrong thing in training (hence bad converters).

What about training mileage?

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So per Williams this graph is the "typical" amount of miles run by experienced marathon runners (not their first) going for a PR marathon attempt. This does not have to be the same dataset he used to create the previous graph, but rather a measuring stick he created. So this original dataset doesn't have to be correlated with success in any way or being a good converter.

So the graph on the surface tells a story that most of us know. The people with faster marathon finishing times run more miles. But you know me, I don't like to look at miles, I like duration. So if I were to standardize these mileages across each subset by either Marathon Pace or EB pace (which tends to be the average pace I schedule runners at or 1.12 times slower than MP), then what does the dataset look like?

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A 2:20 runner runs 1200 miles in 16 weeks. The MP of 2:20 is a 5:21 min/mile. If the 2:20 runner were to average MP for the 16 weeks of training, then they would do 6:40 hours of training per week (or 106 hours total). If we instead used EB, then the 2:20 runner averages 7:28 hours per week. The 2:20 is clearly the outlier, because look at the other subsets of data. The 2:40, 3:00, 3:20, 3:40, 4:00, 4:20, and 4:40 all run about 5:00 hours (if at MP) or 5:30 hours (if at EB) per week. So on the surface the 2:40 to 4:40 runners would appear different, but when taking into account their relative training pace, they're all actually very similar. This comes down to training load and why I like to evaluate training plans by time moreso than mileage. Two runners doing 80% of training at easy with 9 hours of total running per week will be reaping similar training benefits regardless if one runs a 2:20 M and the other a 4:40 M.

For reference, the marathon training plans I write tend to be in the 7-8 hours average range for 16 weeks. So my plans are like the outliers in the 2:20 M time group.

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This is a hard graph for me to interpret. Based on the shape and description, I believe this is a cumulative graph. Meaning that once a runner has been passed in the data set it continues to get counted. So a runner in the 1.06 success portion means that 12% of runners who have sufficient mileage achieve a 1.06. And 60% of runners with sufficient mileage achieve a 1.15 OR LESS. Since the graph does not go down EVER, I don't believe the interpretation of the graph is when r=1.15 is achieved 60% of runners with a 1.15 had sufficient mileage because for that to be the case the addition of insufficient and sufficient on the graph should always equal 100%.

Here's where the interpretation of the graph gets tricky for me. Going back up to the original dataset, there are 580 runners who achieved a 1.15 or better (or 54.19% of the dataset). A total of 60% of runners with sufficient mileage ran 1.15. So the sufficint mileage group and the total group are 60% vs 54.2%. Seems to me these are not very far off from each other. Using this information, I should be able to calculate the number of runners in the 1071 dataset with sufficient mileage and insufficient mileage. I'll save the math, but it comes down to 820 runners have sufficient and 251 runners had insufficient. That allows a 60% success rate in sufficient and 35% success rate in insufficient while maintaining a total of 580 runners in the total dataset.

So going back to 1.06 then, we have 67 total runners at 1.06 OR LESS. From the graph, approximately 12% of the sufficient group hits a 1.06 vs ~5% for insufficient. So, how does that look in the raw numbers? Well that's where I can't make sense of it. If 12% of 820 runners are successful at 1.06 OR LESS, then I've got 98.4 runners. But only 67 runners in the whole data set were successful at 1.06 or LESS. So my original interpretation can't be right, can it? Therefore, I'm confused on this one.

I believe the basic premise is correct, those who run more tend to be more successful. But I can't figure out how to interpret this graph.

What about long runs?

A common consideration for marathon training plans is the long run.

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Can't say I've ever heard of the 5L = 100 mile rule of thumb. Where the 5 longest runs in a 16 week plan summed together equal over 100 miles is a good sign. Again, I standardized this information by time:

View attachment 302787

If a 2:20 runner does 110 miles, then they are averaging 22 miles per Long Run. If the pace is MP, then they are doing it in 1:57:33. If the pace is LR pace (roughly 8% slower than MP), then it's duration is 2:07. So the faster runners, tend to do less total duration on their longest run cumulatively over the course of the plan. Sounds about right to me. I'm of the mindset that the cutoff should be around 2:30 for a training run duration limit at LR pace. Seems like the runners doing 2:20-3:00 marathon times are in that range. And many of the runners doing up to 2:45+ are in the 3:20 or slower M time range. So faster runners are spending less total time in any single training run.

So where the amount of time spent training was near equal across the board, the same doesn't appear for the 5L evaluation. On a training plan like mine, where does 5L typically fall?

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Since it's based on time, I've got the MP and LR paces for different paced M finish times. I then calculated the peak of training as 2:30 duration limit. So a 3:20 runner will max at 18 miles and a 4:40 runner at 13 miles. Then, I like to hit peak only twice during a plan and then reduce every previous "high" week by one mile. So for me, a 2:20 runner would be doing 124 miles as 5L (higher than the 110 from Williams dataset) and a 4:00 runner would do 70 miles (or far lower than the 95 miles in Williams dataset).

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Now, since all of the runners 5Ls are pooled together, I can't evaluate this graph by duration. But I can point out something troubling to me. The grey lines again represent top and bottom 10%. I already showed reasonably well that my assumed dataset matched Williams graphed dataset. Yet, I estimate he has maybe 10 to 11 total runners out of 1071 above or at 1.30 R. This graph shows the bottom 10% of 85, 90, 95, 100, and 110 at or higher than 1.30. How can that possibly be when there are only 10 to 11 runners in this area? Another new dataset? Confused again.

What I do get from this graph is that a difference of 85 (17 mile avg) vs 100 (20 mile avg) yields an R difference of 1.15 vs 1.21. For a 2:00 HM runner, that's 4:26 vs 4:37 (4% diff). Not an insignificant difference, but not as big a difference as the "are faster runners better" difference which was more like 1.10 vs 1.20 from faster runners to slower runners (5-7% difference). So something other than 5L plays a bigger role in predicting good converters vs bad ones.

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So I can take this graph one step further. Williams gives data on 16 week training mileage and 5L from 16 weeks. Which means I can calculate his subset data's % by Marathon time.

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The 2:20 runners had a 5L of 110 and 16 week total of 1200 miles. Therefore, their %5L of total was 9.2%. So not only are the better converters around 10% of total, but so are the faster runners. It's possible then to think that if one were to train like a faster runner/better converter they could achieve a lower R (and better M time relative to HM performance). So balance is important. I preach that a ton. So it's not the total mileage of the 5L that matters near as much as the % of which 5L makes up the total plan. So spend less time on the long run, and more time spent training during the week.

So where do my plans fall?

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As covered previously, a 5L for me for a 3:00 runner will be around 95 miles. They'll do about 7 hours of training on average regardless of current fitness level. Their pace will be around EB (1.12x slower than MP) as an average for the plan. Therefore, we can calculate the average mileage and total mileage for each subset underneath my scheme. This comes out to a nearly identical 11% 5L as a % of the total training mileage across the board. So my plans are closer to the R values of 1.06-1.07 (or my training plans are better representative of runners who tend to get faster M times relative to their HM times).

What about training pace?

In my book, it's pretty darn important. Pace matters more than mileage, because to me mileage is just a function of time and pace spent training.

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Unsurprising to me, runners at the faster paces actually train far slower than final race pace. I hark on this all the time. It suggests that if someone were to slow down in training, they too might yield better race results (or be faster).

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An interesting graph. I interpret this to mean that until your average is about 40 seconds slower than race pace, you are more likely to run slower than a 1.15 conversion then you are to run faster than it. Those who run too fast in training tend to be the ones who run worse relative performances against their HM times. So, train slower! Sure seems like somewhere between 40-70 seconds is a sweet spot. There aren't actually that many runners at 80+ seconds, but those who do are pretty successful relatively on achieving a less than 1.15 R value.

So what about my plans?

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According to Williams, runners with a race pace of 6:00 tend to run on average 72 seconds slower. So they'd be doing about a 7:12 average. Those at 8:00 with 35 seconds slower, at 8:35. For me, my training plans nearly always equal EB which is 1.12x slower than MP. So a 6:00 runner would average 6:43 and a 8:00 runner a 8:58. So my time differential across the board falls between 40-72 seconds. Going back to the graph Williams presented and that just so happens to appear as the sweet spot for beating the R of 1.15 (or being a better converter and achieving a faster M relative to HM performance).

On being rested

And then there's this graph....

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This appears to be saying that peak mileage is reached in "x" week of the 16 weeks. Not surprising to see that the tallest bar is 13 weeks of the traditional taper (3 weeks out). Using the y-axis I can determine how many runners peak at either 13, 14, or 15 weeks of the training plan. It is about 170. The total dataset is 1071 runners. Problem is, when I run through the numbers I only get ~680 total runners, not 1071 runners. Where did the rest of the data set go???

But even ignoring that, the alarming part is this. The traditional taper is 3 weeks. Some do 4 weeks and others 2 weeks. But in this specific dataset there are a huge (roughly 65%) number of runners doing the taper at 5 weeks out or MORE??? Some hitting highest mileage week in Week 1? And not just a few people, but 3% of this graph's population. That seems astoundingly high. Maybe they did 10 miles every week for 16 weeks and thus hit their max mileage in week 1, but that seems odd to me from a dataset standpoint.

Conclusions

The conclusions we can draw from this:

-If HM performance is equal, women are likelier to finish with a faster M time than men.
-Runners of all abilities are capable of a 1.06 or less, and roughly the top 10% of all subgroups from 1:20 HM'ers to 2:00 HM'ers were roughly the same R value (or relative performance).
-Faster runners are better converters with a lower R overall average. Makes sense then why Rigel came up with 1.06 since the elite runners available to him would have been a similar pool to the faster runners in Williams dataset.
-Runners on the slower side of the HM performances tend to have more variability as a group because of the bad converters in their groups, not because of the lack of good converters. So more people on the slower side of HM performance training inappropriately for marathon performance.
-Roughly 5:00 to 5:30 hours per week on average for a marathon training plan is considered "typical" or "sufficient" by Williams.
-Those who run more than 5:00-5:30 hours per week are more successful at being good converters than are runners who run less than 5:00-5:30 hours per week.
-Those who do 5L around 100 barely appear different than those around lesser or higher numbers. The 5L would suggest it is lower on the predictive nature than other variables.
-Those who have 5L be a lower % of total mileage from 16 weeks tend to be the best converters. The faster runners also tend to be the ones with lower %5L values. Relying less on the long runs and more balance yields a better relative performance.
-Those who train at 40-80 seconds slower than race pace more often than not will be a good converter and have a R less than 1.15.

For my marathon training plans:

-The training load I schedule (around 7 hours per week) is sufficient (above 5-5.5 hrs) and is most like a 2:20 marathon runner's training plan.
-Almost none of my training plans would hit the 100 mile rule of thumb 5L. Most would be far far lower. The data suggests this is a minimal variable compared to other things.
-The %5L of training plans is a very good predictor of being a good converter. My plans are about 11% 5L of the total regardless of ability levels. The best converters (1.06-1.07) are around 9-10%. The worst converters (1.17-1.18) are around 20-21%.
-My training plans average pace is between 40-70 seconds depending on one's relative fitness. The point at which you are more likely to achieve a conversion better than 1.15 than not, is between 40-70 seconds. Or exactly where I schedule my paces.

This explains why most of my marathon training plans yield a final marathon time very close to my prediction. They check off all the boxes for optimal race day performance based on Williams conclusions. My predictions between HM and M performance is 4% or almost exactly a value of 1.06. So my runners tend to achieve in the top 25% of relative performances or at around 1.10 or less for an R value.

So a good marathon plan is:
-Over 5-5.5 hrs in duration per week on average for 16 weeks.
-Has a 5L% of 9-11%. So if you do 100 miles as 5L (or five 20 milers), then you better be doing 1000 miles in the 16 weeks of training (or 63 miles per week on average). The more you diverge from this, the worse your HM conversion becomes. Although, you can still be successful at a lower 5L like 60 miles if the 5L% is still in the 9-11% range (or 600 miles total and 38 miles per week) as long as that duration is over 5-5.5 hours for your paces.
-Has you training at roughly 40-80 seconds slower on average for the plan than marathon race pace.

That was fun! Alright, that's what I see. What do you think?

I'm with @TeeterTots! So glad you're so smart and able to interpret all that data into plans that make us successful, because I've read through it a few times and I'm over here like...
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During G's second birthday party at my in-laws they offered to let me use their bike trainer in the basement. After the party was over, I went down in my normal clothes to give it a try. And then I decided just to keep going until someone told me it was time to leave. Got in 25-35 min (didn't start the watch until 25 min) at a HR of about 128-132 for the majority of the ride. Just looked up bike HRs right now and I need to be between around a 106-132 for endurance/recovery goal rides. So my effort and HR seemed to match relatively well even though I haven't ridden a bike in a long time. They said I can come over whenever I want, so I'll be going quite often during this down time.

Overall, it felt good to get a workout in. Didn't have any issues with my leg during the ride. It certainly worked the muscle groups differently. I'll be interested to see how it progresses.
 


It's certainly possible. But a good article or paper should discuss things like a changing dataset and why. Don't leave it to the reader to do some serious leg work to figure it out on there own. It can lead to mistrust from the audience about any conclusions from the paper. The one that confuses me the most is the "Average Rigel number based on 5L". I mean that's a lot of values about 1.40. The original dataset graph should extend to 1.40 if there are values out there. Can't see how they'd get excluded from that original dataset if they were above 10% of the total picture.
Completely agree with you. Wouldn't make it past peer review if it was headed to a technical journal or a conference (although conference reviews seem to be pretty weak these days)

Agreed! Of course, I'd say that the usual runner "targeting a finish" are your typical first time marathoners which I'd recommend be the last people attempting 20 milers (given they tend to be on the slower side of the spectrum of all marathoners).
This is always an interesting topic, because so many of the "big" names have 20 miles (or more) in their 1st time marathon plans (Higdon, Galloway, FIRST, etc). The kind of data from this article really flies in the face of what how so many first time plans are structured. I honestly wonder what the injury profile of 1st timers doing a plan with 20 miles peak vs something like Hanson's "Just Finish" are. I'm not aware of any injury studies that took into account the training plan of the runner.

Well you know how I like to look at things- duration. As an example, say you were doing a 40 mile a week plan and a 2:00 HM runner.

The average pace for a training plan of a 2:00 HM would be 10:47 min/mile (based on 1.17 times higher than HMP (9:09)). That's 7:11 hours of training per week. That's absolutely a healthy amount of training and likely will yield between a 4-6% improvement in time in most cases. Sometimes as high as 10-12%. So that 2:00 HM at the end of a 16 cycle would usually be as fast as a 1:52-1:55. Do that cycle again and they do about 6:44 hours of training per week if they re-used the same 40 mile a week plan with current fitness pacing. That's 30 min less per week (or 8 hours over the course of all the training). Now the improvement might not be 4-6% anymore because the training load is now lower. So maybe 3-5%. Now a 1:47 HM time. So first improvement was 8 minutes, but the second was 5 minutes. Now re-use again... Now down to 6:25 hours per week (almost an hour less per week than when you started). Maybe the improvement shifts down again to 2-4%. Now at 1:43.

Now if the same runner had kept training at 7:11 instead of going 7:11, 6:44, 6:25 in three consecutive cycles they could have been at 6% improvement each of the three times instead of 6, 5, 4. What's the difference in the end? A 1:43 HM on an unadjusted plan versus a 1:39. That's just the difference in about a year's time.

These are all obviously just made up numbers and a simplistic view, but it does show as an example what I believe would occur with a reduced training load (based on duration). That's why I believe that pace and mileage move in unison. If you get faster, then you need to do more mileage. But in essence you can do the same amount of training load. You just do more mileage because you're faster at a set duration.
All of this makes sense, no disagreements. Something I need to contemplate planning for my next marathon cycle (I'm in half marathon mode now). There seems to be a tipping point for me as I increase both speed and distance at around 25-30 mid-week miles (those not from the long run) where my plantar fascia/achilles start giving me problems. I've found that if I keep the mileage under that and speed up, or hold pace and increase mileage, I'm ok.
 


Saw your bike ride on Strava when I logged yesterday's run. Glad to see you moving again, even if it's not your first choice of sport : ) Re: Reynaud's, wondering if this tips the scale at all towards a treadmill for you? Especially if you're reticent to start the medication prescribed?
 
I honestly wonder what the injury profile of 1st timers doing a plan with 20 miles peak vs something like Hanson's "Just Finish" are. I'm not aware of any injury studies that took into account the training plan of the runner.

I wasn't able to find anything in a quick search either. It would certainly be an interesting comprehensive study for sure.

Saw your bike ride on Strava when I logged yesterday's run. Glad to see you moving again, even if it's not your first choice of sport : ) Re: Reynaud's, wondering if this tips the scale at all towards a treadmill for you? Especially if you're reticent to start the medication prescribed?

Happy to be doing something for sure. Going to give it another go tonight. I'm fairly certain we will be getting a treadmill before next winter. Between the amount of time I have off and the soon to be rising temps, I'm not sure there is an immediate need. But Steph and I have discussed possibly getting a Pelton Tread and Bike. Steph has always wanted to do spin classes but there's nothing close to here that makes it reasonable on her extremely tight schedule. If rather she could pop downstairs and do a class while G plays in the basement, then it's a win-win. We haven't made any decisions yet, but that's where we are leaning right now. Before we make any decisions I need to be able to run comfortably again (i.e. heal from the stress fracture and determine if there is any other underlying issue that led to the fracture and then test out different equipment to decide what we like best in home equipment).

But I think the agreement between Steph and I is that if I want to continue to run then I need to have a back-up option in bad WI winter conditions. Because running in -25F weather was doable before but maybe wasn't the best choice. We'll see how things change in the coming months.
 
Just realized it is the fibula bone that has the stress fracture, not the tibia. The fibula is the smaller of the two and bears less weight. Realized it when I was looking up online whether biking on a "tibia stress fracture" was ok and the picture of the bone wasn't matching mine. Never did have to learn the skeletal system as a genetics major. I'll stick to reading charts and graphs from running studies, LOL!
 
Just realized it is the fibula bone that has the stress fracture, not the tibia. The fibula is the smaller of the two and bears less weight. Realized it when I was looking up online whether biking on a "tibia stress fracture" was ok and the picture of the bone wasn't matching mine. Never did have to learn the skeletal system as a genetics major. I'll stick to reading charts and graphs from running studies, LOL!

Trick I learned in anatomy to keep tibia and fibula straight - you have to "f"ind the fibula because it is hiding behind the tibia.
 
Highly recommend the treadmill. :) As much as I don't love it in February, it's usually better than our alternative. Especially with reynauds - which is a huge issue for me too. More wishes for a speedy recovery!
 
Highly recommend the treadmill. :) As much as I don't love it in February, it's usually better than our alternative. Especially with reynauds - which is a huge issue for me too. More wishes for a speedy recovery!

Thanks! I think when the time comes for it, it will be a nice addition. I've done reasonably well the last two bike rides with the first being 25 min of no entertainment and the second 30 min with Netflix. The motivation level is still high, so I'm hoping that continues to pull me through this period of time.
 
The Return to Running and Determining Current Fitness

What best to do with one's time when you can't run (but can bike!)... Figure out an estimate on where you'll be when you make a comeback and what you need to do to make that comeback!

So at first, I found Runner's Connect's system for determining fitness based on time off. It seemed like a good option to work with. But as I was perusing Daniels book, I found a section on planned and unplanned breaks. The calculation seemed simple and I took it a little step further to help me figure out where I'll be current fitness wise come 3/7/18 (with a hopeful return to running).

The chart in the book is simple enough:

Screen Shot 2018-02-21 at 9.27.02 AM.png

Take the number of days off and then adjust VDOT (a measure of current fitness) by the % loss in fitness. Therefore, a 14 day off period is either a 0.973 (or 97.3%) adjustment or a 0.986 adjustment. It's determined by whether you were completely off from activity (without leg aerobic) or were doing some sort of aerobic leg workouts (like swimming and biking). According to Daniels, there is no fitness lost (or more specifically VDOT lost) in the first 5 days off from activity. After 10 weeks of inactivity, you've pretty much maxed out on lost VDOT when doing no other exercise (20% loss).

I decided to take this chart one step further and see if I could get a relationship between these values:

Screen Shot 2018-02-21 at 9.30.20 AM.png

Turns out the relationship is linear (again according to Daniels) and that the rate of loss with aerobic is half as slow as without aerobic. The rate being the value next to x in the formulas (-0.003 for without and -0.0015 for with). It's a nice representation to show that taking proactive steps with aerobic activity during a forced down period can greatly reduce loss in fitness over a long period of time.

So, Dopey was the last time I ran and then off until 3/7/18 because of injury. That's a total of 59 days. Simply plug in my former VDOT and adjust for 59 days off right? Well, not quite so simple for me I guess. I wasn't completely off during this time period. I also wasn't always biking. I also did some running for short spurts of time during this time period. So in my case, I needed to use his information and piece together my individual puzzle. I came up with the following "daily" adjustments.

First 5 days of inactivity = 0 change
After 5 days with no biking = -0.0030 daily change
After 5 days with biking = -0.0015 daily change

But what about when I ran for that short period of time? In my experience it takes me roughly equal to 2x the time off to fully be back in shape whenever I'd take time off post-marathon. If I use Daniels without Aerobic value (-0.0030), which would be what I would do after a normal marathon, and then determine what is the value of gains in order to be back in shape after 14 or 28 days of running.

Screen Shot 2018-02-21 at 9.44.02 AM.png

So per the calculations. If I were to take off for 14 days, I'd have a fitness of 0.9730 of prior VDOT. Then I needed to figure out what the rate of gain needed to be to regain 0.0270 over 14 days. That comes out to roughly 0.192. So if it took 28 days instead, then it would be a rate of 0.096. I decided to go with 0.192 (or 14 days to return to shape) because per my data (How long does it take for me to recover from a marathon?) that seems to be the case more often than not.

So, that leaves me with the following daily adjustments to VDOT over time:

First 5 days of inactivity = 0 change
After 5 days with no biking = -0.0030 daily change (loss)
After 5 days with biking = -0.0015 daily change (loss)
Running = 0.00192 daily change (gain)

I then went through the calendar and determined on each individual day whether I was off, biking, or running.

Screen Shot 2018-02-21 at 9.49.38 AM.png

1/7/18-1/12/18 = First 5 days off no change
1/13/18-1/16/18 = Continued no biking off period
1/17/18-1/25/18 = Restarted running again
1/26/18-1/28/18 = First 3 days off no change (went with 3 days because I'd venture to guess the loss would start sooner)
1/29/18-2/5/18 = Continued no biking off period
2/6/18-2/7/18 = Restarted running again
2/8/18 = First day off no change (again less of a hold period)
2/9/18-2/17/18 = Continued no biking off period
2/18/18-3/7/18 = Started biking

That leads me to this estimated adjustment of 0.9288.

Screen Shot 2018-02-21 at 9.54.35 AM.png

Next, I needed to figure out where my VDOT was prior to Dopey (or the time off period).

Screen Shot 2018-02-21 at 9.56.00 AM.png

-At best, I was in 2:58 marathon shape (or VDOT 54.2). I came to this conclusion based on the effort of running certain paces at the tail end of Dopey training.
-I estimated a likely VDOT of 53.0 by comparing by Dopey HM time in 2016 to my PR in a HM only a few weeks prior (which was a 4% difference). So my 1:30:35 Dopey HM was a 1:26:54 non-Dopey HM time based on what I had been able to do in the past.
-Using just my Dopey training pace which felt appropriate, I have a VDOT estimate of 52.7.
-And at worst using my Dopey 10k time (which was the best race performance of the weekend), I have a VDOT estimate of 52.1.

So adjusting each by 0.9288 gives me the following:

Screen Shot 2018-02-21 at 10.00.12 AM.png

A VDOT of 50.3 to 48.4 as an estimate. But this doesn't include a very important variable. These calculations assume I am of equal weight at Dopey and come 3/7/18. At this moment in time, that's not the case. I was 158 pounds entering Dopey weekend. Today (2/21), I weigh 164 pounds. My weight has been relatively constant since coming back from Disney. It started at 164 on the day we returned, fell to 160 in a week or so, and has been steadily maintaining between 162-164 since Dopey. I've tried my best to hold my weight constant even without exercise by being extra mindful (minus some delicious cake). But I definitely could have been doing a better job during this time period. Daniels has a weight adjustment as well. Simply:

(VDOT x Pre-Weight) / (Current Weight)

with weight in kilograms

So assuming I still weigh 164 pounds on 3/7/18, I get the following:

Screen Shot 2018-02-21 at 10.05.23 AM.png

So that's going to add to the motivation of making sure I try hard to get back to where I was weight wise to make the return to running easier. But what do these VDOT values really mean?

Screen Shot 2018-02-21 at 10.12.35 AM.png

Using all of these adjustment, I can come up with a reasonable pace scheme. Upon returning to running these paces should help minimize the chance for re-injury and trying to come back too aggressively. I'll use these pace estimates in addition to my feelings on effort to help guide me on a current fitness estimate. The other piece to the puzzle in addition to pace will be the time spent training upon returning.

Daniels says that equal time off to time easy is the best strategy regardless if you were doing biking/swimming or not (the lack of other aerobic influences the pace upon returning but not the training load). So if I was off for 50 days, then I need 50 days of easy running before I'm back to close to the same. Since I did some running during this period of time, I didn't feel 59 days of easy running was appropriate. I decided to use the timeframe from when I voluntarily stopped running (which was 1/26/18). This would be 40 days between 1/26/18 and 3/7/18. I've decided to go with a period of easy running of 6.5 weeks (45 days) with a possible return on 4/24/18 to normal training. The time period during the build-up, per Daniels, should be split as follows:

1/3 of time off at 33% mileage per week
1/3 of time off at 50% mileage per week
1/3 of time off at 75% mileage per week

These values are for runners taking an extended period of time off (like over 4 weeks). My peak week mileage was 69.5 miles. So that would be a goal of 23 miles for the first two weeks each, 35 miles for the 3rd/4th week, and 52 miles for the 5th/6th weeks.

So going through these numbers taught me the following (in case I encounter another extended period of time off):

-As much as 5 days off will have negligible effects on VDOT. Although it probably will take away from performance (if it's right before the race) just a touch because there's more than just VDOT.
-Discuss with physician immediately about alternative aerobic leg exercises. This reduces loss in running VDOT by half.
-Maintain weight during the time off as best as possible. A % change in weight is roughly equal to a % change in VDOT. So if you weigh 3% more after the time off, then you lose roughly 3% of VDOT. That could be the difference between a 3:09 marathon and a 3:16 marathon.
-Time off = necessary time easy upon returning.
 
-Maintain weight during the time off as best as possible. A % change in weight is roughly equal to a % change in VDOT. So if you weigh 3% more after the time off, then you lose roughly 3% of VDOT. That could be the difference between a 3:09 marathon and a 3:16 marathon.
Great read! Question, I weigh 173, mostly fat. Lol. 25 %BF. I plan on lossing 20 lbs of that Fat before my next marathon. My Vdot numbers currently puts me at 3.03 marathon time. Can I expect a nice time boost for losinv weight?
 
Great read! Question, I weigh 173, mostly fat. Lol. 25 %BF. I plan on lossing 20 lbs of that Fat before my next marathon. My Vdot numbers currently puts me at 3.03 marathon time. Can I expect a nice time boost for losinv weight?

Great question. The answer is simple and complicated. Yes, if you lose weight you are very likely to improve performance. But the weight loss has to be appropriate and can't sacrifice the training/muscles to get there.

So your weight of 173 and VDOT of 52.5 (3:03 marathon), is an absolute VO2max of 4.1 liters/min.

Absolute VO2max (in liters) = (weight in kg X VDOT) / 1000

If you were to instead weigh 150 pounds and maintain the absolute VO2max at 4.1 liters/min, then your VDOT would be 60.6 instead. A VDOT of 60.6 is a 2:42 marathon. So, in theory losing 23 pounds and getting down to 150 pounds AND maintaining your absolute VO2max at 4.1 liters/min would enable you to run a 2:42 marathon.

In order to maintain your absolute VO2max at 4.1 liters/min, the weight loss needs to be appropriate. Which means you do it slowly over time and that your height and body make-up justify the goal weight. Losing weight while training hard is difficult. In most cases, it's one or the other. So be mindful that losing weight during a peak "A" performance race could be costly towards the "A" race. So you're currently not in an "A" race training plan, thus now is a great time to try and lose weight.

My suggestion is to aim for a pound a week. A pound of weight lost is equal to 3500 calories. So run a deficit of 500 calories per day. If you consistently run a 500 deficit, then after 20 weeks you will have lost 20 pounds. I like to use MyFitness Pal in combination with the data from my Garmin in order to determine caloric intake, exercise calorie loss, and most importantly basal metabolic rate. In my experience, Garmin overestimates BMR and thus you lose weight at a slower rate. To hone in on BMR, use MyFitness pal and be under by 500 calories per week (or tell it you want to lose 1 pound per week and it will do the math for you). Then after 3 weeks, you should be down 3 pounds. If not, adjust your BMR calculation based off how much you have lost and try again. Keep doing it until you start losing at a rate of 1 pound per week. That's how I do it.
 
If you were to instead weigh 150 pounds and maintain the absolute VO2max at 4.1 liters/min, then your VDOT would be 60.6 instead. A VDOT of 60.6 is a 2:42 marathon. So, in theory losing 23 pounds and getting down to 150 pounds AND maintaining your absolute VO2max at 4.1 liters/min would enable you to run a 2:42 marathon.
I appreciate your thoughtful response to my question. I definitely will not try run a 2.42 even if I lose 23 lbs. Lol. That's just theory. I can however see that helping me Go sub 3. Maybe a 2.55. I like your suggestion of starting to lose the weight now before we get into that A race training. During training for a A race, I don't try to lose the weight. I basically maintain. Now is the time. I am so bad at tracking my food intake. I have tried and it works.i will start again. Wish me luck. Again, thank your for your time
 

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