Tuesday, 7 May 2019

Understanding race predictors - Riegel versus Tanda

Predicting the speed (or intensity) that can be maintained for different durations is a difficult subject that has concerned runners for many years. It has long been recognized that as the race duration increases the average speed that can be maintained decreases. This is not surprising since the higher the intensity the more physiological systems are out of steady-state and the faster they will fail.

What is interesting is that the 'average' person can be modelled reasonably well with a very simple equation. There are multiple forms of the equation but the most popular in running is the one Peter Riegel introduced back in the late 1970s/early 1980s. The equation is a simple scaling of one performance to another using an exponent, Whilst the value of that exponent has been discussed and argued about at length, most agree that the equation provides one of the better 'ball-park' values[1,2]. I don't intend to add to that discussion, but I do want to start from the premise that the formula does 'sort-of-work' and that it also represents a way of estimating what a 'maximum' effort might look like at a range of distances.

I have plotted Riegel's formula in the graph below (Figure 1) as the dotted lines for five different marathon preformances.
Figure 1. Average run speed plotted against distance for five different levels of performance and for two race predictors (Riegel dotted lines, Tanda solid lines). The line colours indicate marathon performance times (blue 3:30, green 3:15, yellow 3:00, red 2:45, black 2:30). The very thick purple line indicates the intercepts between the Riegel race performance and the Tanda prediction lines.

First, this graph is complicated for a number of reasons. But, the graph is worth a bit of effort since it encapsulates much of why people hit performance limits. Let me start by taking the example of the yellow dotted lines which is the Riegel line for a 3 hour marathon runner. The dotted yellow line shows the speed the 3 hour marathon runner might hope to maintain for a range of race distances. In a 5km race the runner should manage around 16 km h-1 and in a 15km race about 15 km h-1. The dotted line is simply plotting how a maximum 'race' effort scales with distance. What is noticeable about the dotted lines (which are for faster and slower runners - see figure legend for details) is that the maximum speed that can be maintained drops dramatically at short distances and then changes relatively little at longer distances.

Also plotted on this graph are the race predictions (solid lines) from the Tanda equation. Now here I have taken the liberty of playing with the 'meaning' of the axis labels. Whilst the x-axis is still distance and the y-axis is speed, they are the distance covered in training on an average day and the speed at which it was done. Again the colours match the Riegel prediction times. So, let's go back to the yellow lines. The solid yellow line shows you the average distance and speed you need to run each day to become a 3 hour marathon runner. You could run 10 km each day at 14 km h-1 or 5 km each day at 16 km h-1 or a mixture of the two. As long as you stay on that line (on average) for eight weeks, you should get the 3 hour marathon (actually it is a bit more complicated than that, but to a first approximation it will do). Now, the interesting observation is how the dotted line and the solid line relate to each other. If you train above the dotted line then you are doing an effort, each day, that is HARDER than a race effort. You must be doing the effort as interval training, by definition since you could not have kept up a faster run than your Riegel prediction. If you train below the line then you are below a race effort - each day.

Now, look at the thick purple line. That shows the trajectory for training by doing a race effort every day! If you want to become a 3 hour marathon runner you will need to race a 5km every day. If you want to be a 2:45 marathon runner (red line) you need to race 9km every day. Notice that for a 3:15 marathon runner and slower any race effort every day is more training than necessary to get that time.

So, the faster you are the closer you need to be to sustaining a race effort every day and the longer that race effort has to be. The benefit of running more miles is that you are training much slower than race speed. The damage is far less and the training is 'possible'. So, you definitely want to train below and to the right of the purple line.

Now the take-home message from this is that both the Riegel formula and the Tanda predictor are both race predictors using similar data - they are just different equations. For Riegel you put in any race and time but for Tanda you put in an 8 week average. As I have said before (but, it has not got traction) the Tanda 8 week period is just another race. It is the training race - a race with no defined distance or time but a race nevertheless.

The difference between Riegel and Tanda is that Riegel is the output of a short race effort whereas Tanda is the output of a long race effort - they work from opposite ends of the spectrum. The great thing about the Tanda equation is that you don't need to RACE before the marathon - you just use the training data you have (that is the training race). The second great thing about the Tanda equation is that it predicts from the very stimulus that makes you a marathon runner in the first place, namely the training. It is the bees-knees.

OK, there are other things you need to be aware of - and some of you will out-perform it by some margin - but the formula captures what it takes to train for a marathon. It is just running (and heat adaptation and growing large adrenals etc....but those are either previous posts or posts to come).

Tuesday, 30 April 2019

Can marathon performance be predicted? - Tanda and beyond

I, and others, have made great play of Giovanni Tanda's marathon prediction equation. We have promoted it's use, both as a predictive tool and as a way of shaping training. Yet, it continues to fail for many people - they head-off at what seems an appropriate pace and fail. Whilst some claim it is the execution of the marathon plan that is at fault, and others simply junk the Tanda equation, I think the problem may lie elsewhere. First, I think that the Tanda equation is one of the best equations to predict marathon performance. It is simple to calculate and of all of the equations that I have come across seems to get closest to predicting performance, especially once it is customised to the individual. But, it still fails and can fail spectacularly. Some of those failures are easy to predict because they involve obvious changes in physiology that the equation cannot know about. Colds and infections a few days before a race can wreck the possibility of a decent performance. But, even in the absence of these obvious problems the equation can still fail. And, we should expect it to do so. The statistics tell us it will. The equation was derived from optimal performances - from a dataset of races where a near flat pace was maintained. The Tanda equation (with some individualization) represents the best that can be hoped for. For the best to happen many things need to align - not just the weather, course, pacing, grouping of runners but also a myriad of internal physiological and psychological parameters need to be in the right place. Executing a plan based on 'the best' happening is risky. And, given the cliff edge drop in performance that occurs with even a modestly over-enthusiastic pace, the most likely outcome will be failure. Before Tanda constructed his dataset, a number of performances would have been filtered out. These were performances where the training went well but one of a number of problems occurred to result in a non-flat pace. The result being that the equation is not a fit of what is 'most likely' to be achieved, but what happens when things go well. What many runners want to know is the probability that the prediction will work - and how to finesse that function so that there is a high probability of getting something positive out of the event. Many runners adopt an all-in or should it be an all-out approach. They have a primary goal and adopt an uncompromising strategy to reach it. Modelling this on a pay-out basis would be $1,000,000 for achieving the A goal and $0 for missing it. It is a binary approach which will occasionally work. This is often seen as an heroic approach with the massive detonation or collapse as a sign of willingness to push for the highest level of achievement. I do not doubt this is the case - and respect those capable of committing to this - but, don't blame the science when it goes wrong. You could, however, blame the lack of science. Risk distribution within a race is something we all instinctively engage with. Several times now I have listened to runners justify the collection of gels on their belts at the start of a marathon. Many believe them necessary, but the interesting ones are those people who suspect that the gels probably aren't - but, why take the risk of not having them? When running drafting is common - the closer the better. Now, there is a risk-based decision. How close do you get? When do you over-take? How close to the course edge can you run? The risk profile is important in knowing if the decision being taken is sensible. Your stomach rumbles and the sensations are present - but, do you stop at the portaloo or press on? At the London Marathon the risk is very different to that at a rural event - our nervous systems convolve probability and risk to arrive at an optimal strategy with no graph-plotting involved. Many risks we take, or should they be 'cautions' are instinctive with almost no proper conscious analysis. The problem here arises when the risk is non-linear, highly non-linear. The analogous game that comes to mind is what I think was known as 'Shoffe-Groat'. It can easily be played with a few coins and a table. The idea is to launch your coin towards the other end of the table, getting as close to the edge as possible. The winner is the person who gets closest to the edge without falling off. He or she takes all of the money either on the floor or on the table. Now, in the case of marathon running few people are playing against other players - people are competing with their PBs. By definition those PBs were the best performances - the ones where most things went right. Of course, if you don't have many performances, you may not be close to the limit. But, for anyone who has given the event a good few tests they are going to be close to the table-edge. Of course additional training can make the 'distance' between a previous PB and the failure that is represented by dropping-off the table a bit bigger. But, the space that you are trying to nestle into is tight. The odds are stacked against you. Now, the Tanda prediction - which worked for you before - is getting ever more difficult to achieve. The probability of success is dropping the more you train and the faster you go even though the prediction of what might be possible is correct - it is now simply that the number of times that the equation will 'work' is much smaller. Here is lies an interesting observation. The Tanda equation does not tell us the probability of success. It tells us that people who trained in a certain way have achieved certain times. But, we don't know how many times they have trained that way and failed. It is almost certain that the Tanda equation has a much higher 'success' rate at lower performance times than faster ones. And, this is what is misleading about it. Just because the equation worked before, don't rely on being able to use it to extrapolate your new training space to a faster PB. To be safe you will need to push your training further - that is your PB race pace needs to be executed at a level of fitness which is greater than what you are trying to do. Of course, you may get lucky and get the performance predicted by training. But, a more likely scenario is that you will get your PB and an underperformance relative to the equation - at least until you repeat it a few times. There is an in-race way of doing exactly this. It is the planned negative-split. Start the race somewhat slower than your fitness might warrant. At the appropriate time - and this needs discussion as to when this is - you ramp-up the pace carefully. If this is 'your day' you will sustain the ramp and get a very mildly disappointing time - not the best you could have done, but if you have put in the 'over-training' it will be the PB you wanted. If this isn't your day the ramp won't happen the best you will get is a flattish pace - it is the finishing time you deserved from your fitness and your 'luckiness'. As Alberto Salazar is claimed to have said; “If anyone goes out at a suicidal pace, I’ll probably sit back”.

Monday, 22 April 2019

Marathon performance and junk mile calculator (Tanda race predictor)

Race predictor Version 0.2
Age: Male Female
Previous race distance:
Time achieved (h:m:s):
Pace (mm:ss):

Pace: per km per mile
Distances: Standard Custom

Average weekly distance:
Average weekly pace:

Monday, 28 January 2019

Treadmill and road running - equivalent pace estimations

The effort expended running on a treadmill differs from that on road for a number of reasons, the main one being the lack of wind resistance. It is often stated that a gradient, which is easily set on most treadmills, of between 0.5-1.5% makes treadmill paces equivalent to running on a flat road. Of course, a single value of gradient cannot work for all paces since fast runners will experience a greater wind resistance on the road. Fast runners must therefore require a greater gradient on a treadmill to create an equivalent effort to that experienced when moving through air quickly on road. Equally, we might expect a zero gradient to be required for slow runners as they experience very little wind resistance.

Creating equivalent pace tables, for comparison between running on the road and treadmill, is not only useful for setting the right gradient to mimic a road-based effort - such tables might allow runners to trade treadmill-speed with gradient. This has some important implications, not least making high intensity efforts on a treadmill safer. If one could use gradient increments, in a semi-quantitative way, to replace speed increments then near maximal efforts become possible without recourse to harnesses and large amounts of padding.

If you Google for such tables what pops-up are mostly straightforward pace and speed conversion tools. There does, however, appear to be one table that might provide some better data and that is from HillRunner. That table is in miles per hour and ranges from gradients of 0%-10% and speeds from 5-12mph. In the FAQ Ryan Hill mentions that the data came from some students who were making oxygen measurements both on a track and treadmill, however, no references exist. This is not 'published' work in any formal sense. But, in all likelihood, it is a decent starting point.

In the FAQ Ryan Hill states that the data does not 'nicely' fit a formula and that he cannot see how a 'meaningful' calculator can be produced. I found this a slightly odd statement. My experience is that physiology is often well-modelled by simple maths, and running on a treadmill should be relatively simple to model. Looking at the table of data I wondered if using pace data was what made the maths appear to be 'complicated'. So, I attempted to produce a model. My first step was to convert the pace values to something likely to be easily modelled. We know that oxygen consumption values tend to scale linearly with speed, so that is where I started. I choose meters per second (m/s), although any distance and time unit would have done.

I then plotted the relationship between treadmill speed and the equivalent speed on road, given by the table, for each gradient. What was apparent was that for any one gradient there was a very good linear fit between treadmill speed and road speed (r2>0.99). That surprised me - I was expecting some kind of curve due to wind resistance. But, the straight-line nature of the relationship made the model easy to construct since it was now a simple matter of deriving an equation for the parameters that determine each straight-line fit for a given gradient. Plotting the straight-line fit coefficients (gradient and offset: y=mx+c) against the treadmill gradient revealed that they could be modelled well by second order polynomials. In fact plotting my modelled coefficients versus those calculated from the linear fit showed a linear correlation of r2>0.99999 - so, the model was able to predict the real values very well indeed. In most cases the model calculation of equivalent pace was within 0.5s per km of the table value - and at worst 1.5s away for a few values. The difference between this model and the table was 0.02 seconds per km with an SD of 0.33 seconds per km. That is a pretty good fit.

Here is the formula (metric) where treadmill speed is in kph and grade in percent (i.e. 1% is 0.01) which returns equivalent road pace in mm:ss per km as fractions of 24 hours (which is Excel's built in time unit).

Equivalent Road Pace =0.01157/(Speed*(Grade^2*0.72+Grade*0.0528+0.266)-Grade^2*29.27+Grade*13.656+0.006)

For those who want a 'turn-key' solution or to see the fitting, here is a link to the spreadsheet:
(This link will become inactive after 28th May, 2019 - after which you will need to email: cjs30@cam.ac.uk for a new link)

If you just want to convert a treadmill speed (kph) and gradient to the equivalent road speed then this is the formula you might want to use:

Road speed (kph) =Treadmill Speed*(Grade^2*2.59+Grade*0.19+0.958)-Grade^2*105+Grade*49.2+0.0216

If you would like a bespoke table (either metric or imperial) over a set of gradients, let me know and I will endeavour to produce one (if it makes sense to do so - i.e. it isn't a vast extrapolation).

Friday, 23 November 2018

Heal Force Extraction

Heal Force data extraction utility

This script will extract heart rate data from the Heal Force Prince 180D .DAT (or .ESK) files.

You will need to install and run the ECG Viewer Manager program to import the data from the device into your computer.

Choosing a file then use the 'Select' buttons followed by Ctrl+C to copy the data to the clipboard for export.

[Notes: ECG State: 1=below 0, 2=above 0, 129=QRS. A 300 Hz sampling rate is assumed. There is a 512 byte block of data that is ignored which probably contains useful information...]

Friday, 19 October 2018

Preparing for a fast marathon is all about winning the training race

Winning the Training-race

Yet again I am trying to get into decent shape so that I can run a fast marathon. But, at the age of 52, running a sub-2:45 marathon is looking increasingly unlikely. I was not a runner as a kid and only started running a bit less than 10 years ago. I have completed 41 marathons but have yet to break 2:45. I know that to do it I will first need to win the training-race. By training-race I don't mean win a race in training, or even beat someone else or a previous time of mine on a training run. The training-race is the long period leading up to a marathon where the performance (hence the term race) is the main determinant of the marathon race time.

Redefining the meaning of race

A race is usually an event with a single fixed parameter. Most commonly races are of a fixed distance (e.g. 5K, 10K, half marathon etc). A variant of the fixed distance race is a race of poorly defined distance but all runners complete the same course. Cross-country races are a good example of that. Other races are of a fixed time where the aim is to cover as much distance as possible such as a 12 hour or 24 hour race. The training race is a race of undefined distance and undefined time that starts about 6-8 weeks before the 'real' marathon race. Whilst the training race seems a hard one to win, because neither the distance nor time are defined, your performance in that race is critical - it will determine how fast you can run the marathon you are training for. Most people don't realize that training is a race because the rules of the race aren't obvious - few coaches ever explain what the rules are. There are some parallels here with other races or competitions where the rules are unclear. The caucus-race (Alice in Wonderland) is such a race where everyone runs around in circles for an undetermined length of time before everyone is declared the winner. The rules here are simple, as long as you are 'in the race' and running around you will be one of the winners. In other competitions the rules are more complicated and less obvious, but nonetheless exist. Mornington Crescent is such an example.  Here the players submit to the pretence that rules exist - which, formally, they don't. Any player can win, at any time by saying; "Mornington Crescent". But, to achieve a real win the player must delay saying Mornington Crescent until it can be done so with great comic effect. The suspense generated by prevarications has to be carefully calibrated, in response to audience and player reactions, for the comic effect to work. The rules here are complex but the great comedians have an innate understanding of them.

Performance in one race predicts performance in another

We know that many types of human 'performance' can be predicted or estimated from other similar performances. This is a wide ranging observation. Someone who has an organized desk at work is also likely to have an organized filing cabinet, someone who wears expensive suits is likely to wear expensive shoes. Of course, there are going to be contradictions - but, the saying; "If You Want Something Done, Ask a Busy Person To Do It" has a good deal of truth to it. Someone who does a lot is likely to get a lot done. In many endurance sports we use this form of extrapolation to estimate race performances over different distances. In rowing the obvious example is Paul's Law whilst in running it is the Riegel formula. They are both equations that allow performance at one race distance to predict performance over a different distance. This form of performance-equivalence has become embedded within running in the form of age-graded performance tables. These tables work slightly differently from the Riegel formula in that they are based on the World Record performances at different distances of men and women of different ages. By way of example, as a 52 year old male who has recently completed a 5km road race in 20 mins, I would be ranked as a 73.3% age-grade. Assuming that the age-grade is some form of measure of my aerobic fitness then it would predict that I could run a 3:13:42 marathon - since that would also give a 73.3% age-grade for a 52 year old male. The Riegel formula is a little bit more aggressive, predicting a 3:11:49 marathon from a 20 min 5km. There are plenty of other examples of such predictive formulae that take one race effort and estimate performance over another distance. But, these races are single efforts - they take place at one point in time and are over relatively quickly. Would a formula that takes race performance over a longer period not be more accurate? This is where the training race becomes useful. It is not just a race we all do before a marathon (whether we intend to or not), it is also the training stress that determines our performance.

Defining the training race

Many scientists have tried to define what we might refer to as the training race - that is the combined set of parameters that can be used to predict marathon performance. Many of these predictors are just correlates of performance not causative. For instance, amongst the elite field having dark skin seems to correlate relatively well with performance. Some mistake correlation with causation and then attempt to justify the correlation with spurious assertions. The dark skin issue is just such an example where dark skin becomes the assertion that some athletes are genetically-gifted. Science seems to differ. There are very few genes that have been associated with endurance performance. Of course genes are important - but, the probably only determine a very small fraction of performance, and the number of important genes is likely to be very large indeed.
There are some factors that are both correlative and causative. Weight is a decent example of that. We know that most fast marathon runners are fairly light - and of course being light does not mean you will be able to run a fast marathon. But, if you are training for a marathon losing excess fat - again within reason - will probably result in better performances. It is very simple energetics - the less you weight the faster you travel for a given power output. So, weight probably belongs in the 'formula' that makes-up the definition of the training race. Marathon training will involve some optimization of weight, but it is not the primary determinant.
Of the attempts to correlate training performance with race performance the best that I have come across was a relatively short paper by Giovanni Tanda in 2011. In that paper, which I discuss elsewhere, he proposes that a combination of the number of miles run in the 8 weeks before the marathon and the time it took to run those miles is a good correlate of marathon performance. So, here we have a definition of the training race. It is not a fixed distance, or a fixed time but the output of a formula which includes both distance and time. This is not as complicated as Mornington Crescent, it is a simple collapse of two variables (distance and speed) into a single metric which is the marathon prediction. The winner of this training race is the person that can push this formula to the best marathon performance prediction. By that I mean, when training we need to understand that formula and stop thinking about either just speed or just distance and think about the way in which the two are mathematically combined to produce the marathon prediction.

The Training-Race - an eight week event of undefined distance and duration

So, all of this might sound a bit like waffle, but it isn't. There is a race to be won in training. It is real and we are all taking part. It is a race that determines the performance in the marathon. The winner of the training race is also, most likely, going to be the winner of the marathon. The training race is won by running as far as possible and as fast as possible for 8 weeks before the marathon. You can calculate who has won by putting the average distance and speed into the Tanda formula. The Tanda formula contains within it the mathematical relationship that governs how speed and distance trade. The person with the fastest predicted marathon time is the winner. They have pushed to two parameters (speed and distance) as far as possible. Of course, how you do that is the key question - how do you trade speed in training with distance. Is it better to run another 1 km fast or 5 km slower? These things can be calculated.

[Hastily written - due to be edited 19th Oct, 2018]