Putting Banister To Bed

 

Graph of the Fatigue, Fitness, and Form the Banister model predicted for me based on my training over the the last few years.

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I have blogged a lot about the Banister model. At the bottom of this post you will find a list of my earlier posts on this topic. The input to the Banister Model is daily training Load, where Load is a combination of how long I ride (in minutes) and how hard I ride (which I calculate from my heart rate.) The output of the Banister Model is predicted performance a.k.a. Form. (Think of this as perFORMance.) How well does that prediction match my actual performance? In my most recent post on this topic I said "I have been using the Banister model for more than two years now and it certainly has not been perfect at predicting the impact of my training on my cycling ability, but I have the impression that it does give me hints that are helpful in combination with what my body tells me in optimizing my training." That evaluation is both subjective and qualitative. The management consultant Peter Drucker is famous for his saying "If you cannot measure it, you cannot improve it." In this post I am going to discuss my efforts to quantitatively compare my performance to that predicted by the Banister model.

I have all kinds of subjective impressions about my performance. For example, last May I rode the 60 mile long Art of Survival with my friend Roger and felt that my performance was poor because, despite the fact that I relied heavily on the eAssist of my eBike and despite the fact that he reported that he had not had the opportunity to train enough before the event, I found it very difficult to keep up with him. Obviously that is not a metric I can use to determine if the Banister Model's prediction of my performance is accurate. What could I use? Can I look at the scientific literature concerning the Banister Model for guidance on a metric? I have read a few papers on this topic and the kinds of metrics they use tend to be things like maximum power output during a five minute time trial. (See, for example, this paper.) What I am trying to optimize is average speed during a five hour group ride which is a very different thing. The former is a measure of fast twitch muscle strength whereas the latter relies much more on slow twitch muscle fibers. It would be like trying to determine how strong your legs are by measuring your arms. I am unenthusiastic about using such short term metrics.

I could use a longer time trial to assess my Form. The problem with that is, in my old age, a long time trial is tiring to the extent that the very training I am trying to optimize is disrupted. It is similar in concept to crash testing a car if you only have one car. After the test, you might know the car was safe, but unfortunately it is now destroyed so that knowledge is of no value. So what could I measure that would be relevant to my training goals and would also not disrupt my training? If you look at my recent posts, it's obvious that I have been hoping to use the average speed at which I ride my training rides for that purpose. For many reasons, that is a very imprecise and subjective measure but back in 2021 I did a statistical analysis that my speed on selected subsets of these rides might be useful nonetheless. For this post, I used my speed on a subset of rides all of which were on my Cañada route, where the level of effort I attempted during ride were all the same, and the bicycle I rode was the same. This is how the speed on those rides compared to the performance predicted by the Banister model:

As is shown in this graph, the Banister has essentially no ability to predict my speed on a Cañada ride. R², shown at the top of the graph, is a measure of predictive power that varies between 0 and 1, where a value of 1 means perfect prediction and a value of 0 means no prediction. The value of 0.001 measured here is about as close to 0 as one is likely ever to see.

Why is the Banister model not working for me? There are many plausible explanations, but before I get into them, I think it will be useful to say a little more about how the Banister model works. As noted above, the Banister model takes as its input the Load of each of my bike rides. It then uses that to calculate two hidden variables, Fitness and Fatigue. I call these variables hidden because there is no way to measure Fitness and Fatigue on their own, instead they are used to calculate Form (performance) which can be measured. To calculate Fitness and Fatigue, Banister uses two constants called k1 and k2. It multiplies Load by k1 and adds it to Fitness and multiplies it by k2 and adds it to Fatigue. In modern usage, k1 and k2 are often customized for each athlete but out of the box, the Banister model sets k1 = 1 and k2 = 2 and those are the values I am using. If this was all there was to the model, Fitness and Fatigue would just keep increasing forever. However, because we know that Fitness and Fatigue decrease over time, every day those accumulated values of Fitness and Fatigue are decreased exponentially. Specifically:

FatigueToday = FatigueYesterday x e^-1/Ta

FitnessToday  = FitnessYesterday x e^-1/Tb

Ta and Tb are two more constants whose value can be customized to the athlete, but out of the box, have values of 15 and 45, respectively. I use these out of the box values, and as a result, my calculated Fatigue decreases by half after 10 days and my Fitness decreases by half after 31 days.

Finally Fitness and Fatigue are used to calculate the output of the model which can be measured as follows:

Form = Fitness - Fatigue

...where Form (perFORMance) is related to how fast I can complete a ride. And that is what is not working for me, the Form I calculate has nothing to do with how quickly I complete a ride.

There are reports that Banister model and the related, widely used Training Peaks software package do work for many athletes so this is a problem with me, not with Banister. Given that, I can now turn to the question of why.

1) Maybe the Banister model is not working for me because my training is too constant.

The idea here is that I try to plan my training so that I ride my Cañada rides on days when I am fairly well rested. Thus, if I never vary my Load and resulting Fatigue much, I cannot expect my ride speed to vary much either; what looks like a lack of correlation (low R²) might be a lack of variation in my level of Form caused by a lack of variation in my Fatigue on the days that I measured my performance. It is not that the Banister model cannot predict my ride speed, rather it is that I never gave the Banister Model anything to work with.

Consistent with this idea, if you look at the graph at the top of this post, it looks as if Form doesn't vary much; it is always uniformly high. This is a bit misleading; Form on that graph uses a different Y axis than does Fitness or Fatigue. (I did that to make it more visible.) In fact, over the set of suitable Cañada rides, Form varies 7-fold from a low of 114 to a high of 765. On the other hand, if I look at all days, not just the days I chose to ride a Cañada ride, the variation is 43-fold, from 21 to 894. Perhaps if I had attempted a Cañada ride on a day where my Form was 21, I might have seen a more dramatic effect on my speed.

2) Maybe the Banister model is not working for me because of confounding factors.

If Point 1 were the whole problem, we would see that ride speed doesn't vary much. In fact, it varies between 9 and 12 miles per hour, a range that feels like a big difference to me. If changes in the Banister-predicted Form, Fitness, and Fatigue don't explain this, what does? As I have noted before, I often feel tired after a stressful day, even if that stress is mental rather than physical, a day when my babysitting responsibilities are particularly heavy, for example. Depending on how large the impact of non-cycling stress is, this could obscure the effects of my training.

3) Maybe the Banister model is not working for me because training speed is a bad metric.

In all my reading, I have never come across anyone who has attempted to use training speed as a metric in the way I have. Maybe there is a reason. Coaches recommend time trials as a metric to measure Form. One aspect of a time trial is that, because the athlete is riding as fast as possible, some confounding factors are eliminated. When I go for a training ride, I might be slow because of the Fatigue from an earlier ride or I might be slow just because I am not in the mood to go fast.

4) Maybe the Banister model is not working for me because I have not customized its constants.

Most current writing about the Banister model recommends not using the out of the out of the box constants but rather fitting these constants to the data from each individual athlete. I am working on software to allow me to do that, but to date, have not completed that work and don't know if or when I will. It is possible I will complete this software, fit the constants, and all of a sudden the Banister model will start working for me. If that happens, I will post about it.

5) Maybe (gasp!) the Banister model is wrong. (Not likely, but hear me out.)

There is a lot about the Banister model that doesn't make intuitive sense to me. It is my understanding that most coaches and exercise scientists believe that it is important that an athlete not do a workout (at least a hard workout) until that athlete has recovered from the previous workout. What "recovered" means varies, but at a minimum, it is when their Form has returned to what it was before the workout. According to the Banister model using the out of the box constants, that takes 16 days. A more stringent version of this rule is that "recovered" means until an athlete's form has peaked. According to the Banister model, this would take 39 days. Both of these numbers seem totally bonkers to me. Similarly, I am puzzled that following any reasonable training program means that, according to the Banister model, Fatigue always remains high. As I was laying awake thinking about this one night before bed, I asked myself what seemed reasonable to me. It seemed to me that a linear model of recovery might better fit my experience than the exponential model of Banister, that my Fatigue would be reduced by a fixed amount each day until it was gone entirely. But by how much each day? My experience has been that it takes me two days to recover from a Cañada ride, so I set up a model where my Fatigue decreased by that much. When I fit the same set of Cañada rides I used above to test the Banister model, I again found no correlation between my level of Fatigue and my speed on a ride. However, I remembered my post from last January where I found that the correlation between heart rate and ride speed improved dramatically when I looked at rides over the course of a few months rather than over the course of a few years, so I tried again, using a shorter time frame. In addition, to improve my chances, I used a time frame during which my predicted Fatigue changed substantially. Here is what I found:

An R² value of 0.229 is very unimpressive and not very useful, but it is a lot higher than 0.001. But that is an unfair comparison, my Linear Fatigue only had an R² value of 0.009 when evaluated over all the Cañada rides. What if I looked at the Banister model over the same reduced time frame? It did improve,  with an R² value of 0.079 for Banister Fatigue and 0.082 for Banister Form but not to a degree to be useful.

Conclusion:

For some unknown reason or reasons, the Banister Model is not able to predict my performance. If that changes, I will revisit the subject, but until then, I am through blogging about the Banister model; it's time for me to put the Banister Model to bed.

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Banister Posts:

• "Modeling Fitness, Fatigue, & Form" posted December of 2021
• "My Fitness, Fatigue, and Form" posted May of 2023
• "Cycling Career Saved" posted July of 2023
• "Update on the Banister Model" posted October of 2024

Winter Break

In the blog post I published at the beginning of December, I promised "I will do my best to maintain as much fitness as I can given the weather and will refocus come February 2025." I was probably a bit overconfident in picking February as the precise time when the weather would improve, it is March and the weather is still sketchy, but other than that I feel like I am more or less doing what I had promised, and I will talk more about that below. However, I want to underline what I assure you was a deliberate pessimistic tone to that promise; '... do my best ... given the weather ...'. What's that about?

The Weather

California has a very strong wet season/dry season pattern. During the last seven years, the wet season has run from some time in November or December through some time in February or March. If you look at my cycling log, the impact of this seasonal pattern is unmistakable. My goal for 2024/2025 was to reduce the impact of the rainy season on my fitness level.

Weather impacts my cycling both directly and indirectly. It impacts my cycling directly because, for safety reasons, I don't ride outdoors when the roads are wet. It impacts my cycling indirectly because I know that there will be days that rain prevents me from riding my scheduled ride making it unrealistic to try to work towards any goal that requires a fixed schedule. During the rainy season, my goals have to be both more modest and more flexible, I just try to do the best I can to somehow do enough cycling to maintain my health. This year, the schedule I came up is as follows:

• When the weather cooperates I ride my Cañada route, 17 miles, 90 to 100 minutes, three times a week and recovery rides on my trainer, 30 easy minutes, two times a week, a schedule I referred to hereafter as my Outdoor Schedule.
• If it rains once or twice during the week, sometimes I can move my rides around so I can still stick to the schedule above.
• When I can't just work around the rain, when it rains every day, for example, I ride on my indoor trainer, and therein lies a story.

My Best

I am a huge Clint Eastwood fan, and one of my favorite of his lines is "A man's got to know his limitations." As is the case for many people, a lack of willpower is responsible for much of my suboptimal behavior. I am of the belief, a belief I think most psychologists would support, that simply trying to conjure willpower out of thin air is doomed to failure. Rather, one must treat willpower as a limited resource and deploy it to best effect. I find riding on my trainer boring at best and miserable at worst. The harder I ride on the trainer, the less I can tolerate it. Thus, in the interests of preserving willpower, this year I worked to find routines I could do on my trainer that required a minimum of willpower while generating a maximum of fitness.

I originally set up my trainer for recovery rides, short rides at low intensity (Zone 1*) which have as their purpose facilitating recovery from an earlier, hard ride rather than generating fitness on their own. I was inspired to do this when I moved into the well-named Emerald Hills; those hills made low intensity rides on the road impossible. I find the trainer extremely boring so I originally assumed that recovery rides was all it was good for. This year, I decided to reconsider if I could also use that trainer as a way of dealing with bad weather. The key was not letting Best be the enemy Good. While it is true that given my limited tolerance for boredom meant that my trainer could never be a complete replacement for rides on the road, perhaps there were rides I could do on the trainer that would be better than an uncalled for recovery ride. 

I had previously found one possibility, my Gillen Interval Ride, six sprints in Zone 7. During the last few months, I have found another. While doing the riding that lead to my Counting Talk Test post, I convinced myself that a ride on my trainer in a 71" gear at 70 RPM was a legit Zone 2 ride while at the same time not being that much more unpleasant than a recovery ride at 55 RPM. Thus, on a day where I felt that a recovery ride wouldn't do, I could simply up my RPMs. To be honest, this is still not a great workout but it is much better than nothing and better than a recovery ride. Best of all, this ride is quite sustainable, I can ride it six days a week. If I am feeling especially motivated, I found I could increase the length of that ride from 30 minutes to 60 minutes, doubling the benefit. However, I confess that by the end of those 60 minutes my willpower is exhausted such that I would find it difficult to do more than one of these in a week. So, a sustainable schedule is six Zone 2 trainer rides a week, five of them 30 minutes long, one of them 60 minutes long. Hereafter, I will refer to this as my Indoor Zone 2 Schedule. By way of comparison, the Gillen Intervals take me about 45 minutes to complete and again, I can only manage one of these a week. So my final of the three schedules discussed in this post is five 30 minute trainer rides in Zone 2 and one Gillen Intervals ride, hereafter referred to as my Gillen Schedule.

Sometimes, depending on weather, I do a mix of my outdoor schedule and one one of these trainer schedules. Finally, I occasionally break out of my rut and do something altogether different, but for the remainder of this post I will focus on the three basic schedules described above, my Outdoor Schedule, my Indoor Zone 2 Schedule, and my Gillen Schedule.

Before moving on, I would like to share a thought: I am very lucky to have found outdoor cycling, which I can do most of the year, as a form of exercise I enjoy. Even on a day that I am not in the mood for a ride, a 90 minute outdoor ride is more pleasant and easier to complete than an easier (lower intensity) 30 minute ride on my trainer, and when the weather is nice and I am in a mood to ride, a 400 minute ride can be quite fun.

How Did I Do?

My goal was to do the best I could, given the weather, to cycle enough to maintain my health. Back in 2022, I blogged about cycling for health, describing routines recommended by Coach Hughes, the coach I follow, and by the Medical Community. I am not going to repeat that post, so if you are interested in the details, look there, but briefly, both recommend a Minimal Schedule and an Optimal Schedule. (Coach Hughes also recommends a Super-Optimal schedule which is well beyond my reach so I will speak of it no further.) 

My Outdoor Schedule exceeds the requirements of the Medical Community's Optimum Schedule and Coach Hughes Minimal Schedule. It does not meet Coach Hughes Optimal Schedule but it comes close, it checks all the boxes and has about 80% of the recommended minutes.

My Indoor Zone 2 Schedule exceeds the Medical Community's Minimal Schedule and has about 70% of the minutes of the Medical Community's Optimal Schedule. Coach Hughes is very prescriptive in terms of recommending a specific number of minutes at specific Intensities, but if I can be allowed to count minutes in Zone 2 as minutes in Zone 1, then this schedule meets Coach Hughes minimal schedule except for the minutes in Zone 3. In my opinion, this counts as quite close. However, it comes nowhere near Coach Hughes Optimal Schedule. Clearly, this schedule is way better than nothing and is way better than what I have done in prior years but is clearly less desirable than my Outdoor Schedule.

My Gillen Schedule is the trickiest to compare in that neither the Medical nor Coach Hughes recommendations anticipate the High Intensity Interval Training (HIIT) that is central to this schedule and so I have to estimate some equivalences to make that comparison. For comparison to the Medical Schedule, I am going to use the equivalence claimed in the original Gillen et al. paper that one minute of HIIT is equivalent to 45 minutes of Moderate Intensity exercise. Using that equivalence, my Gillen Schedule easily exceeds the Medical Community's Minimal Schedule and has about 80% of the minutes of the Medical Community's Optimal Schedule making it a bit better than my Indoor Zone 2 schedule. My Gillen Schedule comes nowhere near Coach Hughes Optimal Schedule. Compared to his Minimal Schedule, the total minutes, given reasonable equivalences, is pretty close. I would say it comes about as close as my Indoor Zone 2 schedule but interestingly, deviating in the opposite direction. My Indoor Zone 2 Schedule is missing High Intensity and my Gillen Schedule is missing Low Intensity. This might suggest some mix of these two schedules could be my best compromise for maintaining my health.

In summary, doing the above analysis has left me pretty satisfied that I did a reasonable job this winter of working around both the weather and my distaste for riding on my trainer with schedules that maintain my health. How does this year compare to last year?

Compared to this same time last year, the amount of riding I have been doing has gone up but my speed has gone down. I compared December 2023/January 2024 to December 2024/January 2025. Last year I averaged 208 minutes per week of riding as compared to 291 minutes a week this year. To compare speed, I considered rides on the Cañada route where my intention was a Pace ride (Zones 2 and 3) and where I completed the ride on my Bianchi Volpe (no eAssist.) Last year, I rode 11 rides that qualified and completed them at an average speed of 10.7 miles per hour. This year, I rode 10 rides that qualified and completed them at an average speed of 10.1 miles per hour. There are a lot of ways to look at this data to try to explain away this decrease, and to be honest, I don't think my speed has really decreased by 0.6 miles per hour in just one year, but I think there is no doubt my speed has been decreasing over the last several years, and that decrease does not come from a reduction in training.  This is illustrated in the next two graphs.

The first graph illustrates the drop in my ride speed since my move to California in 2017. This is one of several analyses I have done which show my speed falling over this time period. I have posted about this before. In this analysis, I collected the highest speed on the Alpine route for each month since my move and plotted that as a function of time:

The blue points connected by the jagged line are the data. The red line is the best fit to that data. The R² value of 0.34 suggests that about 34% of the variation is my monthly maximum speed can be explained by its decrease over time and that about 66% is something else. The probability that there has been no decrease in my maximum speed over time is very low. Having said that, what has caused that correlation is open to many explanations. One obvious explanation is that for whatever reason (e.g. increasing boredom) how much I have trained has decreased over time. The next graph addresses that possibility:

Here I have plotted the total number minutes I have cycled each week since my move to California. Again, the data is in blue, the best fit line is in red. Although my training has varied a lot week to week, on average, there is no correlation of that with time. Of course, there are many ways my training could have and has changed that would not be reflected by time on the bike and I have looked for and will continue to look for changes that might be relevant, but this does suggest that my decrease in speed is not due to a change to my training. The next most obvious explanation is that my decrease in speed results from aging. Eight years is a significant length of time at my age so that certainly is a reasonable suggestion.

Whatever the cause, this decrease in my speed has been very impactful. I feel like I can no longer keep up with my friends Roger and Dave even with the help of my Orbea Gain eBike. Not being able to ride with them eliminates what had been a great source of inspiration.  In the past, the need to get ready for rides with Roger and Dave gave me the inspiration to ramp back up come spring, but absent that, what do I have to look forward to this year? Last year, I compensated for that a bit with my Birthday Ride. However, as I noted at the time, that seems like that was a one time thing rather than an ongoing source of inspiration. Coming up with a new source of inspiration, with new ways to have fun on my bicycle, is perhaps my most important cycling-related goal right now.

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* How hard I ride, e.g. how fast, can be expressed in terms of Training Zones, Zone 1 (very easy) through Zone 7 (very hard.)

The Counting Talk Test

Back in November, I reviewed a series of videos from the online cycling magazine GCN. In that review I mentioned that the authors felt that heart rate was not a good way to identify one's Zone 2, but that breathing rate was. The criterion they suggested for the top of Zone 2 was the point where conversation is forced but possible. This metric is used, in various forms, by many coaches and is called the Talk Test. I do not find the criterion used by GCN easy to use because it is vague; what exactly does it mean for conversation to be forced but possible? Recently, I encountered an alternative version of the Talk Test which I found much easier to use, a version called the Counting Talk Test.

The Counting Talk Test (CTT) is a way of quantitating the Talk Test. In the Counting Talk Test, you exhale, take a deep breath, then count "One one thousand, two one thousand, three one thousand..." until you cannot count one number higher without taking a breath. This measurement is made while resting and then during exercise. The results of the Counting Talk Test is expressed as the percentage of number a patient can reach during exercise relative to what they can reach while resting. The table at the top of the post shows the results of my first attempt to use that test. What I did was get on my trainer, set the gears at 61", ride at 60 rpm for five minutes and then executed the CTT. I then increased the gear to 71" (maintaining my cadence at 60 RPM), rode for five more minutes and then repeated the CTT. I repeated this for  80". 91", and 106". At 106" I was only able to continue for 2 minutes. I then reduced the gear to 71" and measured CTT after 5 then 3 minutes. As I acquired more experience with the CTT, I have gotten better executing it. One consequence of this is that I have decided that my resting CTT is closer to 23 counts rather than the 16 counts measured in that first test, so I now calculate my percentages relative to that constant value of 23.

I encountered the Counting Talk Test in the Journal of Exercise Physiologyonline (JEPonline) Volume 5 Number 1 February 2002. This paper, and in fact every paper I have encountered that investigates the Counting Talk Test, considers it in a medical context rather than a sports context (which is why I used the word patient rather than athlete in the previous paragraph.) The medical community mostly uses a three zone Intensity system, Easy, Moderate and Vigorous, as opposed to the seven Intensity zone (Zones 1 through Zone 7) that the coach I follow, Coach John Hughes, uses. However, over the years I have come to the conclusion that the top of most coaches' Zone 2 and the top of the medical communities' Moderate exercise zone are both equal to each other and equal to the aerobic threshold. Since locating my aerobic threshold is probably the most important use I have for the Talk Test, the difference in training zone systems was not a big limitation. What was a big limitation is that the authors of this paper chose not to distinguish between Moderate and Vigorous exercise but considered the two together (they reported a value for the Counting Talk Test of 55% at the bottom of Moderate Exercise and 30% at the top of Vigorous Exercise.) The value I needed, the boundary between Moderate and Vigorous exercise, was not reported. A search for a scientific study that did report that value lead to Frontiers in Physiology Volume 13 article 832647 2022

The Frontiers in Physiology paper was, in fact, a comparison between the Counting Talk Test and an alternative they developed, the Regulated Monosyllabic Talk Test. I was not persuaded to switch to their Regulated Monosyllabic Talk Test but did find this paper useful because it reported the values for the Counting Talk Test at lower and upper boundaries of the Moderate (63% to 48%) and Vigorous (48% to 32%) exercise zones.

Both of these papers had as their goal the use of some version of the Talk Test to find the boundaries of the Moderate and/or Vigorous Exercise zones. To do that, they had to know where these boundaries are and then measure the value of their Talk Tests at these boundaries. How did they define these boundaries? Unfortunately, they did so using Heart Rate, exactly what GCN (and others) have argued should be avoided. In response to that concern, I compared the CTT to the version of the Talk Test used by GCN and determined that the percentages given in the Frontiers in Physiology appear to be about right, at least for me.

How does the CTT compare to heart rate as a way to measure Intensity? The main thing I use heart rate for is to measure average Intensity of a ride and thus cumulative Load over time and the CTT is impractical for that purpose. The reason I initially pursued it was that it was one more test that I could use to determine if I had correctly located my aerobic threshold. Having done that I now continue to use now and again it because it is free of some of the complexities of heart rate. Heart rate can be higher or lower based on fatigue, stress, caffeine, environmental temperature, etc. Based on my experience so far, CTT seems to be much less sensitive to such considerations. Also, heart rate is a lagging indicator, it takes time for it to increase after Intensity increases. As best I can tell, CTT responds to an increase in Intensity with little or no delay.

Does the aerobic threshold I measure using CTT agree with what I had previously assumed it was? The answer to that question is not so simple, as is illustrated by the following output from the software used by my heart rate monitor:

This ride was on my Trainer and done at a constant effort, 70 RPM in a 71 inch gear. The Counting Talk Test yielded a value of 11 counts which corresponds to 48%, the top of Zone 2. However, my average heart rate over the course of that ride is 123 beats per minute which corresponds to the middle of Zone 2. Is this a disagreement? Perhaps, but note that, although I held my Intensity constant over the 30 minute of the ride, my heart rate was not constant but increased during at least the first half of the ride. If I look at only the second half of the ride, my heart rate, estimated by the white line, is at 132 beats per minute, much closer to the top of Zone 2. I suspect that my heart rate during the first half of the ride is not a good indicator of Intensity because heart rate lags behind Intensity. If this explanation is correct, then the Counting Talk Test agrees with the other approaches I have used to locate my lactate threshold.

In summary, I think the Counting Talk Test is a better way to estimate breathing rate than the approaches suggested by the exercise community to date. To be most useful, the exercise community would have to adopt the CTT (or something similar) and calibrate it against reliable laboratory measures of Intensity like blood glucose or O2/CO2 levels in the breath. This would provide a clear, accurate way for the average athlete to locate their aerobic threshold quickly, easily, and inexpensively. 

Heart Rate and Intensity

If I ride a given route quickly, it will leave me more tired than if I ride it slowly despite the fact that I spend more time riding at the slow speed. That assertion  is widely accepted by the vast majority of exercise scientists, coaches, and athletes. How to quantitate that is more controversial. For some purposes, speed (e.g. miles per hour) is used for such a quantitation. For example, many coaches recommend periodic time trials on a fixed course where the speed at which one can ride that time trial is a measure of Fitness. But because simple speed is affected by so many factors (e.g. hills) it is not usually used as a routine measure of Intensity, the generalized term used to quantitate the impact of different riding speeds. The most common measures used to routinely calculate Intensity are heart rate, power, and relative perceived exertion (RPE.) RPE is the simplest, it is just how hard a ride feels. That is the metric I used in last month's post to determine if I had been riding too much or too hard.

Power is something like a normalized version of speed in that it corrects for factors like hills that affect speed. It is measured using a power meter which is incorporated into the drivetrain of the bicycle. These are widely available if somewhat pricey. Power (like speed) needs to be calibrated for differences in the fitness and ability of different athletes. 150 watts of power might be at the upper end of the amount of Intensity I can manage while being an easy ride for a better cyclist, and the meaning of 150 watts would be different for me at the beginning of the season when I am not very fit versus at my peak fitness after I have trained for an important event. I have never owned a power meter and so I use speed on standard routes as something of a proxy for power.

Two months ago, when I posted about Zone 2 training and how the reporter Manon Lloyd used herself as a guinea pig to investigate Zone 2 training, something I did not mention is that when Lloyd developed a training plan with her coach, he specifically advised her to use both a power meter and a heart rate monitor. Why both? In many ways, power is considered to be the superior metric. It responds instantly to changes in Intensity and is independent of many factors that affect heart rate, things such as stress, caffeine, etc. However, power is rapidly affected by training and that changes are significant. At the beginning of her six weeks of training, if Lloyd rode at the top of Intensity Zone 2, she could generate 140 watts of power. At the end of her six weeks of training, she could generate 160 watts of power at the same level of Intensity. Thus, had she used only power to guide her training, she would have been training at too low an Intensity at the end of her training. Heart rate is also affected by training, but on a much longer time scale. Although not given in the videos, it is likely that Lloyd's Zone 2 heart rate at the beginning and end of her six weeks of training would have been similar or identical. In short, for the purpose of keeping her effort within Intensity Zone 2, power was the better metric over the course of one ride but heart rate was the better metric over the course of six weeks of training.

Although I use RPE as my primary measure of average ride Intensity, I use average heart rate as an important secondary measure. The goal of this post was to determine how reliable average heart rate is and specifically, to compare average heart rate of a ride to the speed of that ride on a standard route. I used two standard routes for that comparison, my Cañada route and my Alpine route. As noted above, the impact of training on ride speed would be expected to confound that comparison. As I train and become more fit, I would expect my speed a given heart rate to increase. To remove that confounding factor, I did my comparison over a period of time during which I felt that my fitness stayed relatively constant. The results for the Cañada route are shown at the top of this post. The results for the Alpine route are shown here:

Encouragingly, the results for the two routes were similar. I will focus here on the results for the Alpine route. This graph shows the results for 19 rides on the Alpine route from June 30, 2024 and October 24, 2024. It begins after I had gotten in shape for metric centuries, a period during which I was attempting to maintain my fitness but not trying to increase it. For each ride, I plotted the average speed of that ride on the vertical axis as a function of the average heart rate for that ride on the horizontal axis. The line is the best fit line through those points. The equation for that line (which can be ignored) is shown at the top of the graph as well as the value for R-squared (R².) R-squared is a measure of how effective heart rate is at predicting ride speed. R-squared varies between 0 and 1, and if both heart rate and ride speed were perfect measures of ride Intensity, R-squared would be 1. The value measured for the Alpine route is approximately 0.7, very similar to that measured on the Cañada route. This is a pretty good correlation between speed and heart rate which means that both of them are pretty good measures of Intensity, but that one or both of them are imperfect measures. Besides Intensity, what might affect ride speed? The two things I can think of are fitness and wind. As noted above, I have done my best to control for fitness and my intuition suggests that wind is not a major factor. Besides Intensity, what might affect heart rate? Unfortunately, many things: caffeine, emotional state, and fatigue* to name but a few. This would suggest that speed is a better indicator of Intensity than is heart rate, so why not just use speed? 

There are two reasons not to use speed instead of heart rate as a measure of Intensity:

1. Speed is only a good indicator for one specific route. It is possible that I might be able to map some kind of equivalence for two commonly ridden routes like the Alpine and Cañada routes, though I worry that even this level of data processing could lead to false conclusions. Perhaps more importantly, many of my rides are ridden over a wide variety of routes, none of which I ride commonly enough to provide the data needed to map speed onto Intensity. That is why many cyclists use power meters.
2. The speed corresponding to a given level of Intensity changes with training. The graph at the top of this post shows data for rides on the Cañada route between June 17 and October 26 of 2024. If I do a similar analysis for rides on the Cañada route between July of 2022 and October of 2024, the R-squared value drops from a respectable 0.70 to a useless 0.36. This is because variations in how much I was training and my resulting fitness varied substantially over that longer time period.

Where does this all leave me? In a pretty good place, I think. It is definitely true that heart rate is an imperfect measure of Intensity for any single ride. During the June through October 2024 time period, four of my rides on the Alpine route resulted in an average heart rate of 126 beats per minute. The speeds of those four rides varied between 10.8 and 11.5 miles per hour. However, the most important use I make of average heart rate applies not to single rides but rather to accumulation of fatigue over time, and for that purpose, these variations tend to cancel each other out so that average heart rate is a perfectly adequate metric. In that context, the R-squared value of 0.7 I determined from the comparison of speed and heart rate gives me confidence that recording my average heart rate is helpful to my training. But how do I use that to estimate accumulated fatigue? I plan to discuss that in a future post.

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* Many coaches advise that when an athlete is fatigued, their heart rate will be lower than usual at a given level of effort. A rationalization sometimes given for that result is that the athlete's heart is "too tired" to beat any faster.

Training for Speed

In a post from last September I noted that my cycling speed had fallen significantly since 2020 and proposed to focus my training on attempting to reverse that. How did that go?

Executive Summary

The training schedule I came up with last September to increase my ride speed was poorly thought out. Even so, I rode my fastest ride since 2022 while learning at the same time that, even if I had executed it better, the approach I was taking to increase my speed was probably the wrong approach for me to have taken at that point in time.

The Long Version

From the beginning of February until my birthday ride at the end of July, I followed two relatively familiar training plans, first a plan to get ready for a Metric Century (a 100 kilometer/62 mile long bike ride) and then a plan to continue riding a Metric Century a Month. Once I completed my Birthday Ride at the end of July, I had no additional long rides to prepare for so needed a new plan. Back in September, I posted that I planned to spend the remainder of 2024 attempting to reverse the decline in my cycling speed that has occurred since 2020. My riding in August was intended to allow me to recover from the riding in February through July with my new training plan beginning in September. What training plan did I propose to use to increase my speed? Actually, what I had was more of an aspiration than a plan. The problem is that although I have a well tested and successful plans for building and maintaining endurance (e.g. getting ready for a Metric Century,) I have never developed a plan for building speed. Further, it is my impression that building speed is much more difficult than building endurance; some even say that it cannot be done. Ignoring that discouraging context, I decided to try three things:

1. Increase the speed with which I rode one of my main go-to routes, the Alpine Ride.
2. Add Zone 6 intervals to my training schedule.
3. To avoid overtraining, eliminate my weekly long rides.

How did I execute that plan and how did it go?

Let me start by explaining what I had in mind when I proposed to increase the speed of my Alpine rides. I divide the speed at which I complete rides like this into two general categories named Zone 2 and Pace. For a Zone 2 ride, I carefully modulate my speed, especially uphill, to keep my heart rate within the Zone 2 range, which for me is between 110 and 135 beats per minute. For a Pace ride, I ride at whatever speed feels right. That can result in a range of heart rates from something indistinguishable from a Zone 2 ride (100% Zone 2) to one almost entirely in Zone 3 (135 to 150 beats per minute) and everything in between. What is the difference between a Pace ride where my heart rate is indistinguishable from a Zone 2 ride and a Zone 2 ride? The main difference is one of intent: if I decide to do a Pace ride and come home, look at my TranyaGo Heart Beat Monitor, and see that the entire ride was in Zone 2, I am surprised. Given that distinction, what I meant when I said that I proposed to increase the speed of my Alpine rides was that I planned to ride these as Pace rides rather than Zone 2 rides. Unfortunately, I had not carefully looked back at what riding I had been doing before and as a result it is unclear that this increase ever happened. I had imaged that between February and July most of my Alpine rides had been Zone 2 and that during my subsequent training to increase my speed, most of my Alpine rides would be Pace. In fact when, at the end of the eight weeks of my speed-increasing training I compared the ratio of Zone 2 and Pace rides during those two time periods, they were essentially the same. This was both because I rode more of my Alpine rides as Pace rides back in the first half of the year than I had remembered and because there were many days in September and October when I was feeling quite tired and on those days, I would ride my Alpine rides as Zone 2 rides. In summary, there is no good reason to think my planned change had any impact. There is one counter-argument. My Pace rides during September and October were faster, on average, than my Pace rides during February through July. Specifically, in October I rode an Alpine Ride at 12.3 miles per hour, faster than any Alpine ride since 2022.

The above describes how I did in executing part 1 of my plan (i.e. not well.) I did better in executing parts 2 and 3. With regards to part 3, I rode no long rides during August, September, or October as per the plan. With regards to part 2, my addition of Zone 6 rides was also successful. Zone 6 rides consist of a 15 minute warmup in Zone 1 followed by one or more Zone 6 intervals one minute in length separated by four minute recovery periods, followed by a 15 minute cool-down in Zone 1. I used the same route to accomplish this as I used in my previous Zone 6 intervals back in 2019.  Back then, I was doing three repeats of the one minute Zone 6 Intervals and found that if I tried to do one of these sets a week, I had a build-up of fatigue, and thus switched to one per month. This time, I decided to work up to the three repeats. I started with one repeat, waited a week, did two repeats, waited two weeks and then did three repeats. My plan was to wait four weeks and then do three repeats again, continuing with monthly sets of three repeats through the end of 2024. What happened is that the week I was scheduled to do my second set is the week I diagnosed myself with overtraining and halted this training plan until I felt more rested.

How did I decide I was suffering from overtraining? Mostly it came from listening to my body. In my training log, I track my subjective feeling of tiredness. Two weeks of that log, from September and October, are shown in the figure at the top of this post. I rate my fatigue on a six level scale; Very Tired, Tired, Somewhat Tired, OK, Good, and Strong. As a subjective scale, it has all the problems associated with subjectivity. Might a level of fatigue I call Somewhat Tired for one ride be the same as what I call OK for another? Absolutely. However, an unremitting list of rides rated as Somewhat Tired, Tired, and Very tired is pretty convincing. What does it look like when I am rested? Less convincing, at least on the surface. The best two week period in 2024 is this:

While it is true that this two week period spans the range from Very Tired to Strong, there is a pattern to that variation that makes sense. During this phase of my training I was working on building endurance with weekly long rides on the Alpine-Cañada route. Thus, these were my hardest rides of the week. The general pattern is that I felt good for these rides but was very tired afterwards and then recovered over the next week. This was exactly as it should have been. The problem with my recent riding (shown at the top of the post) is not the Tired or Very Tired days but the fact that I did not recover from them, that there were no Good or Strong days. That absence of Good or Strong days was the primary reason I felt I was overtraining. A secondary but important reason was that, as I was preparing last month's post, I came across a video by a highly respected coach and exercise scientist that described the symptoms of overtraining, and those symptoms closely matched how I was feeling. 

How did this happen? In retrospect, I think did not rest enough after my long rides before attempting this new training plan. Below is my training log for the last two full weeks of that recovery: 

I could easily make the theme of this post what a poor planner I am, but I don't feel that way. When I write a post like this, I force the messiness of real life into an unrealistic, rigid framework. The reality was that I didn't feel all that bad after my Birthday Ride, and yet I had the wisdom to take a bit of a break anyway. Until I wrote this post, I did not have the idea of looking for a trend in several days of my subjective fatigue rating to evaluate my overall fatigue level. When, on Friday, August 23, I went out for a ride on my Alpine route and ended up with a fairly good time (by 2024 standards) and felt pretty good, I really thought I was ready to start the next phase of my training. Looking back with the clarity of thought given to me by the writing of this post, I think that was too soon and that, going forward, I should look for a sustained pattern of lower subjective fatigue before I resume harder training. How am I doing in that regard? Here is my training log for the last two weeks:

Clearly my fatigue is lower than it had been, but not as good as it was back in April. In addition, there is one additional consideration. I will get to that consideration but would like to begin with a question: "What on earth was I thinking, riding a 'Brisk' ride on November 11th?" Brisk rides are my hardest rides. This brisk ride contained intervals in the highest of the Intensity zones, Zone 7. Why would I do a brisk ride during a period of time when my goal is to reduce fatigue? The reason is that additional consideration: we have now entered the Rainy Season here in California. I hate riding in the rain, and when I thought about it, it seemed unwise for an old man like me with my brittle bones to ride on rain-slick roads. This caused me to once again turn my attention to one of my most frequently-referenced publications, Gillen et al.  That publication argues that 3 x 20 second Zone 7 Intervals provides roughly the same health benefits as 45 minutes of Zone 2 training. By increasing that to 6 intervals, an indoor ride on my trainer would, if Gillen is correct, provide about the same benefits as one of my Go-To rides, the Cañada ride. During a week where rain keeps me indoors, I can substitute what I call 'Gillen Intervals' for an outdoor rides and hopefully maintain fitness. I suspect that rain will be a major determinant of how I ride until sometime around the end of January. If I see a pattern in my Subjective Fatigue over a week or two and if weather allows, I may try a few of my Tamarack Sprints (Zone 6) but I am not going to worry if that doesn't happen. I will do my best to maintain as much fitness as I can given the weather and will refocus come February 2025.

GCN and Zone 2

 

Two posts ago, I talked about my attempts to come up with a training plan to reverse the decrease in cycling speed I have been experiencing. In that post I said, with regards to my plan to cut back on long, slow rides in favor of faster, shorter rides, that I had the following concern: "... my slow training in 2021 was based on some of the most respected and widely accepted training advice in the cycling community, the value of Zone 2 training. Even to myself, increasing my speed seemed more like flailing than an upgrade." To address that concern, I am continuing to read and think about Zone 2 training.

[Brief Tutorial: The Intensity (e.g. how fast it is) of a bicycle ride is is usually described in terms of Training Zones, with Zone 1 being the easiest (slowest) ride and Zone 7 being the hardest (fastest.)]

Global Cycling Network (GCN) is an online cycling magazine which I have come to really like. When I have a question about cycling, they often have an answer that is comprehensive, clear, and plausible. I recently stumbled across a four part series they did on Zone 2 training that I found very helpful.

Part 1 was an interview with Iñigo San Millán, PhD, of University of Colorado School of Medicine. He is an exercise scientist and coach to a number of Tour de France riders, including the current wunderkind of cycling, Tadej Pogačar. I did a bit of research on his credentials and I was impressed. He talked about how the slow twitch muscle fibers which are developed by Zone 2 training are critical for supporting the fast twitch muscle fibers used during high intensity racing because they metabolize the lactate generated by those fast twitch muscle fibers. His bottom line recommendation is the same advice I have been reading from several other sources, that the optimum training schedule consists of 80% Zone 2 training and 20% training at higher intensity targeted to one's goals.

Part 2, which was narrated by GCN reporter Simon Richardson, was about how to identify your Zone 2. According to him,  heart rate and power are not good ways to do this, though they are useful for tracking zones once calibrated. Simon's definition of top of Zone 2, confirmed by Dr. Millán, is the point where fat metabolism plateaus. This is determined by measuring O₂ consumption and CO₂ generation during exercise.

The top of Zone 2 is also where blood lactate goes from flat to increasing. There is second level of lactate that is considered significant which is identified by a further increase in the slope of the lactate vs exercise graph and it is useful to describe these two lactate levels together.  As noted above, the first increase in lactate defines the upper boundary of Zone 2. The further increase in the slope of the line defines the upper boundary of Zone 4. Unfortunately, the terminology used for these two levels of lactate is inconsistent and therefore confusing. Even within this series of four videos, different terminologies are used at different times. Some of the names used for the lactate level at the top of Zone 2 are Lactate Threshold (LT), the first Lactate Threshold (LT1) or the Aerobic Lactate Threshold (AeT.)  Similarly names used for the lactate level at the top of Zone 4 are the Lactate Turn Point (LTP), Lactate Threshold 2 (LT2) or the Anaerobic Lactate Threshold (AnT or simply AT.) 

Both lactate and respiratory gas measurements require a laboratory. In the absence of a laboratory, breathing tests are the best measure according to Richardson. The top of Zone 2 where conversation is forced but possible and where one can breathe entirely through the nose. An alternative is to use Relative Perceived Exertion (RPE.) On the standard 6-20 RPE scale, the top of Zone 2 is 12.

Part 3 was both narrated by and focused on GCN reporter Manon Lloyd. (The picture at the top of the post is of Lloyd.) Lloyd had been an elite cyclist earlier in her life, but, in her words, she was "ten times as unfit" now had she had been back then. The premise of this and the next video is that she is going to use herself as a test case for the benefits of Zone 2 training. Besides the results of the experiment, we also get to see a state of the art version of how such an experiment is done.

Lloyd worked with the Human Performance Laboratory of the University of Bath in order to determine her fitness level at the beginning of the test and to establish her heart rate and power output at Zone 2. To do that, her blood lactate and breath O₂/CO₂ were measured every few minutes while she rode an exercise bike at increasing speeds:

Lloyd then met with her former coach to develop a six week Zone 2 training plan.

Part 4 reported the results of that training plan. The same tests were repeated and the results were compared to the results at the beginning of the test. Lloyd saw a significant improvement not only at the lower intensities around Zone 2 but at the high intensity zones as well:

I will go through these results line by line. LT (W) is how much power Lloyd could generate at her lactate threshold. At the beginning of the experiment, it was 140 watts. Six weeks later it was 160 watts. My estimate is this roughly corresponds to an increase in speed on a flat, windless road from 17 mph to 18 mph. LTP (W) (AP on the graph above) is the same value for the Lactate Turn Point and roughly corresponds to an increase in speed from 18 to 19 mph. It can be hard to accurately identify the points on the graph where these two increases in slope occur, and so sometimes these blood lactate levels are identified as absolute concentrations, e.g. 2 mM and 4 mM. The power levels at these two lactate concentrations is shown on lines 3 and 4.

The remaining four lines refer to VO₂peak. This is the more cautious, scientific version of the more commonly used VO₂max and for the purposes of this post, we can consider them to be the same thing. This is the maximum amount of oxygen an athlete can use and occurs near or at their highest level of exercise. Line 5 gives the ratio between the power Lloyd output at LT (the top of Zone 2) and her maximum power output. Line 6 shows the same thing for her power at LTP. Both of these increased during Lloyd's six weeks of training. The seventh line is the absolute value of VO₂peak itself. This increased by about 7% over the six weeks. The values both before and after training would be considered good but not elite. It might be expected that Lloyd could further increase this value with additional training. Finally, in line 8 we see that the maximum amount of power Lloyd could produce increase by about 12% over the six weeks. 

It is unsurprising that the Power Lloyd could generate at LT increased since that is the intensity at which she trained, but it is perhaps less intuitive that her power at LTP and at maximum power (power at VO₂peak) increased as well since these are levels of Intensity much higher than that at which she had trained. This is consistent with an article I posted about in 2021, a case study of an athlete who was having trouble increasing their VO₂max who, when he switched from the Zone 5 and Zone 6 workouts typically prescribed for increasing VO₂max to a three year program heavy on Zone 2, experienced a dramatic increase in his VO₂max.

Besides this four part series, I found some related articles from GCN, one on Sweet Spot training, one on Training Zone definitions, and one on Overtraining. The video on Sweet Spot training was the least useful, but I was pleased that the narrator, reporter Simon Richardson, suggested the same thing I had, that perhaps Sweet Spot training (training at the top of Zone 3 and the bottom of Zone 4) would be useful to cyclists whose time for training is limited. I noted that Dr. Iñigo San Millán was not featured in this video and suspect he would not have agreed. I found the use of training zones in the four part series to be inconsistent, so when I came across a video just about training zones, I had to watch it. The definition of Zones in this video was almost exactly the same as that used by Coach Hughes, which was comforting. The one difference was that Coach Hughes recommends Zone 6 for increasing VO₂max and GCN recommends Zone 5, claiming that Zone 6 is used to anaerobic capacity. That video credited Andrew Coggan as the developer of this 7-zone system, a fun fact I found of interest. Most significant was a third video which was again hosted by Richardson. This video consisted almost entirely of an interview of Dr. Iñigo San Millán. The topic of this video was overtraining. The symptoms of overtraining described in this video described how I am feeling right now with terrifying precision.

How did this series affect my training? As I note frequently, I try to limit the advice I take to one coach, Coach John Hughes, but Coach Hughes' advice is somewhat inconsistent when it comes to the value of training in Zone 2 and Zone 3. Thus, that balance is something I need to decide for myself. I go back and forth on this, and this series of videos pushed me back towards more Zone 2 training. However, the biggest impact on my training came from one of the three extra videos, the one on overtraining. Not that this video told me anything I hadn't heard before and it is not as if I were not wondering if I was suffering from overtraining even before I watched it, rather, it was more like perfect timing. I was ready to hear this message, especially because it came from a prestigious and credible coach and scientist. I let this message sink in, I watched it a second time, and then I decided to take a week off from training. This is not a violation of my determination to focus on Coach Hughes, Coach Hughes also recommends taking a week off from training at appropriate times. If anything, I had been taking off fewer weeks than Coach Hughes recommends. Thus, this video simply focused my attention on something I should have been doing anyway.

Some final, miscellaneous things I learned from this series of videos:

• Lloyd's coach noted that it is important that Zone 2 training rides be long in order to generate the stimulus needed to increased fitness. I have noted in the past that Polarized Training may be more about the lower end of that polarization (Zone 2) than the higher end. Similarly, I am getting the impression that it is the length of Zone 2 rides that makes them valuable.
• Decoupling is the well known phenomenon where heart rate increases at the end of a long ride with no increase in effort. For Zone 2 training, how do you handle that? GCN says when heart rate trends up, you should slow down to bring your heart rate back down. Coach Hughes disagrees. He says to maintain your speed and ignore your heart rate. I haven't decided what I think about this yet, but it is good hear the other side of the story.
• Manon Lloyd complained (as I have) that it is hard not to drift from Zone 2 up into Zone 3 when climbing hills. In the first place, it is comforting for me to realize I am not the only person struggling with this. In the second place, Lloyd's coach said 30 seconds in Zone 3 does not ruin a Zone 2 ride, so that within reason, hills can be ignored. Elsewhere in the series, however, it is noted that it is important to ride at a steady pace because it takes about 5 minutes to feel the intensity of a pace, so such drifts upwards should be kept short. GNC claims that if you do exceed Zone 2 for too long, it takes about 30 minutes to get back to the physiology of Zone 2 where you can obtain its benefits.

Implicit in this post is that I am reexamining my training schedule yet again. I plan to talk about that in more detail in a post in the near future. Stay tuned.

Update on the Banister Model

I track my training to help me train enough to reach my goals while not training so much as to result in overtraining, long term exhaustion, and failure. Listening to my body is my best defense against that, but I find it useful to compare what my body is telling me to how much riding I have been doing to help me decide what rides to do next. The tricky bit is what "how much riding I have been doing" means. It's easy to track how many minutes I spend riding (Volume) and it seems reasonable that, all things being equal, a two hour ride will make me twice as fit (Fitness) and twice as tired (Fatigue) as a one hour ride but how fast I ride (Intensity) during those minutes also affects my levels of Fitness and Fatigue. In that case, however, the question of "By how much?" is not so easily answered. The units of Fitness and Fatigue are arbitrary, so as long as I track only minutes, I only need to worry about relative values, absolute values don't matter.  But when I add how hard a ride was (how fast, how hilly, etc., known as Intensity) I am forced to ask how much an increase of speed of 1 miles per hour (for example) affects my Fitness and Form compared to the effect of adding 60 minutes to the length of that ride. Additionally, not only do Fitness and Fatigue increase in response to riding but both also decrease over time when I don't ride. Finally, how to Fitness and Fatigue interact? In my opinion, the answers to these questions are not known with certainty but I also feel like I should make my best guess to their answers and do the best that I can.

One tool many cyclists use to help answer these questions is the commercial Training Peaks software package. An alternative I have been playing with is the Banister model. Thus, I was excited to stumble across this blog post:  "Implementing the Banister Impulse-Response Model in GoldenCheetah". (GoldenCheetah is an open source software package for analyzing cycling data.) In addition to the contents of the blog post itself, the author cites a scholarly paper by Dave Clarke and Phil Skiba which contains a tutorial and review of the Banister model. The reasons I was excited was the confidence boost I got from the fact that someone besides me is interested in the Banister model and the hope that I could learn from their experiences. One big thing I learned was that the community of scientists, coaches, and athletes using the Banister model is focused on customizing the parameters of that model to each individual athlete, something I blogged about doing myself, though that is still a work in progress. This is a feature that Training Peaks does not have, so someone like me who is using the Banister model without customization is no worse off than one of the many Training Peaks users. Also, the Clarke and Skiba paper suggests that the model is not very sensitive to small changes in the parameters suggesting that customization might not be so important.

I have been using the Banister model for more than two years now and it certainly has not been perfect at predicting the impact of my training on my cycling ability, but I have the impression that it does give me hints that are helpful in combination with what my body tells me in optimizing my training. I hope to post more about this in the future as I learn more. So why post about it now?

Five months ago, I blogged that coming up with an equation for calculating my ride Load was a work in progress.The Banister model includes a formula for calculating Load. Load is a combination of Volume, the duration of a ride in minutes and Intensity (how "hard" a ride is.) They are linked as follows:

Load = Volume x Intensity. 

One way to measure intensity uses Heart Rate and there are many different formulas of calculating Intensity from Heart Rate.  I have compared several of these formulas and a number of them seemed fine. Given that, I decided to use the method proposed by Banister, thinking there might be some value in using the Intensity calculation and the accumulated Form, Fatigue, and Fitness model from the same author.

One disadvantage of the Banister method for calculating Load is that is more more complicated than it needs to be, in my opinion. That said, this complexity doesn't seem to make its estimates any worse and that once I coded this method into the spreadsheet I use to track my training, it didn't make tracking my training any harder, so this is what I am using for now to convert the heart rate I measure to Intensity. 

In an attempt to make Banister's method easier to understand, I am going to break it up into pieces. The first thing to know is that the Banister method is based on Heart Rate Reserve (HRR), the difference between the lowest heart rate an athlete exhibits, the resting heart rate, and the highest heart rate they can attain:

HRR = Heart Rate Reserve = (Maximum Heart Rate - Resting Heart Rate)

Intensity is related to how much of that reserve an athlete uses during a particular level of exercise, what I call Fractional Heart Rate Reserve (FHR):

FHR =  (Exercising Heart Rate - Resting Heart Rate) / (Maximum Heart Rate - Resting Heart Rate)

Finally, FHR is used to calculate Intensity:

Intensity = FHR x 0.64 x e^{(1.92 x FHR)}

0.64 and 1.92 are constants that Banister provides.

I went back and recalculated all my Intensity measurements since I obtained my TranyaG0 sports watch in 2022 and the results consistent with my subjective impressions. Problem solved!

How much of a difference does it make to my training if I track Load instead of just tracking Minutes like most coaches recommend? Not a lot, but some. The way I measure that difference is the ratio of Load to Minutes. If Load made no difference, that ratio would be 1. Since I resumed tracking my heart rate in July of 2022, that ratio (averaged over a week) has gone from a high of 1.5 to a low of 0.4. The 0.4 and similar low ratios occur during weeks when most or all of my rides are Zone 1 recovery rides on my trainer and thus those low values were expected. Perhaps Load is more useful for the weeks where Load is greater than Minutes. As noted on the graph above, it is fairly common for the Load to be 1.25 times as large as Minutes. I have noted in the past that I should try to ride at least 300 minutes a week but if I routinely ride much more than 400 minutes a week I risk buildup of Fatigue. Consider a week when I am feeling strong where I might ride for 400 minutes. I might feel like that was on the edge but not excessive. However, it would not be uncommon that the same week might have a Load score of 500 (Load/Minutes=1.25) making it something worth noting.