### The Next Generation in Impulse Response Modeling

With our success helping athletes answer the question: “What’s my fitness?”, we set our sights on answering the question “What will my fitness be?”. Answering this question is difficult, since it requires a prediction of what is going to happen to your fitness based on the training (or lack thereof) you plan on doing. In order to successfully predict fitness, we’ll need to look for patterns on how fitness had changed based on previous work, or better still *strain *obtained during activities in the past. From these patterns, we can input the training activities you are planning, extrapolate the strain you will obtain and thus predict what your Fitness Signature will be. Moreover, if we are interested in maximizing a fitness outcome and have predefined what available time there is to train together with the target event date, we can establish fitness *potential* as the highest fitness one can attain based on available time to train. The output of this would be the optimal training plan.

The implementation of the Xert fitness prediction and potential model is following a three phase process:

### Phase I – A Standard Impulse Response Model

Today we released the **Xert Progression Management ChartAlso referred to as the XPMC, the chart plots your daily Training Load, Recovery Load (hidden by default), Form, daily...** (**XPMCSee Xert Progression Management Chart....**). The XPMCSee Xert Progression Management Chart.... is based on a new metric – **Xert Strain ScoreAlso called XSS, this quantifies how much strain an athlete endures during an activity. By taking strain, which is measured as...** (**XSSThe Xert Strain Score quantifies how much Strain an athlete endures during an activity. By taking Strain, which is the... More**) – created to provide a way to normalize strainMeasured in joules, this quantifies how much work is performed close to MPA. As MPA drops with fatigue, strain increases... during activities athletes perform. The derivation of **XSSThe Xert Strain Score quantifies how much Strain an athlete endures during an activity. By taking Strain, which is the... More** establishes the value of 100 as the **XSSThe Xert Strain Score quantifies how much Strain an athlete endures during an activity. By taking Strain, which is the... More** value corresponding to 1 hour at **Threshold PowerAlso used as an acronym TP in Xert and sometimes described using the more colloquial term FTP, Threshold Power is...**. This normalization is familiar to many as it is the basis used in practice by many coaches and athletes

The main difference between *power normalization* methods, such as a 30 second moving average, is three fold:

Below is a chart that shows the effects of an equal work-to-rest ratio workout based on various interval durations. We used data from an athlete with a Fitness Signature that has a * Threshold PowerAlso used as an acronym TP in Xert and sometimes described using the more colloquial term FTP, Threshold Power is... *of

**300W**,

*of*

**High Intensity EnergyAlso used as the acronym HIE, this is the amount of energy or work capacity an athlete has above Threshold...****25kJ**and

*of*

**Peak PowerAs one of the three parameters that define an athlete's Fitness Signature, this is an athlete's highest possible power. Sometimes...****1200W**. The scores are based on equal work-to-rest at an interval power of

**350W**with a equivalent rest at

**100W**for

**1 hour workout**:

The scores are similar for durations greater than 40 seconds and less then 200 seconds. As the interval durations decrease below 40 seconds, there is significant divergence as the 30 second moving average does not account for the impact of these shorter efforts. Likewise, as the durations increase and the athlete starts to perform closer their limit, there is also significant divergence. (The athlete’s longest possible interval at 350W/100W equal work:rest is 474 seconds.)

Here is a table with some specific values for comparison:

1 Hour Workout | StressSynonymous with work, this metric is measured in joules and is the total work performed over a given period or... Score | StrainMeasured in joules, this quantifies how much work is performed close to MPA. As MPA drops with fatigue, strain increases... Score |
---|---|---|

Microintervals – 15s on at 350W / 15s off at 100W | ||

60s Intervals @350W with 60s @100W rest-in-between | ||

6 minute Intervals @350W with 6 minute @100W rest-in-between |

Counteracting this divergence is the inflation from rest caused by the use of entire-ride averaging. This ride, for example, has significant divergence between scores as a result of the two stops in the middle of the ride.

In the end, the overall values remain very closely correlated but on an individual activity basis, there can be significant divergence. If one’s activity history contains periods where there is a prevalence of activities that inflate or under estimate strainMeasured in joules, this quantifies how much work is performed close to MPA. As MPA drops with fatigue, strain increases... scores, the difference in accumulated training loads may be material to the interpretation of of the athlete’s data.

#### Xert Equivalent Power

In this latest release, we also introduce another metric – **Xert Equivalent PowerAlso called XEP, this represents the an average power that more closely resembles what the athlete experienced during the activity....** (**XEPSee Xert Equivalent Power....**). **XEPSee Xert Equivalent Power....** is derived from **XEPSee Xert Equivalent Power....** and using average power normalization across activities will be high but unlike **XEPSee Xert Equivalent Power....** may be lower. Conversely, if you have many efforts near your MPA or you have many shorter duration efforts, **XEPSee Xert Equivalent Power....** will be higher. Note that **XEPSee Xert Equivalent Power....** is derived *from* **XEPSee Xert Equivalent Power....** don’t necessarily mean the same relative differences in

Here is a comparison of the same equal work:rest workout as above:

### The Xert Progression Management Chart

Accumulating **XPMCSee Xert Progression Management Chart....** provides a chart of the following:

- Training LoadAlso referred to as TL, and a component of the XPMC, this represents the exponentially-weighted moving average of activity XSS...
- Recovery LoadAlso referred to as RL, this is part of the XPMC and represents the exponentially-weighted moving average of activity XSS...
- FormThis is determined by the formula Training Load - Recovery Load. It is colour-coded on the XPMC chart according to...
- XSSThe Xert Strain Score quantifies how much Strain an athlete endures during an activity. By taking Strain, which is the... More for Activities

The chart also optionally overlays breakthroughs or activities with near breakthroughs – * Best Activities* – overtop the

The **XPMCSee Xert Progression Management Chart....** is a familiar chart to most athletes and coaches that train and race with power. The main distinction is in the use of **XPMCSee Xert Progression Management Chart....** will track in a similar fashion. However, differences can accumulate and end up providing alternative interpretations.

### XSS and XEP in Real-Time

With this release, we are also announcing a new Garmin ConnectIQ App: **XSS and XEP for ConnectIQ** and the availability of **XEPSee Xert Equivalent Power....** for **Xert Mobile**.

**XSSThe Xert Strain Score quantifies how much Strain an athlete endures during an activity. By taking Strain, which is the... More and XEPSee Xert Equivalent Power.... for ConnectIQ** is configured with your Garmin Xert Code and can show **XEPSee Xert Equivalent Power....** in real-time for your entire activity or for the current lap using the settings available in Garmin Express or Garmin Connect Mobile. **XEPSee Xert Equivalent Power....** are now available as selectable metrics on any cell in **Xert Mobile** using tap-and-hold.

### Phase II – A Comprehensive Predictive Model

Athletes and coaches are familiar with the standard impulse response model and it’s part-and-parcel of the methods they use to infer what an athlete’s training status and formThis provides a simpler way to view current Training Load and Recovery Load. The number of stars indicate the total... will be at a given point in time. Predicting fitness is as much an art as it is science in using this tool to plan for fitness and peaks for competitions. To move closer to fitness prediction and potential, are more comprehensive model is needed.

Banister’s Impulse-Response Model provides a well known and proven method used to predict outcomes. It is used as the basis for the standard XPMCSee Xert Progression Management Chart..... In order for the model to have a true predictive capability, it requires that the parameters that govern the fitness predictions are continually updated to reflect the up-to-date information about the athlete. The model looks like this:

## Fitness(t) = Fitness(0) + k1 * Training Load (tau1) – k2 * Recovery Load(tau2)

With Xert, we are using the Xert Strain ScoreAlso called XSS, this quantifies how much strain an athlete endures during an activity. By taking strain, which is measured as... which is a good reflection of the strainMeasured in joules, this quantifies how much work is performed close to MPA. As MPA drops with fatigue, strain increases... obtained from training and racing. However, we can also allocate strainMeasured in joules, this quantifies how much work is performed close to MPA. As MPA drops with fatigue, strain increases... into Peak, High and Low using allocation ratios. Hence, our singular model becomes three separate but linked models:

## PeakPower(t) = PeakPower(0) +pk1 * PeakTrainingLoad(ptau1) – pk2 * PeakRecoveryLoad(ptau2)

HighIntensityEnergy(t) = HighIntensityEnergy(0) +hk1 * HighTrainingLoad (htau1) – hk2 * HighRecoveryLoad(htau2)

ThresholdPower(t) = ThresholdPower(0) +lk1 * LowTrainingLoad (ltau1) – lk2 * LowRecoveryLoad(ltau2)

To apply this three tier impulse response model, regression software needs to be developed that will obtain estimates of the parameters. Then, using breakthrough fitness signatures and strainMeasured in joules, this quantifies how much work is performed close to MPA. As MPA drops with fatigue, strain increases... scores divided into peak, high and low strainMeasured in joules, this quantifies how much work is performed close to MPA. As MPA drops with fatigue, strain increases... scores as data to the regression, parameter estimates can be established. Data from a population of athletes, a sub-population, e.g. male/female, elite/masters or even from a single athlete where sufficient data exists, can be used in the regression software to determine parameter values.

At the moment, the software for this regression has been successfully developed and tested and will soon be part of Xert. When this is coupled with the ability to define future workouts, predictions of what your fitness will be – your fitness signature – on a given day in the future can be made. Fold in the ability to have the software auto-prescribe training that maximizes your signature towards a certain desired goal – the relative change in each fitness signature parameter – and we can then provide a measure of fitness potential and training optimization.

### Phase III – A Machine Learning System

In the third phase, we move beyond Banister’s Impulse Response model and towards an even more sensitive prediction model, one that can use other data such as HRV data and data from other sensors to find patterns not captured by our current models. These new methods will help identify greater details that will improve fitness, identify patterns that lead to over-training and prescribe training that can be used in a variety of activities.