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Modeling Human Performance

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Training Stress Balance (TSB) is There are a method for evaluating the effect number of approaches to modeling how training over timechanges performance and these models have some obvious value in optimizing a training routine, especially for tapering. This approach assumes =The Models=The models assume that given training stress, also known as "training impulse" or [[TRIMP]] ('''TR'''aining '''IMP'''ulse), has both a positive and a negative effect. The positive effect could be considered is called "fitness", and the negative effect could be considered is called "fatigue", and they are combined to provide a value of "performance". This article looks at three models:* Banister. The initial work on modeling human performance was made by Eric Banister in 1975<ref name="CalvertBanister1976"/> and verified by dozens of studies including one on runners<ref name="Morton-1990" />. * Busso. The positive effect work of Banister was refined by Thierry Busso to modify the Banister model to at least partly account for how [[Training Monotony]] impacts recovery<ref name="Busso-2003"/>. * TSB. The Training Stress Balance model is called a simplification of the Banister model by Andrew Coggan which looks at just the relative changes in performance<ref name="TSB"/>. The TSB model will be examined first, as it's the simplest to understand. =The TSB Model=Training Stress Balance (TSB) uses the terms Chronic Training Load (CTL) and the negative effect is called for "fitness", Acute Training Load (ATL)for "fatigue" and Training Stress Balance (TSB) for "performance". Both As with all the models, both CTL and ATL are based on TRIMP, with the effect of a given workout reducing over time, but the effect lasts longer on CTL than on ATL. In addition the TSB method assumes the effect is greater on CTL than on ATL. ==TSB For for a Single Workout==

[[File:TSB Single Workout.jpg|none|thumb|500px]]

The image above shows the effect of a single workout on the Training Stress Balance. You can see the workout creates a peak in both ATL and CTL. The peak is greater ATL, but reduces more quickly than in CTL. The Training Stress Balance is CTL-ATL, and you can see it initially go negative indicating a reduced ability to perform, then rises to be positive as CTL becomes greater than ATL. This green TSB line is the same as that seen in [[Supercompensation]].

 ==TSB for Multiple Workouts==[[File:TSB Multiple Workouts-KaKfSame.jpg|none|thumb|500px]]The effect of a continuous series of identical workouts on TSB is shown in the image above. The ATL rises sharply and reaches a steady-state, with CTL rising more slowly to a greater level. The TSB (CTL-ATL) initially goes negative, but rises towards a positive steady-stateslowly returning to zero. =The value of the TSB model=The TSB model can provide an estimation of how changes in training load affect fatigue and performance. A positive TSB indicates improved performance. Constants=Flaws in the TSB model=There are a number of practical flaws in Because the TSB model. * The first flaw in is simpler than the TSB model is that other two, it ignores [[Overtraining]] and predicts that any possible workload produces improved fitness. Related to this problem is that only requires the model ignores [[Training Monotony]]. Research has shown that training with a high level of monotony reduces the benefits and increases the fatigue from a given level number of training. * The second flaw is days that the values for the constants used in the model are specific to each individual, ATL and possibly to the particular training regime. The verification of the model reverse engineered the constants so that the model accurately predicted the performance changes. These constants are represented below as ** N_a - the CTL decay constant for acute (fatigue) effect of trainingover.** N_f - the decay constant for fitness effect of training.** K_a - the scaling constant for acute (fatigue) effect of training** K_f - the scaling constant for fitness effect of training.** The ratio of K_a to K_f defines the benefit of training. If they are both the same value, then you get no benefit from training, but if K_a is larger than K_f then training improves your performance over time.** If you consider the case of someone typical starting to exercise exactly the same amount every day, you’d find a change in CTL and ATL that would reach a steady level over time. Without a difference in K_a/K_f, the values of would cancel each other out, so CTL-ATL would be zero, showing no improvement from that exercise. See the graphs below.* A third flaw point is that TSB assumes a single value 7 days for that represents the adaptation to performance. In practice, different types of adaptation occur at different rates. {| class="wikitable" |- valign="top"|[[File:TSB-KaKfSame.jpg|none|thumb|500px|A graph showing someone start an exercise program with the same workout every day. You can see that the TSB (green line) returns to zero, indicating no improvement in performance.]]|[[File:TSB-KaKfDiff.jpg|none|thumb|500px|This is the same exercise, but with K_f twice the value of K_a. Now the exercise program predicts an improvement in performance.]]|} =An Advanced TSB=One approach to addressing these flaws is to use the calculated [[Training Monotony]] to change the TSB calculation. Higher levels of monotony should reduce the CTL value, increase the ATL value, and increase the time constant used to reduce the effect of a workout on ATL. I've built this into my [[SportTracks Dailymile Plugin]]42 days for CTL.  ==Calculation Details==

Understanding these details is not required for using the TSB, but you may find them interesting.

 ===The basic formulaTSB Formulas===

The basic formula for calculating ATL/CTL uses an [http://en.wikipedia.org/wiki/Moving_average\#Exponential_moving_average Exponential moving average] that is calculated like this:

ATL_today = [[TRIMP]] * &lambda;_a * k_a + ((1 – &lambda;_a) * ATL_yesterday CTL_today = [[TRIMP]] * &lambda;_f * k_f + ((1 – &lambda;_f) * CTL_yesterdayAs you can see this is an iterative approach, calculating the value for the oldest workout, then iterating through each subsequent workout.  ===Lambda===The calculation for &lambda;_a and &lambda;_f is:

&lambda;_a = 2/(N_a+1)

&lambda;_f = 2/(N_f+1)

Where N_a and N_f are the time decay constants, normally 7 and 42 days respectively. The [http://en.wikipedia.org/wiki/Half-life half-life] for a given value of N is N/2.8854, so 7 days gives a half-life of 2.4 days and 42 days is 14.5 days.

 ===Scaling Factors=Limitations of the TSB model==The values k_{main limitation of the TSB model can be seen in the graph above, which shows that training reduces performance and never improves it. The TSB model only indicates an improved performance when training is reduced, as shown below. [[File:TSB-ReducedTraining.jpg|none|thumb|500px|The TSB model when training is reduced from a} and k_f are stable level of 100 TRIMP per day to zero, showing the scaling factors for rapid drop in fatigue (ATL) and the slower drop in fitness respectively(CTL), resulting in an improved performance (TSB). Normally k_{]]=The Banister Model=The Banister model is a} is set little more complex mathematically than TSB, using an exponential decay to 1 and k_f is set to 2model the effects of training stress. Unlike the TSB model, meaning the Banister model will show that a workout produces twice as much fitness as fatiguesteady state of training will improve performance. Of the available models, Banister's is the most experimentally validated. ==Adjusting for MonotonyThe Banister Formula==The calculation of Monotony formula below looks rather complex, but is covered in actually fairly simple to implement.[[Training MonotonyFile:BanisterFormula.jpg|none|thumb|500px]]Here it is as some simple pseudo-code for those that want to implement it. The modified calculation for ATLm (ATL_monotony) and CTLm (CTL_monotony): ATLm_today fitness = 0; TRIMP[[TRIMP]]_am * &lambda= getDailyTRIMP();_ma * k_a + array of TRIMP for each day for(i=0, i < count(1 – &lambdaTRIMP);_mai++) * ATLm_yesterday CTLm_today { fitness = [[TRIMP]]_cm fitness * &lambda;_f * k_f + (exp(-1 – &lambda;_mcr1) * CTLm_yesterday ===Modified + TRIMP===The value of [[TRIMPtoday]] is modified by monotony:; [[TRIMP]]_am fatigue = fatigue * exp([[TRIMP]] *MonotonyRatio * ATLmStressPercent-1/r2) + (TRIMP[[TRIMP]today] ; performance = fitness * (1 k1 - ATLmStressPercent))fatigue * k2; }=The Busso Model=Thierry Busso created a refinement of the Banister model to try to take account of how an increase in [[TRIMPTraining Monotony]]_cm = (also increased fatigue. This modification of Banister changes k2 from being a constant to being an exponential decay of the training stress. [[TRIMPFile:BussoMainFormula.jpg|none|thumb|500px]] *MonotonyRatio * CTLmStressPercent) + (The value of k2 uses a similar exponential decay:[[TRIMPFile:BussoK2Formula.jpg|none|thumb|500px]] * (1 - CTLmStressPercent))The ATLmStressPercent and CTLmStressPercent =Flaws in the models=There are how much a number of practical flaws in these models. * The main flaw with these models is that the values for the monotony modification constants used are specific to applyeach individual, which defaults and possibly to 50% (0the particular training regime.5)The verification of the Banister and Busso models reverse engineered the constants so that the model accurately predicted the performance changes. ===MonotonyRatio===Using raw monotony tends to have an overly large impact. Instead, * The values of the constants and the resulting predictions also depend on the concept of a 'monotony break even' is performance metric being used, which . * Another flaw is that the monotony level models assume a single value for that an athlete has no negative effects. This defaults represents the adaptation to 1.5performance. In additionpractice, higher levels different types of monotony tend to produce unreasonably high monotony values, so monotony is capped, by default adaptation occur at 4different rates.0* The TSB and Banister models ignore [[Overtraining]] & [[Training Monotony]] and predict that any possible workload produces improved fitness. * The MonotonyRatio is then:TSB model assumes that training does not produce an improved performance. Instead the TSB model only detects a change in training level, with reduced training improving performance and increased training reduces performance. MonotonyRatio = min(Monotony, MonotonyCap) / MonotonyBreakEvenComparison of the Models=* The TSB model is simpler than the other two models as it only has the two decay parameters. ===Adjusting Fatigue Lambda===* The Banister model has more experimental verification than the other models. Because * The Busso model is the most complex, but is the only one that allows for [[Training Monotony]] increases .=Implementing the time that fatigue lasts for, Models=These three models are implemented in the value of &lambda;free [[SportTracks Dailymile Plugin]].=References=<subreferences>a<ref name="Morton-1990"> RH. Morton, JR. Fitz-Clarke, EW. Banister, Modeling human performance in running., J Appl Physiol, volume 69, issue 3, pages 1171-7, Sep 1990, PMID [http://www.ncbi.nlm.nih.gov/pubmed/sub> is modified to create &lambda;<sub>ma2246166 2246166]</subref>: &lambda;<subref name="CalvertBanister1976">maThomas W. Calvert, Eric W. Banister, Margaret V. Savage, Tim Bach, A Systems Model of the Effects of Training on Physical Performance, IEEE Transactions on Systems, Man, and Cybernetics, volume SMC-6, issue 2, 1976, pages 94–102, ISSN [http://www.worldcat.org/issn/0018-9472 0018-9472], doi [http://dx.doi.org/10.1109/TSMC.1976.5409179 10.1109/TSMC.1976.5409179]</subref> <ref name= &lambda;<sub"Busso-2003">aT. Busso, Variable dose-response relationship between exercise training and performance., Med Sci Sports Exerc, volume 35, issue 7, pages 1188-95, Jul 2003, doi [http://dx.doi.org/10.1249/01.MSS.0000074465.13621.37 10.1249/01.MSS.0000074465.13621.37], PMID [http://www.ncbi.nlm.nih.gov/pubmed/12840641 12840641]</subref> * MonotonyRatio * ATLmLambdaPercent + (&lambda;<subref name="TSB">a<TrainingPeaks, http://www.peaksware.com/articles/cycling/sub> * (1 the-science- ATLmLambdaPercent))The ATLmLambdaPercent is how much of -the monotony modification to apply-performance-manager.aspx, which defaults to 50% (0.5).Accessed on 11 May 2013</ref></references>

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