Training Simulation with Nothing but Training Data

Simulating Performance based on Training Data

Without the Help of Performance Diagnostics in a Laboratory

Melanie Ludwig, David Schaefer and Alexander Asteroth

Computer Science Department, Bonn-Rhein-Sieg University o.A.S., Grantham-Allee 20, 53757 St. Augustin, Germany

Keywords:

Training Model, Performance Simulation, Model Fitting, Field Study.

Abstract:

Analyzing training performance in sport is usually based on standardized test protocols and needs laboratory

equipment, e.g., for measuring blood lactate concentration or other physiological body parameters. Avoiding

special equipment and standardized test protocols, we show that it is possible to reach a quality of performance

simulation comparable to the results of laboratory studies using training models with nothing but training data.

For this purpose, we introduce a ﬁtting concept for a performance model that takes the peculiarities of using

training data for the task of performance diagnostics into account. With a speciﬁc way of data preprocessing,

accuracy of laboratory studies can be achieved for about 50% of the tested subjects, while lower correlation of

the other 50% can be explained.

1 INTRODUCTION

It is widely accepted that the right dose of exercise is

a very important factor in efﬁcient training. However,

the right dose strongly depends on each individual and

may change during training periods. Professional ath-

letes therefore have a coach, trainer, sport scientist, or

are under doctoral maintenance and their exercise ses-

sions are individually supervised and controlled by a

professional.

Professional coaches make use of the athlete’s

physiological data, e.g., blood lactate concentration

max, measured during standardized test pro-

tocols. Based on this data the current athlete’s per-

formance level is assessed and an appropriate training

plan is generated. To put it the other way round, an ap-

propriate training plan is mostly dependent on partic-

ular equipment and a specialist interpreting measured

data and generating a plan.

But not only athletes and professionals are inter-

ested in appropriate and individual training plans. For

amateur athletes and in leisure sports, the usage of

activity tracking systems is increasing these days as

cited in (Krebs and Duncan, 2015). With these appli-

cations they can track their activities and analyze past

training sessions—with more or less accuracy (Yang

et al., 2015; Lee et al., 2014). But so far they can not

accurately predict the progress of training nor create

a suitable training plan including next steps to do.

Regarding outdoor cycling performance, (Balmer

et al., 2000) found peak power for a certain time to be

a useful predictor. Furthermore, (Tan and Aziz, 2005)

found that laboratory determined absolute peak power

might predict cycling performance on a ﬂat course,

and that relative peak power seems to be a useful pre-

dictor of performance during uphill cycling. But here,

too, laboratory tests are necessary beforehand in order

to predict the outdoor cycling performance.

Therefore, the goal of this study was to exam-

ine the feasibility in simulating performance—which

can be used for generating individual training plans—

without invasive methods like blood lactate measur-

ing, coaches, laboratory studies, or any other special

equipment. As a ﬁrst step towards this direction and

to compare the results to the results of laboratory stud-

ies, the method was tested on ambitious (leisure) cy-

clists only.

Recently, (Schaefer et al., 2015) described a

method for generating individual training plans based

on the Fitness-Fatigue model (Calvert et al., 1976),

a common antagonistic model for performance diag-

nostics.

Using the traipor concept, this paper presents

a new possibility in preprocessing non-standardized

data before ﬁtting necessary model parameters to an

individual without any laboratory measurements or

invasive methods. Combined with generating training

plans, ambitious sportsperson can easily ﬁgure out an

Ludwig, M., Schaefer, D. and Asteroth, A.

Training Simulation with Nothing but Training Data - Simulating Performance based on Training Data Without the Help of Performance Diagnostics in a Laboratory.

DOI: 10.5220/0006042900750082

In Proceedings of the 4th International Congress on Sport Sciences Research and Technology Support (icSPORTS 2016), pages 75-82

ISBN: 978-989-758-205-9

individualized training plan following personal con-

straints and based on nothing but their own training

data which they might already have collected.

2 STATE OF THE ART

The most common mathematical method to describe

and analyze the physiological adaption of the human

body to physical training was invented in the mid-

dle of the seventies and is known as Fitness-Fatigue

model (Calvert et al., 1976). This approach in per-

formance diagnostics is used and evaluated in several

studies, which are usually based on standardized or at

least controlled conditions and on a small amount of

mostly well-trained athletes. In spite of many alter-

native models that have been proposed since then, the

Fitness-Fatigue model is still one of the most impor-

tant and fundamental models in training control. Ba-

sically, performance is made up of two antagonistic

principles: training results in improved performance,

but it also induces fatigue which diminishes perfor-

mance. So the two-component model can be seen as

difference between ﬁtness and fatigue. A more feasi-

ble version is given by (Busso et al., 1994) as:

ˆp

= p

∗

+ k

n−1

∑

t=1

·e

−(n−t)

−k

n−1

∑

t=1

·e

−(n−t)

where ˆp

describes performance at day n and p

∗

is the

original performance level before workout. The input

w (e.g., wattage) is considered for the past n −1 days

of training. Here, τ

< τ

are time constants while

< k

are multiplicative enhancement factors.

Furthermore, Busso et al. compared different

modiﬁcations to the Fitness-Fatigue model in analyz-

ing the training effect in hammer throwing and cy-

cling on an ergometer (Busso et al., 1991; Busso et al.,

1994; Busso et al., 1997). They came to know that the

Fitness-Fatigue model with two components properly

simulates training response, while a more complex

version estimating time-varying parameter might im-

prove results.

At about the same time, Mujika et al. analyzed

the Fitness-Fatigue model relating to pre-competition

preparation in swimming. Despite a high variance

in parameters and regarding the correlation between

modeled and measured performance, the model is

appraised as useful for this purpose (Mujika et al.,

1996).

In 2006, Hellard et al. tried to estimate the useful-

ness of the Fitness-Fatigue model in monitoring train-

ing for elite swimmers. In that regard, the model pa-

rameters variances are found too high and no physio-

logical interpretation of these parameters can be moti-

vated, such that the model is evaluated as not useful in

monitoring this kind of training (Hellard et al., 2006).

In about 2000, Perl et al. invented a similar model

for performance diagnostics, called Performance Po-

tential Model (PerPot) (Perl, 2000). Pfeiffer et al.

compared PerPot to the Fitness-Fatigue model within

two cycling studies based on three college-aged stu-

dents each. He conﬁrmed the difﬁculties in interpret-

ing parameters of the Fitness-Fatigue model and con-

cluded a slightly better quality using PerPot (Pfeif-

fer, 2008). Despite its good simulation quality in

the majority of subjects, in our studies the PerPot

model exhibited instabilities in a signiﬁcant number

of cases making it less suitable for automatized gen-

erating training plans.

3 EXPERIMENTAL SETUP AND

METHODS

An online training portal called traipor was devel-

oped and was used to obtain the training data utilized

within the traipor concept. The portal offers the func-

tionality to ﬁt the Fitness-Fatigue model to the indi-

vidual user based on the user provided training data.

With the individual training parameters and the tech-

niques described in (Schaefer et al., 2015) the portal

is able to generate optimized training plans leading to

the given goals of its user while supporting a variety

of constraints, like a weekly training cycle or a maxi-

mum training load.

By using nothing but training data obtained from

the users themselves, the setup of the described

study is very different from laboratory based stud-

ies, especially since the training took place without

any mandatory training schedule, standardized perfor-

mance measurements or control of data quality.

3.1 Data Base

Among ambitious cyclists, measuring wattage and

heart rate during training is quite common. A per-

sonal analysis is then widely done using the train-

ing analytic software GoldenCheetah

or similar soft-

wares like Trainingpeaks™WKO+. To facilitate the

usage of traipor for the potential target group of am-

bitious cyclists, data can be uploaded from a CSV-

ﬁle exported directly from GoldenCheetah or similar

software. These data exports contain various train-

ing and performance metrics, enabling traipor to run

model ﬁttings for the users. Metrics were evaluated

http://www.goldencheetah.org/

icSPORTS 2016 - 4th International Congress on Sport Sciences Research and Technology Support

(a)

Age

(b)

Training

(c)

km in 2014

10k

15k

Figure 1: Subject’s distribution concerning (a) age, (b) av-

erage weekly training time, and (c) overall cycling distance

in 2014.

with respect to the attainable simulation quality us-

ing the presented experimental setting. Underlying

measures here are 60 minutes Peak Power (PP60)

for performance, and Training Stress Score (TSS) for

strain. The PP60 is used because of the lack of physi-

ological parameters like blood lactate concentration,

max or similar conditioned by the data gather-

ing, but is found a useful measure for outdoor cy-

cling performance (Balmer et al., 2000; Tan and Aziz,

2005). Since solely values deduced from measured

values were available, we compared the RMSE ﬁtting

quality of different TRIMP values, Skiba’s bike score

and TSS. Here, TSS reached best results, although all

measures were located in a very similar range.

Out of 52 cyclists that registered only 20 supplied

sufﬁcient data for ﬁtting, i.e., including both a value

for the strain metric and for the performance metric

and generating data using a power meter. Figure 1

shows the distribution of all 20 subjects concerning

age, average weekly training time and performed cy-

cling distance in 2014 per subject. All subjects had

been familiarized with the utilization of their pro-

vided data for research purposes and have been ac-

quaint about their self-responsibility in training and

data elicitation. Data privacy is ensured by design and

by pseudonymization.

3.2 Fitting Concept

In terms of adapting a performance model to a sub-

ject, the model’s parameter set has to be ﬁgured out.

A least squares approach is used to ﬁt parameters to

given data as widely suggested, e.g., by (Busso et al.,

1997). In preliminary comparative studies we found

any state of the art Quasi-Newton method to show

similar or better performance than stochastic search

methods while being computationally less expensive.

One of the model parameters describes the con-

cept of an initial performance level which is mod-

eled by p

∗

in the Fitness-Fatigue model, while the

other parameters are time constants describing how

fast a subject adapts to strain. p

∗

represents the per-

formance level without any speciﬁc training. It is also

the level an athlete returns to after stopping training.

Usually, laboratory studies make a speciﬁed train-

ing plan compulsory for each subject and often last

between 4 to 60 weeks, cf. (Pfeiffer, 2008). Per-

formance is often tested every three to ﬁve weeks

(cf. (Hellard et al., 2006; Busso et al., 1991)). In

these plans, ﬂuctuating strain is provided in order to

ﬁt model parameters to the subject’s adaptability. Fur-

thermore, subjects are aware of their responsibility

and controlled by some training supervisor. Since the

idea of the traipor concept was to simulate or pre-

dict performance process without laboratory studies

and ﬁxed training plans, such data can not be taken

as assured here. To deal with training data from non-

predeﬁned workout and without a certain quality, a

special ﬁtting concept is elaborated.

The therefore designed traipor concept for ﬁtting

can be subdivided in two parts: 1. data cleansing, and

2. data grouping. After this concept of preparing data,

subject’s individual parameters are determined using

a least squares approach evaluated on training days

only. Following parameter ﬁtting, a training plan can

be generated as described in (Schaefer et al., 2015)

regarding individual constraints.

3.2.1 Data Cleansing

Restricting the duration of training data to the cur-

rent and last year: As stated before, laboratory stud-

ies usually ﬁt their models over a one to few month

period of time. These studies predeﬁne a training plan

for subjects and can control the execution. Usually,

subjects can perform a variety of different load and

performance levels, whereby performance limits were

tested regularly. Since there is no supervision or con-

trol in this study, any performance development has to

be extracted from training data itself. A longer period

for ﬁtting therefore is beneﬁcial, since adaptability of

the human body to training can be mapped to the set

of system inherent variables. This is stated as general

adaptability to ﬁtness and fatigue within the param-

eter set. But if the ﬁtting period is too long, body

might have changed this adaptability over years and

react different to training.

Rejecting data which do not include both a value

for the strain metric and for the performance metric:

This step is necessary to avoid unusable data since

both values are inalienable.

3.2.2 Data Grouping

Group data sets according to the subjects speciﬁca-

tion: Within each group, the highest performance

Training Simulation with Nothing but Training Data - Simulating Performance based on Training Data Without the Help of Performance

Diagnostics in a Laboratory

ttf tf tf

Strain (TSS)

Measured Performance

Assumption

TSS / PP60

Figure 2: Grouping of data. The highest performance value

of each group tf is chosen to replace other performance val-

ues within this time frame (dotted line).

value replaces all values inside this group. Consid-

ering that even ambitious sportsperson do not reach

their personal performance limit within each training,

using every single performance value in ﬁtting might

lead to highly ﬂuctuating performance in a short time.

Therefore, information is needed about the approx-

imate time frame in which the subject does usually

reach its performance limit, e.g., weekly, biweekly, or

monthly. This information was provided by the sub-

ject itself. The highest performance in this speciﬁc

time frame approximate the real performance limit

more accurate and therefore is chosen for all perfor-

mances within this period. An example is illustrated

in Figure 2. For the speciﬁed length of the time frame

tf, given data set excerpt is divided into three groups.

Strain performed within a training session is repre-

sented by rectangles. After identifying the highest

performance value, all other performance values are

substituted with the very same and depicted as dotted

lines.

Accumulate all strain data performed on one day:

To use just one single value of strain and performance

for each day, strain is accumulated if training was per-

formed on several occasions same-day. Performance

value remains at the maximum performance value de-

termined beforehand during grouping of data.

3.3 Experiments

We divided our experiments into three main parts:

1. Ability of the presented concept to improve ﬁtting

quality for outdoor training data in general.

2. Comparison of results between this concept and

laboratory studies to prove usability.

3. Analysis of the underlying data in cases where ﬁt-

ting does not reach a reliable accuracy.

When comparing our results to laboratory studies,

ﬁtting correlation serves as reference value: In (Pfeif-

fer, 2008), results are evaluated using the intraclass

correlation coefﬁcient r

ICC

in version of r

ICC

(1,1)

(one-way random, single measure) regarding (Shrout

and Fleiss, 1979). The study of (Busso et al., 1991)

uses the Pearson correlation coefﬁcient r, and (Hel-

lard et al., 2006) and (Mujika et al., 1996) are using

the coefﬁcient of determination r

. Accordingly, re-

sults from the described ﬁtting concept are stated as

ICC

, r or r

value. Correlation measures are com-

puted between the simulated performance curve ac-

cording to estimated parameters from the ﬁtting con-

cept, and measured performance values.

3.4 Statistical Analyses

Considering performance analyses, it is important to

know the accuracy of the ﬁtting for a speciﬁc method.

The quality of a method is often given by the deviation

between a simulated curve compared to the measured

one.

Let n be the number of data points, x

the mea-

sured values with mean x and let y

be the simulated

values with mean y, i ∈ {1,2,...,n} . The absolute er-

ror is deﬁned by e

= |x

−y

|. The sum of squares er-

ror (SSE) is deﬁned by SSE =

∑

i=1

, while the total

sum of squares (SST) is given as SST =

∑

i=1

−x)

A total sum of squares for the simulation is indicated

with SST

. The root-mean-square error (RMSE) is

deﬁned by RMSE =

SSE

and serves as kind of a

standard deviation between the measured and the es-

timated curves.

Since different studies use different sta-

tistical measurements as described before,

these values were computed as well with

r =

∑

i=1

− x) · (y

− y) / (

√

SST ·

SST

= 1 − SSE/SST, and r

ICC

= ICC(1,1) according

to (Shrout and Fleiss, 1979). In all of these corre-

lation measures, a correlation value of 1 indicates a

good correlation and values near 0 indicate a missing

correlation. A value near -1 in r or r

ICC

correlation

value implies a negative correlation respectively.

Regarding statistical measures such as r with time

series with within-series dependencies, some difﬁcul-

ties have to be considered. With correlation coefﬁ-

cients, goodness of ﬁt and accuracy can not be mod-

eled adequately, it does only model the time-series

behavior in general. A good correlation value is

achieved if the curve structure of measured perfor-

mance and simulated performance are similar to each

other independent of possible variation in range or

scaling. Furthermore, if the measured performance

is given by a straight line such that the total sum of

squares sums up to zero or some small value near

zero, r and r

are undeﬁned or quite low even if

the simulated performance contains only small vari-

ances. Figure 3 shows an example where the r-value

is undeﬁned and indicates no correlation whereas

icSPORTS 2016 - 4th International Congress on Sport Sciences Research and Technology Support

0 5 10 15 20 25 30

100

200

300

400

days

TSS / PP60

Strain (TSS)

Measured Performance

Simulation

Figure 3: Example where the ﬁtting process results in a

small deviation, whereas the r-value is undeﬁned.

Table 1: Comparison of the RMSE and r-value both as

mean, median and standard deviation with and without the

traipor concept.

raw data concept

RMSE

mean 35.77 14.13

median 40.59 12.07

std 18.27 6.43

r-value

mean 0.27 0.57

median 0.26 0.65

std 0.12 0.25

the simulated performance curve does not deviate

much (RMSE = 8.72) from the measured performance

curve.

Therefore, we consider the r-value as one exem-

plary correlation measure to analyze a possible gen-

eral similarity between the ﬁtting and the measure-

ment. But for measuring the ﬁtting quality itself, we

particularly consider the RMSE.

4 RESULTS

Following we prove that the concept is useful to im-

prove ﬁtting quality for outdoor training, and is com-

parable to laboratory studies in some cases. Cases

were correlation can not reach such high values as in

laboratory studies are further analyzed in the end.

4.1 Usefulness of the Presented Concept

To prove that presented concept is able to improve ﬁt-

ting quality for outdoor training data, Table 1 shows

the average, median and standard deviation of the

RMSE and r-value over all subjects for both cases,

the raw data and the preprocessed data according to

the traipor concept. While the error can be reduced

more than 50%, the correlation value doubles for the

processed data sets proving both, a better correlation

and smaller deviation compared to the highly ﬂuctu-

ating raw data.

0 5 10 15 20

0.2

0.4

0.6

0.8

Fitting Correlation

ICC

Figure 4: Correlation values of r

ICC

, r, and r

for all 20

subjects (sorted).

Table 2: Average r

ICC

-value, median and standard devia-

tion over the correlating amount of subjects for studies from

Pfeiffer and the traipor concept.

Pfeiffer 1 Pfeiffer 2 traipor

Subjects 3 3 11

Mean 0.67 0.28 0.75

Median 0.64 0.45 0.78

Std. 0.12 0.38 0.10

4.2 Comparison to Laboratory Studies

Training data used in this study was obtained with-

out any quality control. Therefore, we analyzed the

reachable correlation according to the correlation val-

ues r

ICC

,r, and r

for all single subjects. Figure 4

shows these correlation values for each subject, sorted

descending by the corresponding value. Notwith-

standing that these three values were sorted indepen-

dently of each other, all three measures indicate a

high ﬁtting correlation for up to the same 11 sub-

jects. We therefore restricted the following compar-

isons to these subjects ﬁrst. The remaining nine sub-

jects are analyzed more individually afterwards in

subsection 4.3.

The ﬁrst comparison is made between the traipor

concept and two studies described in (Pfeiffer, 2008).

Table 2 shows average, median and standard devia-

tion computed for the intraclass correlation coefﬁcient

ICC

for the correlating results. The mean and median

value conducted over the best 11 subjects indicates a

higher correlation than in results from (Pfeiffer, 2008)

and even standard deviation is much smaller.

Table 3 illustrates the comparison of the presented

method with a study from (Busso et al., 1991). Here,

results of the presented traipor concept reach similar

correlation in median as Busso’s laboratory study, but

seems to have more variation according to the stan-

dard deviation and the greater variation to the average

r-value. A restriction to eight subjects is able to reach

the same average correlation.

Regarding r

-value and the study from (Mujika

et al., 1996), Table 4 (left) indicates similar results:

Training Simulation with Nothing but Training Data - Simulating Performance based on Training Data Without the Help of Performance

Diagnostics in a Laboratory

Table 3: Average r-value, median and standard deviation

over the correlating amount of subjects for the study from

Busso and the traipor concept.

Busso traipor

Subjects 8 11 8

Mean 0.83 0.78 0.83

Median 0.81 0.80 0.82

Std. 0.06 0.09 0.07

Table 4: Average r

-value, median and standard deviation

over the correlating amount of subjects for studies from Mu-

jika and Hellard and the traipor concept.

Mujika Hellard traipor

Subjects 18 9 11 9 2

Mean 0.65 0.79 0.61 0.65 0.82

Median – 0.78 0.64 0.64 0.82

Std. 0.12 0.13 0.14 0.12 0.13

traipor concept’s average r

correlation regarding

nine subjects is stated in a similar range as the av-

erage correlation coefﬁcient in Mujika’s study, for 11

subjects it is slightly below. Solely results of the study

from (Hellard et al., 2006) (Table 4, middle) achieve

an obvious better average correlation (0.79) than the

traipor concept which yields comparable results for

the best two subjects only. Depending on the particu-

lar study except for Hellard et al., data of between 8

and 11 subjects reached comparable correlations for

simulating performance.

4.3 Analysis of Lower Correlated Data

The remaining nine data sets where results were not

able to reach comparable correlation as in laboratory

studies are analyzed in more detail. These nine data

sets are therefore subdivided into groups with a sim-

ilar performance behavior. Since it was necessary

to exclude three data sets for comparison to Busso’s

study, these are analyzed ﬁrst.

Two out of three subjects which are excluded for

comparison to Busso’s study are identically to the

subjects excluded for comparison to Mujika’s study.

Exemplary, data of two of these subjects is illustrated

in Figure 5. Data of the third one shows a similar be-

havior as depicted in Figure 5a showing some huge

performance leaps which are not always reasonable

according to the underlying strain. As an example,

the performance gain between day 67 and day 118

based solely on the performance peak right before on

day 66. But with a training pause of over a month,

real performance would rather decrease than stay at

this higher level. Leaps like this are therefore ques-

tionable and a behavior like this is certainly not sim-

ulated by the model. Figure 5b shows a different be-

(a)

0 100 200 300 400 500 600

100

200

300

400

days

TSS / PP60

Strain (TSS)

Measured Performance

Simulation

(b)

0 50 100 150 200 250 300

100

200

300

400

days

TSS / PP60

Strain (TSS)

Measured Performance

Simulation

Figure 5: Exemplary subjects which has to be excluded for

the comparison with Busso.

havior: Here, performance does not change much at

all and varies around a mean performance value. As

explained in subsection 3.4, the r-value is often very

low when data is altering sparsely around its mean

value.

For a better overview, the remaining nine subjects

are numbered consecutively from 1 to 9.

Subjects 1-4: Regarding all 20 subjects, four of

them stated a weekly reaching of the individual per-

formance limit. But all of these four subjects are

inside the set of the excluded nine subjects. There-

fore, we analyzed correlation and ﬁtting quality for

these subjects again, assuming a monthly reaching of

the performance limit. Table 5 shows the compar-

ison between assuming a weekly and monthly per-

formance limit for these subjects. Since the r-value

of one subject reaches only a signiﬁcance-level of

p < 0.5% while the other three are signiﬁcant at a

p < 0.01% level, correlation and error values are con-

sidered for three and four subjects respectively. Re-

garding three subjects, assuming the reaching of a

monthly performance limit improves the average cor-

relation from r = 0.42 up to r = 0.57 within these

subjects, while evaluating all four subjects shows an

average improvement from r = 0.4 to r = 0.47. Ex-

Table 5: Assuming a weekly or monthly reaching of the

individual performance limit regarding 4 or 3 speciﬁc sub-

jects.

4 Subjects 3 Subjects

weekly monthly weekly monthly

RMSE

mean 26.52 17.74 29.27 19.10

median 28.18 14.80 31.95 15.93

std 8.45 7.24 7.86 8.22

r-value

mean 0.40 0.47 0.42 0.57

median 0.40 0.55 0.44 0.58

std 0.07 0.22 0.08 0.05

icSPORTS 2016 - 4th International Congress on Sport Sciences Research and Technology Support

(a)

0 100 200 300 400 500 600

100

200

300

400

days

TSS / PP60

Strain (TSS)

Measured Performance

Simulation

(b)

0 100 200 300 400 500 600

100

200

300

400

days

TSS / PP60

Strain (TSS)

Measured Performance

Simulation

Figure 6: Example for a subject stating a weekly reaching

of the individual performance limit.

0 100 200 300 400 500 600

200

400

600

800

days

TSS / PP60

Strain (TSS)

Measured Performance

Simulation

Figure 7: Example without huge performance gain resulting

in a minor r-value.

emplary, Figure 6a shows a simulation with weekly

assumed performance limit while Figure 6b illustrates

the same dataset with a monthly assumed reaching of

the performance limit.

The remaining ﬁve subjects with a correlation

value of r < 0.6 can be classiﬁed into two classes:

Subjects 5 to 8 could not achieve any distinct per-

formance changes and varied around their average

performance as shown exemplary in Figure 7. This

problem has been explained before.

Subject 9: Data of the last subject again shows the

converse behavior including large unexplainable per-

formance leaps additional to some ﬂat performance

in the end. The overall performance did not change

much over the whole time as shown in Figure 8.

0 100 200 300 400 500

100

200

300

400

500

days

TSS / PP60

Strain (TSS)

Measured Performance

Simulation

Figure 8: Example without huge performance gain but some

leaps in the middle resulting in a minor r-value.

4.4 Evaluation and Discussion

Considering the intraclass correlation, a high corre-

lation is accomplished with even better results than

those achieved in the corresponding laboratory stud-

ies from (Pfeiffer, 2008). Pfeiffer himself found that

results of his study 2 are inacceptable, but stated re-

sults from study 1 as good and very acceptable out-

comes. For up to eleven subjects, the traipor concept

reached higher correlation values than study 1.

Regarding the ﬁtting correlation in comparison to

studies from (Busso et al., 1991) and (Mujika et al.,

1996), results implicate that the traipor concept is as

accurate as laboratory studies for 8 to 9 out of 20 sub-

jects, since average correlation values are stated in a

similar range. Fitting accuracy of the traipor concept

is only clearly inferior compared to (Hellard et al.,

2006). One reason for this might be because of dif-

ferent types of athletes. The study of (Hellard et al.,

2006) was performed for nine elite swimmers. (Mu-

jika et al., 1996) analyzed performance in swimming,

too, but regarding the considered studies, only Hellard

et al. explicitly state dealing with elite sportsperson.

Data of the traipor concept originates from ambitious

but non-professional sportsperson, in case of the re-

stricted data aged 34 to 49 years, whose ﬁtness is cer-

tainly not comparable to elite swimmers. This differ-

ence regarding the subjects might be a reason for this

various correlation quality.

As stated before, the elaborated traipor concept

for ﬁtting has some differences compared to labo-

ratory studies. These lead to few limitations which

might lessen the accuracy and correlation of ﬁtting.

Even in this approach it is necessary for a suitable

ﬁtting that the subject reaches its personal limit regu-

larly, e.g., weekly or monthly. Without reaching the

own individual limit, a realistic performance progress

is not possible using the traipor concept. Further-

more, an oscillating training strain might lead to an

inconvenient parameter set modeling a constant strain

located between both performance values. Regarding

correlation coefﬁcients, the data grouping might lead

to straight line performances resulting in an undeﬁned

r-value as explained in subsection 3.4. Additionally,

this procedure might result in unrealistically high per-

formance values during a training pause if computing

a monthly performance maximum includes both, the

training break and a high performance value achieved

before the rest. Despite the ﬁtting on training days

only, some unrealistic performance changes may oc-

cur. These limitations are due to the unsupervised

and uncontrolled training without any speciﬁed per-

formance gain and the therefore constructed data pre-

processing.

Training Simulation with Nothing but Training Data - Simulating Performance based on Training Data Without the Help of Performance

Diagnostics in a Laboratory

5 CONCLUSION AND FUTURE

WORK

Compared to laboratory studies, the presented traipor

concept yields comparable results with similar ﬁtting

accuracy using the Fitness-Fatigue model.

Since this model is based on a convolution with

an exponential function, a straight line as it results by

replacing all measurements within one period (e.g.,

month) by the maximum value can generally not be

approximated. Changing this concept should there-

fore be considered. Other approaches using differ-

ent ﬁlters should be analyzed. Using a moving maxi-

mum function might also reduce leaps between differ-

ent performance measurements. This way, unrealistic

performance values near to a training break might be

avoided or reduced at least.

Predicting future performance based on a given

training plan is an interesting application of train-

ing models, e.g., to generate training plans to reach

a certain goal. Using the described method, it is

possible to predict training effects for the upcoming

month with similar accuracy as achieved in ﬁtting

(RMSE = 16.56). Even predicting six month into

the future yields acceptable results (RMSE = 20.62)

in all 11 subjects. Since in prediction preload plays

an important role (i.e., accumulated strain at T = 0)

special treatment of initial performance p

∗

was nec-

essary. Further research will be required to examine

the inﬂuence of preload as it should generally be con-

sidered in model identiﬁcation.

Analysis of further performance metrics, espe-

cially for submaximal performances as these are more

common in non-athletes, would be promising by en-

abling the utilization of training models in mass sports

and training devices. To verify accuracy results, fur-

ther experiments with more subjects, even less ambi-

tious cyclists and additional laboratory control exper-

iments have to be conducted.

ACKNOWLEDGEMENT

This work was supported by a funding of the state

North Rhine-Westphalia, Germany.

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