# Velocity quotient - endurance athlete's performance parameter

Jure Voglar

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Jure Voglar. Velocity quotient - endurance athlete's performance parameter. 2024. hal-04519203

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# Velocity quotient - endurance athlete's performance parameter

Jure Voglar¹*

¹National Institute of Chemistry, Department of Catalysis and Chemical Reaction Engineering, Ljubljana, Slovenia

* Correspondence: jure.voglar@ki.si

## Abstract

**Purpose:** Performance assessment and analysis of aerobic endurance athlete usually requires the use of expansive measurement equipment in a laboratory setting. The main motivation for the paper was the fulfilment of a goal of obtaining a reliable, objective and easily measurable endurance athlete's performance parameter, which would serve coaches and athletes to track their progress, as well as a benchmark for comparison amongst the athletes competing in the same discipline.

**Methods:** The main idea of the paper originates from the fact that each individual endurance workout causes a physiological response in a human body. Therefore, the newly developed athlete's performance parameter - velocity quotient (VQ) considers both the athlete's actual performance (velocity) and his/her response (heart rate) to it. The VQ parameter's behavior was theoretically investigated in case of running. The reliability of the VQ parameter was also experimentally validated with dataset obtained during multiple running exercises of a single recreational level athlete.

**Results:** The velocity quotient showed potential for being a reliable predictor of endurance runners' performance on a theoretical base which was supported by the preliminary experimental validation study, which produced the value of Pearson's correlation coefficient between the velocity quotient and the sports watch estimated VO2max of 0.7942.

**Conclusion:** The behavior of the velocity quotient was predicted at various exercise intensities (average heart rates) and fitness levels. Fairly good correlation between the velocity quotient and the sports watch estimated VO2max was found while more daily variations of VQ than for VO2max were observed.

**Keywords:** performance analysis; endurance exercise; running; heart rate; health

## 1 Introduction

There are multiple available methods and parameters for assessment of performance of athletes. Examples of some of them include: (i) maximal oxygen uptake - VO2max (Legaz-Arrese et al., 2007; Lounana et al., 2007; Storer et al., 1990), (ii) movement (running) economy (Barnes & Kilding, 2015), (iii) fractional utilization (usually expressed in percentage of VO2max) (Scrimgeour et al.,
1986), (iv) velocity at maximal oxygen uptake - vVO2max also known as maximal aerobic speed - MAS (Bellenger et al., 2015; Sandford et al., 2019) and (v) lactate threshold - LT (Ghosh, 2004). Also, parameters considering physiological responses during endurance workout were developed, for example: (i) rating of perceived exertion - RPE (Arney et al., 2019), (ii) TRIPM (training impulse) method (García-Ramos et al., 2015) and (iii) training stress score - TSS (van Erp et al., 2019).

However, the majority of the athlete's performance parameters do not simultaneously consider both the athlete's performance and physiology and their connection. For example, VO2max is highly praised in the running and cycling community. On the other hand, this parameter on its own is not a perfect metric for assessment of endurance athlete's performance (Bassett & Howley, 2000). This could originate from the fact that the VO2max testing does not include the endurance aspects of performance and it does not consider the actual performance of an athlete (velocity). Similarly, all the other endurance athlete's performance parameters are not standalone and usually have to be considered together (e.g. VO2max, running economy and LT) to give an accurate estimate of the athlete's performance.

The idea for development of an objective athlete's performance parameter, which considers both athlete's performance (velocity) and physiological response (heart rate) came up. This kind of performance parameter should be able to accurately predict/determine the athlete's actual performance and enable him/her to track the progress during the season/seasons. The work of Vesterinen et al. (Vesterinen et al., 2014) showed promising results by formulating the heart rate-running speed (HR-RS) index, which requires a baseline maximal field test and is only considered and applicable to runners. Our theoretical insight into the (self)assessment of endurance athlete's performance with development of the velocity quotient (VQ) performance parameter was inspired by the work of Maffetone (Maffetone, 2010) and his so called MAF (maximal aerobic function) test, where improvement in performance is defined as having higher velocity at the same (or similar) MAF heart rate, defined by the famous (180 - age) formula.

The main objective of the article is development and preliminary experimental validation of an objective, reliable endurance athlete's performance parameter, which considers both athlete's performance and physiological response, while being determined with the use of inexpensive measuring device. This can ensure that the developed performance parameter will be easily accessible both to professional and recreational level endurance athletes.

## 2 Methods

Since almost every athlete usually wears a GPS (global positioning system) sports watch with an accurate (Stahl et al., 2016) optical (or a chest strap) heart rate measuring device (Karvonen & Vuorimaa, 1988), the athlete's velocity and heart rate are easily accessible pieces of information about each workout. The newly proposed parameter is therefore easy to determine, because it needs only data of time-averaged velocity and time-averaged heart rate during the continuous-type athletic workout. The velocity quotient (VQ) is combining both the athlete's actual performance (velocity - v) and physiological response (heart rate - HR) during the activity:

$$VQ = \frac{v}{HR}$$
The VQ quotient is therefore a simple and reliable assessment and self-evaluation metric of endurance athlete's performance. This metric could be used across different endurance athletic disciplines e.g. running, cycling, swimming, rowing and many others. The values of the VQ would not be comparable between the different disciplines; since efficiencies of the movement are much different (e.g. cycling has higher efficiency compared to running). On the other hand, it would be interesting to determine, which alethic disciple exhibits the highest value of the VQ parameter and consequently the highest movement efficiency, especially at the elite level athletes.

Both the velocity and heart rate values in the above formula should be time-averaged values of the whole workout to be representative. The workout for assessment of VQ should be done at a selected constant submaximal level of intensity (below 80% of MAS); with only small variations of both the pace and the heart rate during the workout. The duration of the activity should last long enough to detect the endurance performance aspects of an athlete (at least 10 minutes) while at the same time not so long to induce cardiac drift (Dawson et al., 2005). Instantaneous value of the VQ parameter could on the other hand also be constantly monitored during each endurance exercise to give athlete an instantaneous feedback.

The limitations and conditions when using the VQ for assessment of athlete's performance should be carefully considered. The conditions and factors affecting the values of the VQ are:

* Athletic discipline and the used equipment (both influencing movement efficiency),

* Environmental factors (weather, altitude gain),

* Athlete's characteristics (baseline heart rate, body mass index, stress levels, age and sex),

* Duration of the activity (or the total travelled length).

One of the drawbacks of the VQ parameter seems to be its multiple above-mentioned factors affecting its determination. If the VQ parameter will be commonly used in the endurance athlete's community it might evolve and get some correction factors for the testing conditions during its determination (e.g. factors for weather conditions, exercise duration), which might on the other hand reduce its simplicity of determination.

The unit of the velocity quotient is in travelled length per heartbeat (e.g. in metric system meters per heartbeat or in short meters per beat - mpb). The higher the VQ value, the more distance the athlete covers in a single heartbeat, which means that his/her aerobic fitness/performance is better.

The first attempt of experimental validation study of the velocity quotient as endurance athlete's performance parameter has been done by the author (physically active male adult - recreational level runner; age: 31 years, body mass: 80.3 kg, body height: 1.91 m, body mass index: 22.0 kg/m²) via measurement of his own time-averaged running velocity and time-averaged hart rate by use of the sports watch with an optical hart rate monitor (Garmin Forerunner® 235). Thirty running workouts were conducted outdoors via running on the road with one workout per day. On average the daily workout had length of 16.48 km. The collected data was statistically analyzed. The calculated values of VQ parameter were compared (via statistical methodology) to the sports watch assessed VO2max values with an indirect method (Buttar et al., 2019).
## 3 Results

The theoretical investigation of the behavior of the VQ parameter during running starts with observation of Vesterinen et al. (Vesterinen et al., 2014), who based their HR-RS index on the linear relationship between heart rate and running speed, which was also observed by Lambert et al. (Lambert et al., 1998). It is worth noting that the linear HR-RS relationship is valid and observed at submaximal intensities, since when intensity increases (above 80% of MAS) the heart rate stops following the linear trend with running velocity (Boudet et al., 2004), which is called the deflection point in the heart rate-running velocity relationship (Vachon et al., 1999). Consequently, our theoretical investigation is valid for submaximal intensities, which are representing the majority of endurance athlete's exercises. For example, runners run marathons between 60 and 75% of their VO2max levels (Maughan & Leiper, 1983).

The linear relationship between running velocity and heart rate is expressed as:

$$v = a \cdot HR + b = A \cdot (HR - HR_r)$$

and presented on Fig. 1 a). Symbols a, b and A are coefficients while $HR_r$ is the athlete's resting heart rate.
<figure><img src="image_2.png" /><figcaption>**Fig. 1** Velocity vs. heart rate (a) and velocity quotient (VQ) vs. heart rate (b) plots at the reference state: A = 0.1 km/(h·bpm) = 1.667 mpb, HRr = 58 bmp and after endurance adaptation (EA): A = 0.25 km/(h·bpm) = 4.167 mpb, HRr = 50 bmp; and comparison between values of velocity quotient (VQ) and sports watch estimated VO2max (c) after each of the 30 individual outdoor running workouts performed by the same athlete on consecutive days</figcaption></figure>
The coefficients a and b are related to coefficient A and the resting heart rate as: a = A and b = - A·HRr.

The velocity quotient (VQ) can be expressed as:

$$VQ = a + \frac{b}{HR} = A \cdot \left(1 - \frac{HR_r}{HR}\right)$$

which is accompanied with its graphical presentation (Fig. 1 b) for the two cases: reference state (ref) and endurance adapted state (EA) of an endurance athlete.

The preliminary experimental validation study of the VQ parameter was done with the dataset presented on the Table 1, which summarizes the recorded and calculated parameters (time-averaged velocity - v, time-averaged heart rate - HR, VQ and VO2max) on each of the 30 workouts performed on consecutive days. The values of mean of the velocity, heart rate, VQ and VO2max are 10.6 km/h, 144 bpm, 1.23 mpb and 51 mL/(kg·min), respectively. Standard deviations of the velocity, heart rate, VQ and VO2max are 0.211 km/h, 4.96 bpm, 0.0350 mpb and 0.76 mL/(kg·min), respectively.
<table><caption>Table 1 Experimental validation dataset with the calculated performance parameters</caption><thead><tr><th>Workout (/)</th><th>v (km/h)</th><th>HR (bpm)</th><th>VQ (mpb)</th><th>VO2max (mL/(kg·min))</th></tr></thead><tbody><tr><td>1</td><td>10.6</td><td>146</td><td>1.21</td><td>50</td></tr><tr><td>2</td><td>10.6</td><td>148</td><td>1.19</td><td>50</td></tr><tr><td>3</td><td>10.6</td><td>152</td><td>1.16</td><td>50</td></tr><tr><td>4</td><td>10.5</td><td>147</td><td>1.19</td><td>50</td></tr><tr><td>5</td><td>10.6</td><td>147</td><td>1.20</td><td>50</td></tr><tr><td>6</td><td>10.2</td><td>136</td><td>1.25</td><td>51</td></tr><tr><td>7</td><td>10.4</td><td>137</td><td>1.27</td><td>51</td></tr><tr><td>8</td><td>10.5</td><td>142</td><td>1.23</td><td>51</td></tr><tr><td>9</td><td>10.5</td><td>141</td><td>1.24</td><td>51</td></tr><tr><td>10</td><td>10.6</td><td>141</td><td>1.25</td><td>52</td></tr><tr><td>11</td><td>10.3</td><td>138</td><td>1.24</td><td>52</td></tr><tr><td>12</td><td>10.6</td><td>140</td><td>1.26</td><td>52</td></tr><tr><td>13</td><td>11.0</td><td>148</td><td>1.24</td><td>52</td></tr><tr><td>14</td><td>10.8</td><td>148</td><td>1.22</td><td>51</td></tr><tr><td>15</td><td>10.7</td><td>151</td><td>1.18</td><td>51</td></tr><tr><td>16</td><td>10.5</td><td>149</td><td>1.17</td><td>50</td></tr><tr><td>17</td><td>10.6</td><td>151</td><td>1.17</td><td>50</td></tr><tr><td>18</td><td>10.4</td><td>148</td><td>1.17</td><td>50</td></tr><tr><td>19</td><td>10.3</td><td>137</td><td>1.25</td><td>51</td></tr><tr><td>20</td><td>10.2</td><td>135</td><td>1.26</td><td>51</td></tr><tr><td>21</td><td>10.5</td><td>137</td><td>1.28</td><td>52</td></tr><tr><td>22</td><td>10.9</td><td>147</td><td>1.24</td><td>51</td></tr><tr><td>23</td><td>10.6</td><td>144</td><td>1.23</td><td>51</td></tr><tr><td>24</td><td>10.9</td><td>146</td><td>1.24</td><td>51</td></tr><tr><td>25</td><td>10.7</td><td>141</td><td>1.26</td><td>52</td></tr><tr><td>26</td><td>10.3</td><td>144</td><td>1.19</td><td>51</td></tr><tr><td>27</td><td>10.6</td><td>143</td><td>1.24</td><td>51</td></tr><tr><td>28</td><td>10.6</td><td>138</td><td>1.28</td><td>52</td></tr><tr><td>29</td><td>10.9</td><td>143</td><td>1.27</td><td>52</td></tr><tr><td>30</td><td>10.9</td><td>148</td><td>1.23</td><td>52</td></tr></tbody></table>

Since the sports watch has a built-in algorithm for assessment of the VO2max, the calculated values of velocity quotient (VQ) were presented along with the estimated VO2max (Table 1, Fig. 1 c). The fitted linear trendline between the two parameters has the equation:

$$VQ = 0.0363 \cdot VO2max - 0.6264$$

while the coefficient of determination (R²) is equal to 0.6307, which means that the Pearson's correlation coefficient equals to 0.7942.
# 4 Discussion

If an athlete is able to maintain higher heart rate while avoiding cardiac drift, his/her VQ is also higher, which converges to the value of A with increasing heart rate (Fig. 1 b).

However, the higher athlete's performance (adaptation to endurance training regime - EA) means that the slope (A) will have a larger positive value and the resting heart rate (HR) should be slightly lower (Carter et al., 2003) compared to the reference state (ref) before the endurance adaptation; Both of these factors contribute to the increase of the values of VQ (at the same heart rate) as can be observed on the Fig. 1 b).

The preliminary experimental validation study of the VQ parameter revealed that the two parameters (VQ and estimated VO2max) seem to have a fairly good correlation. However, there are more daily variations of VQ than for VO2max (Fig. 1 c), which could be attributed to the built-in algorithm considering previous workout history and/or some other factors (e.g. environmental conditions) and the fact that values of VO2max take up only integer values, which gives this parameter lower resolution.

# 5 Conclusions

The velocity quotient (VQ) parameter could be used as a metric for determination of movement efficiencies of various different endurance athletic disciplines, which would enable comparison between them.

The preliminary experimental validation study on a dataset with multiple running workouts supports the claims of reliability and ease of measurements and determination of the VQ parameter.

The velocity quotient (VQ) could be used for assessment of athlete's performance in many sorts of aerobic endurance sports: running, cycling, swimming, rowing and others.

The sports equipment (sports watch) manufactures could easily add a new built-in algorithm for determination of velocity quotient VQ to help their clients with tracking their performance.

The VQ parameter could also be used for aerobic and cardiovascular health assessment amongst the general population via physical examinations by general medical doctors.

The sports science and medical researchers are encouraged to do further (laboratory) testing (on multiple endurance athletes and in various disciplines) and assessments of quality of the VQ parameter for purpose of assessment of endurance athlete's performance and as a predictor of general cardiovascular health.

The article is summarized in Fig. 2, where its methodology, main results and conclusion are presented.
# Velocity quotient - endurance athlete's performance parameter

<figure><img src="image_3.png" /><figcaption>Fig. 2 Graphical summary of the article</figcaption></figure>

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