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Original Research

Energy Expenditure During Tennis Play: A Preliminary Video Analysis and Metabolic Model Approach

Botton, Florent1,2; Hautier, Christophe2; Eclache, Jean-Paul1

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Journal of Strength and Conditioning Research: November 2011 - Volume 25 - Issue 11 - p 3022-3028
doi: 10.1519/JSC.0b013e318234e613
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Tennis is a complex activity involving both anaerobic and aerobic metabolism (9,11,16). As a consequence, it is difficult to evaluate the physiological demands during matches. On average, the physiological responses to tennis matches have been reported to be rather modest, with the average exercise intensity generally being <60–70% of the O2max (9,11,16). Owing to the intermittent nature of the game involving periods of high-intensity, mean aerobic values are not sufficient to fully understand the demands of tennis. Despite the fact that everyone is aware of the anaerobic load of modern tennis, very few studies have been conducted to evaluate these levels during matches. Blood lactate concentration is considered to be a marker of anaerobic energy expenditure and has been measured at around 1.8–2.8 mmol·L−1 during a match (9), which can increase to 8 mmol·L−1 during long and intense rallies (5), suggesting the increased involvement of anaerobic glycolytic processes for supplying energy. However, blood lactate is an imperfect marker of anaerobic energy expenditure because it is only a reflection of the balance between lactate production and clearance. All the methods used in previous studies are reliable enough for estimating the total energy expenditure during a tennis match, but nobody has measured or estimated the instantaneous metabolic load, and particularly during the high-intensity periods, which are so crucial in a match.

It has been demonstrated that the energy demand in soccer can be estimated through video analysis, in combination with a metabolic model (23). In previous studies, we suggested initially evaluating the oxygen consumption requirement known in this study as “metabolic power” (MP) of constitutive activities in tennis such as running and hitting the ball (2,3). This model has to be carried out and validated to be used by a sport coach to evaluate the MP and energy expenditure during tennis matches or training sessions.

The first aim of this study was to put forward and to validate a method to assess the MP and energy expenditure of tennis. In this way, the amount of aerobic energy calculated during tennis games will be compared with the energy measured via a portable gas analysis device. Once validated, the model was applied to analyze additional games and calculate the aerobic and anaerobic energy expenditure during games, points, and strokes.


Experimental Approach to the Problem

The method used in this study can be broken into the following 5 stages: (a) The MP involved in the main fundamental activities (FAs) in the game of tennis was estimated (strokes, services, movements) in line with the studies of Botton and Eclache (2) and Botton et al. (3). (b) Video analysis enabled us to sequence each phase of the game and to determine the activity profile during the match. This was used to calculate the MP. (c) Using a simplified model based upon the mathematical Astrabio© model, which consists of a series of mathematical equations describing the metabolism response to an input stress (8), we were able to assess the aerobic and anaerobic energy expenditure. (d) The quantity of O2 consumed as estimated by the model was compared with the values obtained with the portable gas analysis system K4b2 (Cosmed, Rome, Italy). (e) Once validated, the model was applied for 1 tennis set without the player wearing any equipment.


Eight competitive healthy and regionally ranked male tennis players agreed to participate as subjects in the experiment (mean ± SD: age 25.2 ± 1.9 years, weight 79.3 ± 10.8 kg, O2max 54.4 ± 5.1 ml·kg−1·min−1). All subjects in the study gave informed consent. All the players were involved in regular tennis competitions, and all of them have a similar level (international ranking 3). The mean training background of the players was 11.0 ± 4.3 years, which focused on tennis-specific training and aerobic and anaerobic training. All the participants were right-handed tennis players. They were briefed about the experimental conditions and the risks associated with the experiment. The Institutional Review Board for Human Investigation approved all the experimental procedures.

O2max was determined directly during an incremental test on an ergocycle (Monark 824 E, Stockholm, Sweden) at 80 rpm with an increase of 20 W·min−1 to reach exhaustion in <17 minutes (2,3). The ergocycle protocol was chosen to permit a medical examination of arterial pressure and electrocardiogram. Gas samples were analyzed in real time by the Mariane© system previously described (TBM, Chassieu, France) (2): Ventilated air volume was measured breath by breath by integration of air flow measured through a turbine, and the expired air composition was analyzed for O2 concentration (zirconium analyzer) and CO2 concentration (infrared analyzer). Maximal oxygen consumption was determined when the subjects reached the oxygen uptake plateau (“leveling off” criterion).

All the experimental sessions were conducted in the morning during summer. The players were advised to have no strength or endurance training at least 48 hours before the test and to take a carbohydrate-rich meal 2 hours before testing. Hydration level was not checked, but we instructed the players to avoid any risk of dehydration.


Step 1: Determine the Metabolic Power of the Fundamental Activities of Tennis

The tennis game was broken down into 5 FAs (2): walking, running movements, sitting on a chair to rest, hitting the ball (forehand and backhand), and serving. For each FA, through calibration, it was possible to assess the MP as expressed in liters of O2 equivalents per minute.

Walking: Relative oxygen consumption (milliliters per kilogram per minute) while walking was measured by means of an incremental protocol on the court. The subjects started at 3.5 km·h−1 (56.2 m·min−1), and the speed increased by 0.5 km·h−1 every 105 seconds until a speed of 7.0 km·h−1 (112.5 m·min−1) (Figure 1).

Figure 1:
Aerobic energy expenditure by velocity (V) for walking (○) and for running movements for 4 different sudden turn rates (▴) (2). The straight lines (—) are generated by equations 1 and 2.

The linear relationship obtained between oxygen consumption and walking velocity (Figure 1) allowed us to calculate the following equation:

The EEO2p Y-intercept was the postural consumption of oxygen equal to 5.0 ml·kg−1·min−1, and the slope of the relationship CE was the energy cost of walking estimated at 0.084 ml·kg−1·min−1, the subject mass was expressed in kilograms, and V was the walking velocity (meters per minute).

Running: Relative oxygen consumption of running was measured during an incremental protocol of linear movement, with an initial phase of 3.5 km·h−1 (56.2 m·min−1) and an increase in velocity of 1.0 km·h−1 every 105 seconds until a velocity of 11.5 km·h−1 (187.5 m·min−1). Additionally, the energy expenditure during shuttle running (linear movement) was assessed for 3 rates of sudden turns (22, 33, and 50 turns per minute) and 4 running speeds (3, 4, 5, and 6 km·h−1) (Figure 1): the level duration was fixed at 2 minutes for each running speed and for a given turn rate resulting in an 8-minute experiment for each turn rate. The distances between the 2 markers increased at each level to increase the speed without changing the level duration (2).

The MP was obtained from the following equation:

The EEO2p Y-intercept equals 5.0 ml·kg−1·min−1, the CE of the run equals 0.169 ml·kg−1·min−1, ω is the sudden turn rate (turns per minute), V is the speed (meters per minute), the subject's mass in kilograms and the p and q coefficients equal 0.019 and 1.193, respectively.

Resting: Oxygen consumption over the periods spent sitting down and resting was measured for 10 minutes.

The EEO2p is equal to 3.67 ml·kg−1·min−1, and the mass is expressed in kilograms.

Hitting the ball: In line with the study of Botton et al. (3), the EEO2 for hitting the ball was measured on the court during the incremental protocols for the forehand and the service: the rate of racket strokes (ω) increased from 4 to 18 strokes per minute for the forehand and from 4 to 12 strokes per minute for the service. An experienced professional coach was instructed to throw up the tennis ball at a constant speed in the same direction to allow the player to realize the forehand stroke without displacement. The oxygen consumption values yielded by the K4b2 were then averaged out for the final 30 seconds of each 2-minute phase.

These stroke frequencies were chosen to obtain linear relationships between oxygen consumption and the stroke frequency (ω) (strokes per minute). The maximal rate of the racket strokes was determined to limit the intensity under the anaerobic threshold estimated during the preliminary laboratory test (Figure 2). These relationships were described by straight lines where the slope yielded the energy cost of the stroke (CE) (milliliters per kilogram per stroke):

Figure 2:
Oxygen consumption–stroke frequency relationships determined for the forehand (·) and service (▴).

The EEO2p Y-intercept is the postural oxygen consumption, which equals 4.8 and 7.8 ml·kg−1·min−1 for the strokes and services.

The MP of the strokes was obtained from the following equation:

The CE is the energy cost of the stroke (milliliters per kilogram per stroke), and dt is the stroke duration (minutes).

The CE of forehand strokes and services equaled 2.1 ± 0.5 and 3.0 ± 0.1 ml·kg−1·per stroke, respectively (3). The duration of strokes and services were estimated, respectively, at 0.88 ± 0.10 and 1.22 ± 0.05 seconds for strokes and services (2).

Step 2: Video Analysis and Sequencing of Games

During games, movements and strokes were recorded by a Canon MVI 850i digital camcorder with a Canon A28 wide-angle lens positioned off the court, 6 m behind the baseline and at a height of 5.55 m. This allowed the half of the court nearest the camera to be filmed. The video analysis followed the belt of the player with the Kinovea® software and calculated the x and y coordinates in pixels (px) on the computer screen. We created a geometric X (meters) and Y (meters) projection on the map of the playing area to calculate the subjects' displacements.

The tracking method was calibrated using 86 points whose location was known to within 1 cm, covering the full length of the OX (parallel to the net) and the OY axes (going back from the net). The correlation coefficient between the X and Y positions calculated and the real position came to 0.99 (p < 0.0001); the mean prediction error stood at 0.25 ± 0.25 and 0.23 ± 0.16 m, respectively, along the OX and OY axes. By analyzing movements and detecting racket strokes, it was possible to break the tennis match down into 5 FAs, to establish the duration and velocity of displacements and to estimate the MP.

Step 3: Calculation of the Proportion of Aerobic and Anaerobic Metabolism in Supplying Energy

The oxygen consumption (EEO2mod) (liters per minute) was calculated for each FA using a monoexponential model:

If EEO2mod (i) ≥ O2max, then EEO2 (i) = O2max.

EEO2mod(i − 1) is the initial value of EEO2mod at the start of the FA(i), dt(i) is the duration of the FA(i), and τ is the time constant of the aerobic metabolism.

During the on-transient EEO2 kinetic (i) (MP(i) > EEO2mod(i − 1)), τ was a mean value set at 0.70 minutes (14,25).

During the off-transient EEO2 kinetic (i) (MP(i) < EEO2mod(i − 1)), τ equaled 1.00 minute. The value was determined by calculating the mean response time (MRT) for a triexponential model (17) applied for the off-transient phase after a supratransitional running exercise (25).

The amount of EO2mod(i) aerobic energy calculated at the end of the FA(i) with a duration of dt(i) was the integral of EEmod(i) for dt(i):

The anaerobic energy expenditure (EEanmod) was the difference between MP(i) and EEO2mod(i). The total quantity of the anaerobic energy (Eanmod) at the end of an FA(i) corresponded to the calculated oxygen deficit, in accordance with the method proposed by Medbo et al. (19).

The total energy expenditure (EEtot) (equivalent liters per minute) calculated across different time ranges was the ratio between the total amount of energy (EO2mod + Eanmod) and the duration of the range of time considered.

Step 4: Comparison of the Modeled Consumption of Oxygen and the Consumption of Oxygen as Measured by the K4b2

The experiment took place on a resin-covered tennis court (e.g., category 3 court surface, asphalt court). After a standardized 15-minute warm-up involving 10 minutes of low-intensity forward, sideways, and backwards running, acceleration runs, and 5 minutes of ground strokes, the 8 subjects participating in the study played 2 games while wearing the K4b2, with their activity profile being measured by the video analysis system. The MP for each FA was calculated as described earlier: EEO2mod and EO2mod were evaluated based upon the simplified bioenergetic model (8). The modeled quantities of O2 (EO2mod) were compared with those measured under experimental conditions (EO2mes) with the K4b2 used for each game. In accordance with manufacturer's guidelines, the K4b2 was warmed up for 40 minutes before calibration. Calibration involved 10 pumps of a 3-L syringe into the Cosmed turbine, a room air calibration (20.93% O2 and 0.03% CO2) and a calibration with a standard gas mixture of O2 (15.6%) and CO2 (5.66%) for the analyzers.

Step 5: Estimation of the Respective Proportion of Aerobic and Anaerobic Metabolism during Games, Points, and Strokes

The players performed a 1-set training match without wearing any equipment. Video analysis was applied to determine the activity profile, and the simplified model was used to calculate averaged and instantaneous aerobic and anaerobic energy expenditure.

Statistical Analyses

A Student test for matching data was used to compare the quantity of O2 consumed as estimated by the model (EO2mod) with the values obtained with the K4b2 portable analysis system (EO2mes) across all 16 games (StatGraphics Centurion XVI). Correlation coefficient (r) between the EO2mod and EO2mes and the standard estimate error (SEE) for the 16 games played by the 8 players were calculated. The SEE was calculated according to the following formula:

The significance level was set at p ≤ 0.05.



The mean duration of the 16 games played with the K4b2 was 3.1 ± 1.3 minutes. There was no significant difference between EO2mod and EO2mes for the 16 games analyzed (p = 0.763). The correlation coefficient between EO2mod and EO2mes reached 0.93 (p < 0.0001), and SEE stood at 0.018 L·kg−1.

The mean calculated for the EEO2mod for the 16 games was 51.7 ± 10.5% O2max and for EEO2mes, it was 52.0 ± 9.1% O2max.

Proportion of Aerobic and Anaerobic Metabolism during the Match

Thirty-five games were played over the course of 4 training matches without wearing the K4b2. The mean duration of the games was 2.5 ± 1.3 minutes, and the mean duration of a point was 4.6 ± 0.7 seconds. The effective playing time was 19.5 ± 2.2% of the total game time.

The EEO2mod during the total 35 games and including the rest phases spent sitting down stood at 49.4 ± 4.8% O2max; excluding the rest phases between games, it stood at 53.8 ± 7.0% O2max if. EEtot stood at 78.9 ± 8.7% O2max during the games, 186.0 ± 11.2% O2max during the points, 250.3% O2max for forehands and 255.2% O2max for services (Figure 4).

For the sequence involving games and rest phases, the proportion of anaerobic metabolism for the total energy supply was 26%; this was 32% across all the 35 games. The relative amount of anaerobic metabolism accounts for 67% of the total energy expenditure for points and 95% for racket strokes (Figures 3 and 4).

Figure 3:
Example of the result showing aerobic energy expenditure EEO2(i) (—) and metabolic power MP(i) (---) for a game of 3.63 minutes for 1 subject (Figure 1O2max = 3.40 L·min−1).
Figure 4:
Estimates of the proportion of aerobic (EEO2mod) and anaerobic (EEanmod) metabolism in the total energy expenditure for different phases of the tennis games.


The aim of this study was to put forward a new and simplified method that can be used in tennis, making it possible to estimate aerobic and anaerobic energy expenditure by analyzing player movements and racket strokes. This study showed that even when the EEO2 average is quite low and nears 50% of O2max, the total energy expenditure of a point can reach up 2 or 3 times the O2max of the subjects. In tennis, it is important to have recourse to anaerobic metabolism, and this can account for around 30% of the total energy expenditure per game and almost 70% during points.

The amount of aerobic energy during games, as estimated by the model, shows no statistical difference with the amount measured with the K4b2 (p < 0.05), and the 2 measurements are very strongly correlated (r = 0.93, p < 0.0001). The average aerobic energy expenditure modeled by the game is close to the measurement with the K4b2 (51.7 ± 10.5% O2max vs. 52.0 ± 9.1% O2max), in agreement with the values given in previous studies of between 50 and 60% O2max (9,11,16). However, given the intermittent nature of tennis, the average values of the aerobic intensity are not sufficient for working out the physiological demands of this activity. The idea behind the method used was therefore to provide an indirect estimate of the amount of anaerobic energy by calculating the oxygen deficit. This method has often been used in the field to estimate the proportion of anaerobic metabolism during simple and fundamental activities such as running and swimming (1,7,22,27,28). In this method the MP required for FAs such as running and racket strokes during tennis needs to be established in advance (2,3). However, it should be noted that it is principally acceleration and deceleration, which have the most significant impact on the energy cost of movement (6,23). This is the reason why the energy cost of sudden turns has been taken into account for this study. In accordance with a recent study (10), the present results demonstrate that hitting the ball is an FA, which requires a high MP reaching 2–3 times the O2max of the player for the forehand (MP = 11.6 ± 1.7 equiv·L·min−1) and the service (MP = 12.5 ± 1.9 equiv·L·min−1) (Figure 4). Given the MP values generated during the FA, and the average duration of points of 4.6 ± 0.7 seconds and the inertia of the aerobic metabolism (i.e., at the onset of square wave exercise, the O2 uptake attains a steady level only after 3–4 minutes), anaerobic energy represents roughly 70% of the total energy expenditure estimated for points and 95% for racket strokes (Figure 4). In support of the assumption of Mendez-Villanueva et al. (20), during points, energy comes almost exclusively from the anaerobic metabolism. On the other hand, given the duration of points and considering that rest phases represent 80% of the total time, we can advance that players are likely to rely on phosphocreatine to replenish adenosine triphosphate. This tends to explain why the blood lactatemia measured during the match remains generally low, between 2 and 4 mmol·L−1 (16,30), and only rarely rises to 8 mmol·L−1 during intense and/or long rallies (5). The lactatemia therefore varies depending on the type of game and the type of surface: it is higher for players playing from the back of the court and also for matches on clay in terms of the average length of points and a larger effective playing time (18,21). Once the energy expenditure is calculated for a period of time including points and the rest phases, the aerobic metabolism becomes more significant and the anaerobic metabolism accounts for only 26% of the total energy expenditure (Figure 4). This result bears comparison with the estimated values for other activities involving bursts of exercise such as football (11–27%) (23). This could be explained by the excess postexercise oxygen consumption (13) mainly related to the lactate metabolism and phosphocreatine resynthesis during rest phases (15).

Apart from the fact that this method provides a valid estimation of the role of aerobic metabolism, its main appeal is that it provides an estimation of the instantaneous MP and the contribution of anaerobic metabolism. Assessing anaerobic metabolism is important in understanding performance because it has been demonstrated that too much reliance on this metabolism can lead to muscle fatigue (4,12,20). Our method presents the advantage that it is easy to apply and requires only simple and inexpensive equipment: a camera, a computer, and tracking software. The method also addresses the main criticisms, which are leveled at conventional techniques, for example, regarding an increase in the mass transported, mechanically impeded movement, and the extreme difficulty of applying the method in a competition environment. The main restrictions of this simplified predictive model revolve around the calculation of an identical energy cost for both forehand and backhand shots regardless of the velocity of the ball; the fixing of the time constant in the EEO2 on-transient phase and the use of an average MRT. It can be assumed that the energy cost increases with the ball velocity, and it is held that the time constants vary depending upon the aptitude (26,29) and the power of the active phases (24). The use of this model should therefore be restricted to a simple average estimation of different metabolisms in the game of tennis, and for it to be applied to a particular subject, all of the parameters would have to be tailored to the individual.

In conclusion, this preliminary study shows that it is possible to estimate aerobic and anaerobic metabolisms using video analysis and a simplified bioenergetic model. It has been shown that anaerobic metabolism makes up 30, 70, and 95%, respectively, of the total energy expenditure during a game, point, and a racket stroke. Further experimental studies should be conducted in this topic to analyze longer competitive tennis matches or different training sessions.

Practical Applications

A sports coach could use this method to estimate the physiological requirements of a training session or a match by estimating the aerobic and anaerobic energy expenditure and MP. This model can also be applied using simple sequencing without video analysis to estimate the average MP of an exercise and a training session. It should provide trainers with a descriptive and quantitative basis upon which to develop on-court training drills that better target selected fitness training goals. For example, it can be calculated that for a series of 12 forehand shots per minute with no displacement involved, there would be an average MP value of around 55% O2max. This would be suited to technical work without bringing on too much tiredness. However, if the aim of the session is to develop the player's physical condition, then it would be possible to go to 90% of O2max with a series of 20 racket strokes per minute. A higher intensity should include repetitive displacement between strokes and a higher strokes frequency. Finally, if the model was used in a match situation to calculate players' instantaneous energy expenditure, it could help in the future for making strategic choices.


The results of this study do not constitute endorsement of the product by the authors or the National Strength and Conditioning Association.


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aerobic; anaerobic; tennis match; tennis strokes; metabolic power; oxygen consumption; performance analysis

© 2011 National Strength and Conditioning Association