Women’s modern pentathlon scoring systems and predictive modelling for decision support

1Introduction

The modern pentathlon originated from the ancient Olympic pentathlon. It was created by the founder of the modern Olympic Games, Pierre de Coubertin, who also introduced modern pentathlon into the Olympic Games in Stockholm in 1912. The women’s modern pentathlon was first adopted as an Olympic sport at the 2000 Sydney Olympic Games (Heck, 2012). It has introduced various changes to increase popularity. The biggest change was introducing the laser run, combining shooting and running into a single event, in 2009. An early study of the laser run at a World Cup event found that shooting accuracy of the top third ranked athletes in the overall competition was greater than that of the remaining athletes (Meur et al., 2010). This in turn resulted in a lower shooting time for the top third, but running times did not significantly differ between top third ranked athletes in the overall competition and lower ranked athletes (Meur et al., 2010). At the Olympic Games, this change came into effect in the London Olympics of 2012 (Heck, 2013). As the name implies, the modern pentathlon is a multisport in which each athlete performs five activities, namely fencing, swimming, horse riding, pistol shooting and cross country running in a single day (Cohal, 2019). The first event is fencing. Each athlete fences épée with all the other athletes and has to score one point in one minute; if neither athlete scores a point within a minute then both lose the bout. The second event is 200 m freestyle swimming. Athletes can use any stroke or style. The third event is show jumping in horse riding. Athletes ride random horses and jump over fifteen obstacles. The last event is the laser run which combines two activities; pistol shooting and running. The athlete starts with a handicap that is determined by the three previous events’ scores. This handicapping process ensures that the order in which athletes complete the laser run will correspond to their rank order in the overall modern pentathlon event. The laser run consists of an initial run to the shooting station, then four rounds of five laser pistol shots each followed by 800 m running. Depending on the circumstances, the order of events can be changed and there are no riding events in the qualifying round. Fencing, riding, and shooting can be classified as technical sports; skill and experience are of paramount important. On the other hand, running and swimming represent physical sport, requiring strength and endurance (Lim et al., 2018; Muniz-Pardos et al., 2020) as well as efficient technique.

Research in multisports has analysed the scoring systems used and suggested the disciplines they favour. For example, in the heptathlon Westera (2007) found that the largest relative variability between performers is in the 100 m Hurdles and Long Jump while the lowest is in the Javelin and Shot Put. Slavek and Jović (2012) also found that the 100 m Hurdles and Long Jump were more preferentially awarded points than the throwing disciplines. Gassmann et al. (2016) provided further evidence that the heptathlon scoring system favoured sprint and jump events more than throwing events. In the decathlon, Trkal (2003) highlighted the need for scoring systems to avoid the possibility of athletes who specialise in one discipline being more successful than more versatile athletes. Further research into the top 100 all-time decathlon performances revealed that the scoring system favoured sprinting events and the long jump more than throwing events and the 1500 m (Barrow, 2014). Similar analyses have been applied to modern pentathlon data to identify events favoured by the scoring system. Le Meur et al. (2010) found that the overall World Cup ranking and the laser run ranking are highly correlated, and that riding performance also has a significant impact on the overall modern pentathlon score. In 2014, the scale of the scoring table changed dramatically. Other minor rule changes were made, such as introducing a bonus round in fencing and changing the minus point per 0.5s in swimming. The changes in the rules and scoring table have impacted on the total points scores achieved (Barrow, 2014; Dadswell et al., 2013).

Irrespective of the criticisms made about the scoring systems used in multisports, these scoring systems are being used and, therefore, it is important for athletes and coaches to understand how to best improve athletes’ overall scores based on these scoring systems (Ofoghi et al., 2016). This has motivated the development of predictive modelling approaches that can identify areas where improvements can make the biggest difference to the overall points score. One such approach was proposed for the decathlon (Jayal et al., 2018). This used previous performance data to determine the possible range of improvements in points for each discipline within a year given the current performance level in the discipline. In general, the higher the performance level, the more restricted the amount of improvement that can be made in the next season. The approach of Jayal et al. (2018) can be criticised for analysing variability in pairs of performances by the same athletes separated by one calendar year where the points awarded increased. Year to year change in performance can also be negative. Modelling year to year improvement in points scored for disciplines was also done for the heptathlon (Dinnie and O’Donoghue, 2020). This used a multivariate approach that recognised that improvement in a discipline may be related to improvement in other disciplines with similar fitness requirements. Emphasising different events in training was simulated by ensuring that the predicted improvement in the prioritised disciplines was in the top 50% or 75% of the known range of improvements based on previous evidence. This is a limitation of the approach because no matter how much a discipline is emphasised in training, there is no guarantee that the athlete’s year to year change in the discipline will be among the highest improvements observed in the discipline.

Despite the importance of modern pentathlon as an Olympic sport, little is known about performance in each discipline (Dadswell et al., 2013). It is necessary to look at the distribution of points scored in each discipline as well as their correlations. Moreover, in the early years of the modern pentathlon’s history, frequent rule changes caused a lot of confusion which affected atheltes’ performance and training methods (Heck, 2013). Fencing in the modern pentathlon plays a major role in qualifying and performing well in the finals. By contrast, swimming has the least impactful role on the overall performance (Lee et al., 2020).

The purpose of the current research paper is to analyse women’s modern pentathlon performances and evaluate an approach to target setting that overcomes the limitations of approaches previously used in the decathlon (Jayal et al., 2018) and the heptathlon (Dinnie and O’Donoghue, 2020). This involves answering the following research questions:

The research includes five parts as shown in Fig. 1. The first three parts analyse modern pentathlon data (Analysis I, II and III). Part 4 describes an approach to identifying the discipline a modern pentathlete should focus on, and Part 5 is an evaluation study. In Analysis I, women’s modern pentathlon performances under the current scoring system (2014–19) are compared with performances under the former scoring system (2009–13). This analyses the proportion of the total points scored coming from each discipline under the two scoring systems and examines the relationships between points scored in different pairs of disciplines. Analyses II and III as well as Parts 4 and 5 of the research are concerned solely with the currently used scoring system. Analysis II compares year to year change in womens’ performances in the between the disciplines of the modern pentathlon. It is also important to compare the variability in the change of points between different disciplines. Analysis III models year to year change in the points scored for each discipline in terms of performance level in the first of the two years. Part 4 is not a study like the first three parts. Instead Part 4 describes an approach to identifying the disciplines where female modern pentathletes can most improve their overall points score. This approach uses simulation to predict year to year change when different disciplines are emphasised in training. The simulation uses the models from the Analysis III as well as evidence about variability in year to year change in performance. The approach is intended to help female modern pentathletes make strategic decisions about disciplines to emphasise in training. Part 5 evaluates the approach to identifying the disciplines to be emphasised using year to year change for six modern pentathletes as examples. This considers the year to year changes predicted by the approach compared to the actual improvements made by these athletes. The paper is completed with an overall discussion and conclusions.

Fig. 1

The five parts of the research study.

2Analysis I: Comparing the current scoring system with the former scoring system

2.3Results

Figure 2 shows that, under each scoring system, more points come from the laser run than any other discipline. The box plots in Fig. 2 make the distribution of scores look similar between the two scoring systems. However, the percentage of the total points score coming from swimming and riding is significantly lower under the current scoring system than the former scoring system while the percentage of the total points score coming from the laser run is significantly greater under the current scoring system. The significance levels are shown in Table 1. Table 1 also shows that scoring system has a very large effect on the percentage of the total points score coming from each discipline (d≥1.44). Levene’s test of equality of variances shows that the percentage of the total points score coming from each discipline is significantly more consistent under the current scoring system than under the former scoring system.

Fig. 2

The percentage of the total points score derived from each discipline under the two scoring systems.

Table 1

Percentage of total points score achieved in each discipline (mean±SD)

Discipline	Former	Current	p	p	Cohen’s d
	(n = 836)	(n = 1165)	(Mann Whitney U test)	(Levene’s test)
Fencing	16.17±1.91	16.03±1.74	0.077	0.077	1.81
Swimming	22.09±1.61	21.69±1.30	< 0.001	< 0.001	1.44
Riding	22.34±1.57	22.10±1.34	< 0.001	< 0.001	1.44
Laser run	39.40±2.44	40.18±2.10	< 0.001	< 0.001	2.25

Tables 2 and 3 show the correlation coefficients (Pearson’s r) between each pair of disciplines for under the former and current scoring systems respectively. The absolute correlations are very low under both scoring systems, with smaller absolute correlations being observed under the current scoring system in four out of six pairs of disciplines.

Table 2

Correlations between disciplines under the former scoring system (n = 836)

	Laser run	Riding	Swimming
Fencing	+0.092	+0.054	+0.076
Swimming	+0.042	–0.001
Riding	+0.170

Table 3

Correlations between disciplines under the current scoring system (n = 1165)

	Laser run	Riding	Swimming
Fencing	–0.020	+0.064	–0.019
Swimming	–0.035	+0.020
Riding	+0.089

3Analysis II: Comparing the year to year changes in points awarded between the different disciplines

3.3Results

Figure 3 shows the year to year change in the points scored in the four disciplines. A Friedman test revealed a significant difference between disciplines for the year to year change ( χ32 = 9.7, p = 0.021) with Bonferroni adjusted Wilcoxon signed ranks tests showing significantly more improvement in fencing than in swimming (p < 0.001). However, the effect size was very small ( ηp2 = 0.019). There were no significant differences between the year to year changes for any other pair of disciplines (p > 0.05). Levene’s test revealed that the spread of year to year differences was significantly different between each pair of disciplines (p < 0.001). Table 4 shows that there was a meaningful positive correlation in year to year changes in points scored for swimming and the laser run (r = 0.387, r² = 0.15), but all of the other absolute correlations were low (|r|≤0.101).

Fig. 3

Year to year improvement in points scored in the four disciplines (n = 243).

Table 4

Correlations between year to year change score in disciplines under the current scoring system (n = 243)

	Laser run	Riding	Swimming
Fencing	–0.090	+0.020	–0.101
Swimming	+0.387	–0.042
Riding	–0.014

4Analysis III: Modelling year to year improvement in each discipline

5Part 4. An approach to identifying the disciplines where the greatest points gains can be made

5.2Representing variability in year to year change

The regression models shown in Table 5 are applied to an athlete of interest to predict their year to year change as well as determine the potential variability about the predicted year to year change. Modern pentathlon performance is then simulated based on the initial performance level, predicted year to year change and applying the evidenced variability in each discipline to produce a range of total points scores. Disciplines can be experimented with to simulate emphasis being made on them during training. This is the most important aspect of the approach because it allows simulation results to be compared between situations where different disciplines are emphasised. This type of simulation is suitable because it allows us to place emphasis on different disciplines allowing overall effect of such emphasis to be studied (Dinnie and O’Donoghue, 2020). The resulting information can assist female modern pentathletes and their coaches to make informed decisions about which disciplines to concentrate on most.

The magnitude of the residual values for year to year change in swimming is negatively correlated with the predicted value as shown in Table 6 (r = –0.229). Essentially, the more an athlete is expected to improve from one year to next at swimming, the less variability we expect in that year to year improvement. Splitting the 243 pairs of year to year performances into three equal thirds ordered on predicted value shows that the standard deviation of the residual values is 8.640 to 6.997 to 6.356 for the first 81, second 81 and third 81 cases of ordered data respectively. The mean predicted values for these thirds of the data are –5.807, –1.901 and 1.474 respectively. A crude linear regression applied to these values suggests that the standard deviation that should be applied to the residual values for year to year improvement in swimming should be as shown in Equation (1).

(1)

SD=6.6734-0.3165 predicted value for year to year improvement

Applying this equation to the predicted values for year to year change for swimming gives a range of standard deviations from 4.182, for the athlete predicted to improve the most in swimming points, to 10.781, for the athlete expected to improve least.

5.3Simulation (without emphasising any disciplines)

The approach involves applying the regression model to an individual athlete. This is illustrated using Sehee Kim of Korea as an example. Her best performances in 2018 and 2019 are shown in Table 7. The regression equations shown in Table 5 were used to determine the predicted year to year change from 2018 to 2019.

A Microsoft Excel spreadsheet was programmed to simulate 2019 performance for the athlete 1000 times. In each of these simulations, a residual value was chosen at random for fencing, riding and the laser run from the 243 residual values for these disciplines that were determined in Analysis III. Each residual value had an equal chance of being chosen.

It was necessary to truncate the simulated performances for riding to ensure they did not exceed the maximum of 300 points. An exploratory analysis added the predicted year to year change for each of the 243 athletes used in Study 3 to determine the 243 predicted values for this discipline. The full set of 243 residuals for year to year change were added to each of these values to give 59,049 simulated values for year two swimming points. These values ranged from 245 to 302 points after rounding with 4.16% of the values being greater than 300. Given the low percentage of values that exceeded the maximum of 300 and the relatively small extent to which they exceeded the maximum, it was decided to simply truncate riding values to 300 if the simulated value exceeded 300.

An extended version of this process was used with swimming because the variability of the residuals had to be scaled depending on the athlete’s predicted performance for this discipline. When equation (1) is applied to the predicted year to year change value of –2.07 for Sehee Kim, we get a standard deviation to be used of 7.33. Table 6 shows that the standard deviation of the residual values for year to year change in swimming is 7.43. Therefore, the residuals for swimming needed to be multiplied by a factor of 7.33 / 7.43 when used to simulate year to year change in swimming for this athlete. Table 7 shows that there is a range of predicted performances with the mean simulated performance being 1296 points which is short of the 1321 points the athlete actually achieved in 2019. However, 247 of the 1000 simulations did predict a points total of 1321 or higher. It is worth considering that the data used in this paper contains four 2018 and two 2019 performances for Sehee Kim. In 2018, her overall performance improved over the year from 1155, to 1219, 1251 and finally 1279. Similarly, her best performance of 2019 was the second of her two performances in the data (1278 and 1321). The predicted 1296 points sits between her two performances in 2019.

Table 7

Actual and simulated performances for Sehee Kim without emphasising disciplines

Discipline	Actual		Predicted	Simulated 2019 performances
	Performance		change	(n = 1000)
	2018	2019		Mean±SD	Minimum	Maximum
Fencing	208	223	–2.47	206.0±20.8	157	266
Swimming	279	272	–2.07	276.9±7.3	256	297
Riding	292	296	–2.69	289.4±11.0	247	300
Laser run	515	530	+8.56	523.5±31.5	428	593
Total	1294	1321		1295.8±40.3	1158	1411

5.4Simulation (experimenting with different disciplines)

The next stage of the approach experimented with different disciplines to determine the impact that emphasising these would have on the simulated performances of an athlete. The initial simulations for Sehee Kim, that are summarised in Table 7, gave each of the 243 residual values for a discipline an equal chance of being added to the athlete’s predicted score. Hence a uniform probability distribution was applied to determine the row of the ordered residual table to look up (1 to 243). Emphasising an individual discipline was represented by changing this uniform distribution to a sloped uniform distribution as illustrated in Fig. 4. Let N be the number of residuals being used in the simulation process (in our case 243). The probability distribution is actually a finite discrete distribution of N values, as shown by the columns in the background of Fig. 4. The probabilities increase with a uniform interval allowing the probabilities to be calculated using a straight line that passes through the mid-points at the tops of the columns. The “bias” for a discipline is the probability that an athlete’s year to year change for a discipline (not including the predicted improvement according to the given regression model) will be in the top 50% of the residual values for the discipline. Therefore, a bias of 0.5 is represented by a standard uniform distribution, as shown in Fig. 4, with each residual having a probability of 1/N of being used in the simulation. The maximum bias used in this approach is 0.75 meaning that higher residual values are more likely to be selected than lower residual values. The reason for 0.75 being the maximum is that this probability for the top half of residual values is achieved by a sloped uniform distribution running from the (row location, probability) co-ordinates (1,0) to (N, 2/N) with a gradient of 2 / (N(N-1)). Figure 4 uses the term “gradient factor” which is the gradient multiplied by N(N-1). If the gradient factor were any greater than 2, the sloped uniform distribution would be suggesting negative probabilities for the lowest residual values. With the gradient factor of 2, the lowest residual has a 0 probability of being selected at random, the highest residual has a 2/N probability of being selected at random with the i^th residual having a probability being determined by the equation of this line. The gradient and intercept of the equation of the sloped uniform distribution are given in equations (2) and (3) respectively. These are determined using the bias that has been applied.

Fig. 4

Use of a sloped uniform distribution to represent emphasis on a discipline during training.

A bias of 0.75 means that the area under the line from 1 + 0.5(N-1) to N must be 0.75. Therefore, the line must pass through the co-ordinate (1 + 0.75(N-1), 1.5/N) if this is a sloped uniform distribution. The bias of 0.75 also means that the area under the line from 0 to 1 + 0.5(N-1) must be 0.25. Therefore, the line must pass through the co-ordinate (1 + 0.25(N-1), 0.5/N). In general, where we have a bias between 0.5 and 0.75, the line must pass through the co-ordinates (1 + 0.25(N-1), 2(1-Bias)/N) and (1 + 0.75(N-1), 2 Bias/N). The gradient of a straight line between these points is as shown in equation (2).

Any sloped uniform distribution based on a bias between 0.5 and 0.75 must pass through the co-ordinate (1 + 0.5(N-1), 1/N) for the total area of the N columns to be 1. This in combination with the gradient shown in equation (2) allows us to determine the constant (intercept) of the line. This is the probability for a 0th row in the ordered residual table and is given by equation (3). Where the bias is 0.75 and the gradient is 0.000034 (gradient factor is 2), this gives a small negative number (–0.000034) allowing the probability for the 1st row of the ordered residual table to be 0.

(2)

Gradient=(8Bias-4)/(N(N-1))

(3)

Intercept=1/N-(1+0.5(N-1))((8 Bias-4)/(N/(N-1)))

The simulator was programmed to apply the sloped uniform distribution to determine the row location of the residual to be applied. The user enters a value of 0.5 for the bias for any discipline not to be emphasised any more than usual in training and a value between 0.51 and 0.75 for a discipline to receive special emphasis in training. Table 8 compares the points simulated for Sehee Kim when each of the disciplines are emphasised with different biases. Biases of 0.75 are used with each of the disciplines being emphasised with the others remaining with biases of 0.5. However, the laser run combines running and pistol shooting and may therefore require greater emphasis to give the same probability of being in the top half of year to year change values than would be the case in the other disciplines. Therefore, the laser run was simulated using a bias of 0.625.

Table 8

Simulated points for Sehee Kim when emphasising different disciplines (mean±SD)

Discipline	Discipline being emphasized in training
	None	Fencing	Swimming	Riding	Laser run	Laser run
		Bias = 0.75	Bias = 0.75	Bias = 0.75	Bias = 0.75	Bias = 0.625
Fencing	206.0±20.8	217.5±18.4	205.6±20.4	206.8±20.2	206.3±20.1	206.7±21.2
Swimming	276.9±7.3	276.9±7.4	281.4±6.2	277.1±7.8	276.7±7.6	277.5±7.5
Riding	289.4±11.0	289.3±10.7	289.2±10.7	294.7±6.1	289.8±11.0	289.3±11.0
Laser run	523.5±31.5	523.1±30.7	524.5±30.5	522.8±31.4	540.2±23.3	531.8±28.8
Total	1295.8±40.3	1306.8±37.6	1300.6±39.0	1301.5±38.7	1312.3±33.1	1305.4±37.8

The simulations suggests that the two events where emphasis would have the greatest impact on Sehee Kim’s total points score are fencing and the laser run.

6Part 5. Evaluation Study

The simulation approach, described in Part 4, was applied to six different female athletes to determine the discipline to emphasise to best improve their total points score. These athletes were selected due to the variety of relative strengths and scope for improvement they had in different disciplines as well as for the range of improvements actually observed. For example, Misaki Uchida had a relatively low score for fencing in the initial year while Sophia Hernandez had a relatively low score for the laser run, Eevi Bengs had a relatively low score for swimming, and Aurora Tognetti had a relatively low score for riding. The results of the simulations are summarised in Table 9. Table 9 shows that irrespective of which discipline the athletes had their lowest scores in, the simulation process suggested the greatest improvement to points score would be achieved by emphasising fencing followed by the laser run. Considering the actual initial results and results a year later, Sehee Kim, Sunwoo Kim, Misaki Uchida, and Sophia Hernandez all improved their points in fencing and the laser run to a greater extent than they did in the other two disciplines. Eevi Bengs, despite apparently having the greatest potential to improve her score in swimming, made the greatest gains in fencing and riding. Aurora Tognetti did improve her points total by 49 points in riding achieving the maximum score of 300 in 2019. Her greatest points gain was, however, in the laser run.

7Discussion

Analysis I found that the scoring system used has a significant and meaningful effect on the proportion of the total points score derived from each discipline. Therefore, coaches and athletes should make strategic decisions based on the most up-to-date rules and scoring system used in the sport. The currently used scoring system in the modern pentathlon results in a greater proportion of the total points score coming from the laser run than before while the other disciplines contributed to a lower proportion of the total points score than they did before 2014.

The four events of the modern pentathlon have low correlations. This is in contrast to what is seen in other multisports such as the heptathlon where factor analyses have identified performance dimensions with absolute correlations of greater than 0.7 with some disciplines (Gassmann et al., 2016; Dinnie and O’Donoghue, 2020). Similarly, the first two principal components derived from decathlon performances have absolute correlations greater than 0.7 with the points scored in more than one discipline each (Jayal et al., 2018). In the triathlon, swimming position and speed significantly correlate with cycling and running race position (Wu et al., 2014). The absence of such high correlations between pairs of disciplines in the modern pentathlon suggests that athletes in this sport need to be more versatile than athletes in the heptathlon, decathlon and triathlon. The International Modern Pentathlon Union (UIPM) has confirmed that horse riding will be removed from the modern pentathlon after the 2024 Olympic Games in Paris (Church, 2021). If horse riding is replaced by a discipline where performance is highly correlated with an existing discipline, the modern pentathlon may favour certain types of specialist athletes rather than more versatile athletes.

Table 1 shows that for the average modern pentathlete the largest proportion of their total points score comes from the laser run followed by riding, swimming and fencing. However, this does not reflect the true importance of each of these disciplines to the overall points score. If all of the athletes were scoring a similarly high number of points in a discipline then effort expended on this discipline would not have the same impact as effort expended on a discipline with higher variability in year to year improvement. It is high variability in performance that makes disciplines important, particularly variability in improvements that can be made in performance. Figure 3 shows that the laser run has the largest variability in year to year change. Part of the explanation for this may be because the laser run is usually the final discipline of the modern pentathlon and some athletes may not be as competitive as in earlier disciplines if their final finishing position has been largely determined by the previous disciplines. There is a tendency for variability due to negatively skewed distributions in the final discipline of other multisports. For example, most outliers in the 800 m of the heptathlon (Dinnie and O’Donoghue, 2020) and the 1500 m of the decathlon (Jayal et al., 2018) are where athletes have scored a low number of points in these disciplines. The points scored in the preceding disciplines are used to determine the time handicap used in the laser run. The handicaps applied to the athletes mean that the athlete finishing first in the laser run will be the winner of the overall modern pentathlete. The knowledge of position during the laser run means that athletes only need to run as fast as they need to in the last 800 m section to achieve the best position they can feasibly achieve. This means that athletes may not run as fast as they are capable of running in the final 800 m. A further factor explaining the high variability in year to year change in laser run performance is that the running courses used in this discipline may vary due to cross country type courses being used, with varying terrains, rather than standard athletics tracks. For example, rubberized surfaces have smaller impact forces for runners than asphalt and acrylic surfaces (Dixon et al., 2000). Running on harder surfaces also leads to increased leg stiffness compared to running on softer surfaces (Ferris et al., 1998). Surface can also effect the mechanics of running stride (Creagh et al., 1998). Much of the variability in the laser run may be explained by the fact that this discipline typically has higher points scores than the other disciplines. However, athletes and coaches must still recognise that, in absolute terms, improvements the laser run have a higher impact on the overall points total than similar rank improvements in other disciplines.

The discipline with the second highest variability in year to year change in points score is fencing. Thus even though fencing makes the lowest contribution to the overall points total for most athletes, it has much greater scope for athletes to improve their points total from one year to the next than riding or swimming. This disagrees with the findings of Le Meur et al. (2010) that riding was the second most impactful discipline after the laser run. The disagreement between the findings of Le Meur et al. (2010) and the current investigation can be explained by Le Meur et al.’s study being conducted on performances under the scoring system that applied at the time which was different to the currently used scoring system. A further factor that may explain the high variability in fencing performance is that the athletes have to compete against all of the other competitors. The athletes obviously cannot compete against themselves in fencing meaning that the best fencer will be competing with inferior fencers while the worst fence will be competing against superior fencers. Thus even though the sets of opponents are largely the same for each fencer, points scored for wins will differ between athletes the same way as they would be expected to do so in a round robin tournament in a team sport.

There is a greater variability in points scored in riding than swimming, both when variability is considered between different athletes and year to year improvement within the same athletes. This may be explained by athletes having to ride random horses. The analysis of variability in the current study agrees with previous research that concluded that swimming is the discipline with the lowest impact on the points total (Lee et al., 2020).

The current study found that irrespective of athletes’ abilities in the different disciplines, the greatest gains in the total points score would be achieved by emphasising the laser run in training. The only exceptions to this year to year change pattern in the evaluation study was for the athlete who’s overall points score decreased from one year to the next. This finding is explained by variance in year to year change in points being unrelated to athlete ability in three of the disciplines. This disagrees with approaches used in the decathlon (Jayal et al., 2018) and heptathlon (Dinnie and O’Donoghue, 2020) where higher ability was associated with lower variability in year to year improvement for most disciplines. The approach developed in the current paper suggests that heptathletes’ primary focus should be on the laser run. This is supported Le Meur et al.’s (2010) finding that the correlation between laser run ranking and world cup ranking was higher than other events. Preparation for the laser run needs to optimise the elements of shooting accuracy and speed in this discipline (Madalena et al., 2020).

Fencing is the second most important discipline according to the current research. Therefore, modern pentathletes need to specifically prepare for the demands of this discipline including the technical demands (Lee et al., 2020) and physical demands (Wylde et al., 2013, 2014). A final point to make about any analytics approach is that decision making should not rely solely on quantitative analysis but should also consider training and competition context (Alamar, 2013).

There are some limitations in the approach used to identify the disciplines athletes have the most potential to improve their total points in. Firstly, there was a correlation of 0.387 between year to year improvement in swimming and the laser run (Table 4). This correlation between the year to year change in these disciplines was noted in the current research, but it could not be included in a predictive model due to the year to year improvements in events being unknown at the time the models would be applied in practice. However, when using the approach, biases above 50% could be applied to both of these disciplines given the knowledge of the relationship between them. The residual values used in the simulation are based on 243 year to year changes observed in international women’s modern pentathlon competition. The approach would be improved with a greater volume of year to year change data for athletes. A third limitation is the use of a sloped uniform distribution to determine the location of the residual to be applied within a simulated performance. This does allow a consistent method to compare the impact of emphasising certain disciplines in training. Therefore, the relative results of the simulations may be sound. However, if data were available where athletes reported which disciplines they gave special emphasis to between one year and the next, we might find that this results in a different distribution to a sloped uniform distribution. A further limitation was using the higher of two or more modern pentathlon performances in the same calendar year in the analysis of year to year improvement.

In conclusion, this study reveals that the scoring system used since 2014 has resulted in more consistent points scoring in all disciplines. The study has also found that performance in the four disciplines have low correlations with each other, suggesting modern pentathletes need to be more versatile than athletes in other multisports. The most important disciplines are those with the greatest potential to improve the overall score. The current research suggests that the laser run and fencing are the two most important disciplines in this respect. Future research could be extended to applying the predictive modelling technique within coaching scenarios, to real athletes and receiving feedback on whether it helped their decision making and preparation. Another area of future research is to analyse points scored in the modern pentathlon after riding is replaced by an alternative discipline.