While watching the 2024 Olympic Heptathlon competition, I used to be reminded that the points scores by event within the heptathlon all the time show a pattern: the primary event, the 100 metres hurdles, normally sees large points numbers across the board, while the shot put, the third event, tends to return a few hundred fewer points per athlete.
This prompted me to have a look at two questions: i) why do the points come out as they do, and ii) does this mean that some events are more essential than others, to the tip of winning the heptathlon competition? The identical questions apply to the decathlon too, after all, and this can also be examined here.
I collected the outcomes for the World Championship heptathlon and decathlon competitions from 2007 to 2023 from Wikipedia . These are the elite levels of performance for the 2 multi-event competitions, so the insights gained from this evaluation apply to only this high level and never necessarily to heptathlon or decathlon competitions basically. Details on the scoring systems were found on SportsCalculators, and are originally published by World Athletics.
Within the evaluation that follows I’ll use the word ‘rating’ to seek advice from the physical performance mark recorded by the athlete in each event (height, length/distance, or time), and ‘points’ to seek advice from the variety of heptathlon or decathlon points which are received for that rating.
Points spreads
The common (median) variety of points received for the heptathlon events in Table 1 shows clearly the pattern we’re talking about: the sprint events (200m and, particularly, 100m hurdles) provide around 200 points more, on average, than do the throwing events (javelin and shot put). This seems surprising, but shouldn’t be necessarily of any importance, since all athletes are competing in all events, so it is barely the points scored relative to 1 one other that matter. The third column within the table above shows the interquartile range of points; that’s, the difference between the twenty fifth and seventy fifth percentiles, or, the zone through which the ‘middle half’ of athletes lie. Here we see that the running events show the bottom spreads in points, while the high jump and javelin have the most important ranges. This implies that the difference between performing quite poorly and quite well (relative to World-Championship-level competitors) is more essential, in points terms, in some events that it’s in others.
Scoring system
The explanation for this effect is the scoring system. The systems for each heptathlon and decathlon have been of their current form since 1984, and use for every event an equation of the shape
points = a * (difference between rating and reference rating b) ^ c
where ‘^’ means ‘to the ability of’. Each event subsequently requires three coefficients, a, b, and c, to be defined. The values of the coefficients aren’t comparable individually between events, but the mixture of the three creates a points curve for every event, as shown in Figure 1, below. The World Athletics document on the scoring systems explains that one consider the number of the coefficients is the world record in each event: it’s desired that a world-record performance in any event should yield the identical variety of points. They note that, in practice, because of this ‘the most effective scores set in each individual event will vary widely’, but that it’s more essential that ‘the differences within the scores between different athletes in a single event are roughly proportional to the differences of their performances’.
The blue lines in Figure 1 show the connection between rating and points in each event. The lines are almost straight, particularly throughout the green shaded rating regions, which is where 80% of scores are contained, meaning that the scoring system can, practically, be thought to be a linear system. (There’s a slight upward bend to a few of the curves, particularly on the high-score end of the long jump and 800m, which implies that exceptional performance is rewarded barely greater than would occur in a really linear system, but these differences are small and aren’t the important thing point of this evaluation.)
What’s more interesting is the range of points which are realistically available from each event. That is indicated by the vertical arrows, which show the points increase obtained by moving from a rating on the tenth percentile (left fringe of the green area) to a rating on the ninetieth percentile (right fringe of the green area). 8 out of 10 performances occur in these ranges, and anything lower or higher is somewhat exceptional for that event. The dimensions of this points range (the peak of the arrow) is clearly larger in some events, most noticeably the javelin, than in others, most noticeably the 100m hurdles. This is nearly the identical information as seen within the interquartile range numbers earlier.
The position of the world records in each event (dashed red lines) show why the common variety of points is lower within the throwing events: the common heptathlete can only throw about 60% so far as the world record (best specialist, single-event athlete) for shot put or javelin, but the identical heptathlete can attain a speed of between 85% and 90% of the world record (converted from time) within the 100m hurdles and the 200m.
There might be several reasons for this, but one essential follow-on point that it seems fair to assume is that an event through which performances are removed from the world record has more potential for improvements than an event through which performances are already near their ultimate limit. To place this one other way, evidently most heptathletes are in a position to run fairly well in comparison with the specialists in those events (including the 800m), but within the javelin, their performances generally show relatively large deficiencies in comparison with what is feasible within the event. Importantly though, as the broader rating spread for javelin shows, some heptathletes can throw the javelin fairly well.
To make this more clear, next, I take advantage of the distributions of scores in each event to measure the points gain that might result from an athlete improving her performance within the event from the fiftieth percentile (higher than half of her competitors) to the sixtieth percentile (higher than 6 in 10 competitors). The intention with this metric is that this improvement is likely to be equally difficult, or equally achievable, in each event, because it is measured by what other heptathletes have achieved. When finding the percentile levels, to avoid problems with the discrete nature of scores within the high jump (only jumps every 3 cm are possible), the raw scores from each event are modelled as distributions (normal normally, and log-normal within the cases of high jump, 100m hurdles, and 800m), and the percentiles computed from these.
The outcomes (Figure 2) confirm that improving by the identical amount relative to 1’s peers earns more points in the sphere events than within the running events. A ten% improvement relative to the competition within the javelin can be essentially the most useful performance gain to make, earning the heptathlete 28 points. Later we are going to discuss whether or not it is really as easy to make a ten% throwing improvement because it is to enhance scores by 10% within the track events.
The image within the decathlon is broadly much like that described for the heptathlon. In Table 2, we discover that, again, the javelin shows the largest interquartile range for points scored, followed by the 1500m (which sits much higher up the list than the ladies’s most similar event, the 800m) and the pole vault. Conversely, the sprint events (100m, 110m hurdles, and 400m) show smaller points spreads. The difference in spreads between the highest and bottom events shouldn’t be quite as severe because it is within the heptathlon.
The rating distributions and points curves (Figure 3) show, through the length of the arrows, the events through which the everyday range of scores (the width of the green areas) yields essentially the most points difference: the javelin, pole vault, and a few way behind, the discus and 1500m. Again, the sprint hurdles shows a small points spread: the worst hurdlers aren’t penalised much compared to the most effective hurdlers.
The 1500m sits lowest in points terms of any event, with a tenth percentile performance price only around 600 points. It is a results of the steepness of the blue line, which dictates how much the decathlete is penalised for every additional second that they’re away from the world record. The blue line doesn’t need to seem like this, however it does in consequence of the selection of the coefficients a, b, and c. On the plus side, the steepness of the road creates a comparatively large points difference between different scores within the 1500m, as seen below.
Using the identical technique as before of modelling event scores as distributions (log-normal for 1500m, 110m hurdles, and javelin, and normal for the remainder) and computing percentiles, Figure 4 shows the identical pattern because the heptathlon events: the identical percentage improvement in rating yields essentially the most points in javelin, and the fewest points within the sprint events.
The above results suggest that just a few of essentially the most technical events needs to be those that athletes deal with to achieve points most easily. Nonetheless, training in a single event will naturally result in improvements in another events as well (and possibly degrade performance in others), so it shouldn’t be as simple as to have the option to think about each event in isolation. The worth of effort spent on one event will depend upon each the points gain that is feasible in that event and the complementary advantages obtained in other, similar events.
The correlation plot of Figure 5 shows how scores in each of the heptathlon events are correlated with each other. The best correlations are between the 200m, 100m hurdles, and long jump. This shouldn’t be surprising, as a very good sprinter will likely perform well in all of those events. There are also correlations, though smaller, between scores in long jump and high jump, and in shot put and javelin.
It’s notable that the javelin shows the least correlation with the opposite events overall. That is consistent with it being an event requiring its own specific technique, and a heptathlete doesn’t naturally turn out to be significantly better on the javelin by improving in some other events, apart from (somewhat) the shot put. Javelin even shows a small negative correlation with each the 200m and 800m: the higher javelin throwers in heptathlon are inclined to be the more severe runners.
In decathlon (Figure 6), the sprint events are correlated with each other, as are shot put and discus, whereas pole vault, javelin, and 1500m show quite weak correlations with almost the entire other events.
This changes the message from the previous section. While improving relative to the remainder of the sphere in javelin, pole vault, or middle distance running should provide the largest points gain per unit of improvement, the advantage of that is undercut by a possible decrease in performance in other events. However, improving skill in considered one of the sprint-based events tends to create gains in similar events at the identical time, perhaps making this a more efficient approach to the competitions overall.
Finally, the right-most column in each of the correlation grids (Figures 5 and 6) seems to verify this. This column shows the correlation between scores in each event and final position within the heptathlon or decathlon competition (multiplied by -1 in order that a high finish becomes the most important number). The most important correlation with position — that’s, the event through which the athlete’s rating most dictates where they finish in the general competition — is present in the long jump in each heptathlon and decathlon, followed by hurdles and high jump in heptathlon, and by hurdles and 400m in decathlon. The importance of long jump is probably going on account of its ‘centrality’ within the competitions: its relatively high correlations with several other events. Conversely, performance within the 1500m is the least correlated with finish position in decathlon. This might be because the most effective 1500m runners tend not to carry benefits in other events too, so often find yourself lower in the general standings. The decathlon is more often won by a robust sprinter, because this athlete is rewarded several times over for this skill, with points within the 100m, hurdles, 400m, and long jump.
Insights on how best to approach the heptathlon and decathlon turned out different from how I expected at first of the evaluation. Although evidently effort to enhance one’s rating within the javelin is essentially the most efficient method to increase total points, the athletes that perform best overall don’t are inclined to do particularly well in javelin. This is probably going because the talents required for javelin, and to a lesser extent, pole vault, discus, and high jump, don’t transfer well to other events, so the advantage of the trouble is restricted to a points return in that event only.
It might be speculated that these are essentially the most technically demanding events, through which it is probably possible, though difficult, for the athlete to ‘unlock’ big gains in performance through small adjustments in technique, whereas a few of the other events are more controlled by strength or fitness, through which only incremental gains are feasible. Probably the issue in making those technical improvements, combined with the shared advantages of general fitness improvements, suggestions the balance in favour of improving scores within the sprint-related events.
This balance is nevertheless controlled by the scoring system. Each of the blue lines in Figures 1 and three is anchored at one point by the world record, however the gradient of the road appears to be a selection that might have been made otherwise. The larger the gradient, the more emphasis is placed on the difference in rating between the most effective and worst athletes in that event. In truth, the big gradients for the javelin and other events could also be essential to balance these more isolated events against the shared advantages of improvements within the sprint events. If the points bars of Figures 2 and 4 were equal across all events, there can be less incentive to focus effort on the technical events instead of the more intercorrelated sprint events.
There isn’t a likelihood of the multi-event scoring systems changing within the near future. I’d suggest that the right-most columns of Figures 5 and 6 show that the systems currently work well, as there are not any events which are completely uncorrelated with finish position (which might mean that performance in those events didn’t matter to the general result). If there have been to be changes to the system, it is likely to be a very good idea to focus on more even correlations on this column, which might mean increasing the points gradient within the 800m and 1500m, particularly, to extend the advantage of performing well in these events, on the expense of the long jump and hurdles, which currently have a much bigger bearing on the ultimate standings.
