Patterns in efficiency and reward within the heptathlon and decathlon
Whereas watching the 2024 Olympic Heptathlon competitors, I used to be reminded that the factors scores by occasion within the heptathlon at all times present a sample: the primary occasion, the 100 metres hurdles, normally sees massive factors numbers throughout the board, whereas the shot put, the third occasion, tends to return a few hundred fewer factors per athlete.
This prompted me to take a look at two questions: i) why do the factors come out as they do, and ii) does this imply that some occasions are extra essential than others, to the top of successful the heptathlon competitors? The identical questions apply to the decathlon too, in fact, and that is additionally examined right here.
I collected the outcomes for the World Championship heptathlon and decathlon competitions from 2007 to 2023 from Wikipedia . These are the elite ranges of efficiency for the 2 multi-event competitions, so the insights gained from this evaluation apply to solely this excessive stage and never essentially to heptathlon or decathlon competitions usually. Particulars on the scoring techniques had been discovered on SportsCalculators, and are initially printed by World Athletics.
Within the evaluation that follows I’ll use the phrase ‘rating’ to seek advice from the bodily efficiency mark recorded by the athlete in every occasion (peak, size/distance, or time), and ‘factors’ to seek advice from the variety of heptathlon or decathlon factors which might be obtained for that rating.
Factors spreads
The common (median) variety of factors obtained for the heptathlon occasions in Desk 1 reveals clearly the sample we’re speaking about: the dash occasions (200m and, particularly, 100m hurdles) present round 200 factors extra, on common, than do the throwing occasions (javelin and shot put). This appears shocking, however just isn’t essentially of any significance, since all athletes are competing in all occasions, so it is just the factors scored relative to at least one one other that matter. The third column within the desk above reveals the interquartile vary of factors; that’s, the distinction between the twenty fifth and seventy fifth percentiles, or, the zone during which the ‘center half’ of athletes lie. Right here we see that the operating occasions present the bottom spreads in factors, whereas the excessive soar and javelin have the most important ranges. This implies that the distinction between performing fairly poorly and fairly effectively (relative to World-Championship-level rivals) is extra essential, in factors phrases, in some occasions that it’s in others.
Scoring system
The rationale for this impact is the scoring system. The techniques for each heptathlon and decathlon have been of their present type since 1984, and use for every occasion an equation of the shape
factors = a * (distinction between rating and reference rating b) ^ c
the place ‘^’ means ‘to the ability of’. Every occasion subsequently requires three coefficients, a, b, and c, to be outlined. The values of the coefficients are usually not comparable individually between occasions, however the mixture of the three creates a factors curve for every occasion, as proven in Determine 1, under. The World Athletics doc on the scoring techniques explains that one issue within the choice of the coefficients is the world document in every occasion: it’s desired {that a} world-record efficiency in any occasion ought to yield the identical variety of factors. They observe that, in observe, which means ‘the perfect scores set in every particular person occasion will range broadly’, however that it’s extra essential that ‘the variations within the scores between completely different athletes in a single occasion are roughly proportional to the variations of their performances’.
The blue traces in Determine 1 present the connection between rating and factors in every occasion. The traces are virtually straight, significantly inside the inexperienced shaded rating areas, which is the place 80% of scores are contained, which means that the scoring system can, virtually, be thought to be a linear system. (There’s a slight upward bend to among the curves, significantly on the high-score finish of the lengthy soar and 800m, which signifies that distinctive efficiency is rewarded barely greater than would happen in a very linear system, however these variations are small and are usually not the important thing level of this evaluation.)
What’s extra fascinating is the vary of factors which might be realistically accessible from every occasion. That is indicated by the vertical arrows, which present the factors improve obtained by shifting from a rating on the tenth percentile (left fringe of the inexperienced space) to a rating on the ninetieth percentile (proper fringe of the inexperienced space). 8 out of 10 performances happen in these ranges, and something decrease or larger is considerably distinctive for that occasion. The scale of this factors vary (the peak of the arrow) is clearly bigger in some occasions, most noticeably the javelin, than in others, most noticeably the 100m hurdles. That is virtually the identical data as seen within the interquartile vary numbers earlier.
The place of the world information in every occasion (dashed purple traces) present why the common variety of factors is decrease within the throwing occasions: the common heptathlete can solely throw about 60% so far as the world document (finest specialist, single-event athlete) for shot put or javelin, however the identical heptathlete can attain a pace of between 85% and 90% of the world document (transformed from time) within the 100m hurdles and the 200m.
There may very well be a number of causes for this, however one essential follow-on level that it appears honest to imagine is that an occasion during which performances are removed from the world document has extra potential for enhancements than an occasion during which performances are already near their final restrict. To place this one other manner, it appears that evidently most heptathletes are capable of run pretty effectively in comparison with the specialists in these occasions (together with the 800m), however within the javelin, their performances usually present comparatively massive deficiencies in contrast to what’s attainable within the occasion. Importantly although, as the broader rating unfold for javelin reveals, some heptathletes can throw the javelin pretty effectively.
To make this extra clear, subsequent, I take advantage of the distributions of scores in every occasion to measure the factors acquire that might outcome from an athlete enhancing her efficiency within the occasion from the fiftieth percentile (higher than half of her rivals) to the sixtieth percentile (higher than 6 in 10 rivals). The intention with this metric is that this enchancment could be equally troublesome, or equally achievable, in every occasion, as it’s measured by what different heptathletes have achieved. When discovering the percentile ranges, to keep away from issues with the discrete nature of scores within the excessive soar (solely jumps each 3 cm are attainable), the uncooked scores from every occasion are modelled as distributions (regular normally, and log-normal within the instances of excessive soar, 100m hurdles, and 800m), and the percentiles computed from these.
The outcomes (Determine 2) affirm that enhancing by the identical quantity relative to at least one’s friends earns extra factors within the discipline occasions than within the operating occasions. A ten% enchancment relative to the competitors within the javelin could be essentially the most helpful efficiency acquire to make, incomes the heptathlete 28 factors. Later we’ll talk about whether or not or not it’s really as straightforward to make a ten% throwing enchancment as it’s to enhance scores by 10% within the monitor occasions.
The image within the decathlon is broadly just like that described for the heptathlon. In Desk 2, we discover that, once more, the javelin reveals the largest interquartile vary for factors scored, adopted by the 1500m (which sits a lot larger up the record than the ladies’s most comparable occasion, the 800m) and the pole vault. Conversely, the dash occasions (100m, 110m hurdles, and 400m) present smaller factors spreads. The distinction in spreads between the highest and backside occasions just isn’t fairly as extreme as it’s within the heptathlon.
The rating distributions and factors curves (Determine 3) present, via the size of the arrows, the occasions during which the standard vary of scores (the width of the inexperienced areas) yields essentially the most factors distinction: the javelin, pole vault, and a way behind, the discus and 1500m. Once more, the dash hurdles reveals a small factors unfold: the worst hurdlers are usually not penalised a lot compared to the perfect hurdlers.
The 1500m sits lowest in factors phrases of any occasion, with a tenth percentile efficiency price solely round 600 factors. It is a results of the steepness of the blue line, which dictates how a lot the decathlete is penalised for every extra second that they’re away from the world document. The blue line doesn’t need to appear like this, however it does because of the selection of the coefficients a, b, and c. On the plus aspect, the steepness of the road creates a comparatively massive factors distinction between completely different scores within the 1500m, as seen under.
Utilizing the identical approach as earlier than of modelling occasion scores as distributions (log-normal for 1500m, 110m hurdles, and javelin, and regular for the remainder) and computing percentiles, Determine 4 reveals the identical sample because the heptathlon occasions: the identical share enchancment in rating yields essentially the most factors in javelin, and the fewest factors within the dash occasions.
The above outcomes recommend that a number of of essentially the most technical occasions ought to be those that athletes give attention to to achieve factors most simply. Nevertheless, coaching in a single occasion will naturally result in enhancements in another occasions as effectively (and probably degrade efficiency in others), so it isn’t as simple as to have the ability to contemplate every occasion in isolation. The worth of effort spent on one occasion will depend upon each the factors acquire that’s attainable in that occasion and the complementary advantages obtained in different, comparable occasions.
The correlation plot of Determine 5 reveals how scores in every of the heptathlon occasions are correlated with each other. The very best correlations are between the 200m, 100m hurdles, and lengthy soar. This isn’t shocking, as an excellent sprinter will doubtless carry out effectively in all of those occasions. There are additionally correlations, although smaller, between scores in lengthy soar and excessive soar, and in shot put and javelin.
It’s notable that the javelin reveals the least correlation with the opposite occasions total. That is per it being an occasion requiring its personal particular approach, and a heptathlete doesn’t naturally change into a lot better on the javelin by enhancing in another occasions, apart from (considerably) the shot put. Javelin even reveals a small unfavourable correlation with each the 200m and 800m: the higher javelin throwers in heptathlon are usually the more serious runners.
In decathlon (Determine 6), the dash occasions are correlated with each other, as are shot put and discus, whereas pole vault, javelin, and 1500m present fairly weak correlations with virtually the entire different occasions.
This modifications the message from the earlier part. Whereas enhancing relative to the remainder of the sector in javelin, pole vault, or center distance operating ought to present the largest factors acquire per unit of enchancment, the good thing about that is undercut by a attainable lower in efficiency in different occasions. Then again, enhancing ability in one of many sprint-based occasions tends to create positive factors in comparable occasions on the similar time, maybe making this a extra environment friendly strategy to the competitions total.
Lastly, the right-most column in every of the correlation grids (Figures 5 and 6) appears to substantiate this. This column reveals the correlation between scores in every occasion and closing place within the heptathlon or decathlon competitors (multiplied by -1 so {that a} excessive end turns into the most important quantity). The largest correlation with place — that’s, the occasion during which the athlete’s rating most dictates the place they end within the total competitors — is discovered within the lengthy soar in each heptathlon and decathlon, adopted by hurdles and excessive soar in heptathlon, and by hurdles and 400m in decathlon. The significance of lengthy soar is probably going attributable to its ‘centrality’ within the competitions: its comparatively excessive correlations with a number of different occasions. Conversely, efficiency within the 1500m is the least correlated with end place in decathlon. That is most likely as a result of the perfect 1500m runners have a tendency to not maintain benefits in different occasions too, so usually find yourself decrease within the total standings. The decathlon is extra usually received by a powerful sprinter, as a result of this athlete is rewarded a number of instances over for this ability, with factors within the 100m, hurdles, 400m, and lengthy soar.
Insights on how finest to strategy the heptathlon and decathlon turned out completely different from how I anticipated firstly of the evaluation. Though it appears that evidently effort to enhance one’s rating within the javelin is essentially the most environment friendly solution to improve complete factors, the athletes that carry out finest total don’t are inclined to do significantly effectively in javelin. That is doubtless as a result of the abilities required for javelin, and to a lesser extent, pole vault, discus, and excessive soar, don’t switch effectively to different occasions, so the good thing about the trouble is restricted to a factors return in that occasion solely.
It could be speculated that these are essentially the most technically demanding occasions, during which it’s maybe attainable, although troublesome, for the athlete to ‘unlock’ massive positive factors in efficiency via small changes in approach, whereas among the different occasions are extra managed by energy or health, during which solely incremental positive factors are possible. Most likely the issue in making these technical enhancements, mixed with the shared advantages of basic health enhancements, suggestions the steadiness in favour of enhancing scores within the sprint-related occasions.
This steadiness is however managed by the scoring system. Every of the blue traces in Figures 1 and three is anchored at one level by the world document, however the gradient of the road seems to be a alternative that would have been made in another way. The larger the gradient, the extra emphasis is placed on the distinction in rating between the perfect and worst athletes in that occasion. In reality, the big gradients for the javelin and different occasions could also be essential to steadiness these extra remoted occasions towards the shared advantages of enhancements within the dash occasions. If the factors bars of Figures 2 and 4 had been equal throughout all occasions, there could be much less incentive to focus effort on the technical occasions instead of the extra intercorrelated dash occasions.
There is no such thing as a probability of the multi-event scoring techniques altering within the close to future. I might recommend that the right-most columns of Figures 5 and 6 present that the techniques at present work effectively, as there are not any occasions which might be utterly uncorrelated with end place (which might imply that efficiency in these occasions didn’t matter to the general outcome). If there have been to be modifications to the system, it could be a good suggestion to focus on extra even correlations on this column, which might imply growing the factors gradient within the 800m and 1500m, particularly, to extend the good thing about performing effectively in these occasions, on the expense of the lengthy soar and hurdles, which at present have a much bigger bearing on the ultimate standings.