Decathlon scoring explained, with the actual arithmetic

A decathlete runs 10.90 for the 100m and the scoreboard says 883. Not a ranking, not a percentage, not a comparison with anybody else in the field. Eight hundred and eighty-three, produced instantly, and almost nobody in the stadium could tell you where it came from.

It comes from a formula with three constants. Decathlon scoring explained honestly means starting there, because everything else people say about the event, that it rewards all-rounders, that the throws are worth less, that the 1500m decides it, is either a consequence of those constants or is wrong. The tables are published, the arithmetic is short, and once you can do it yourself the event becomes a different thing to watch.

What follows is the whole calculation, the rules that surround it, and what falls out of the shape of the curve.

Decathlon scoring explained: three constants and one exponent

There are two formulas, and they are the same formula written for two directions.

For a track event, where a lower number is better:

Points = INT( A × (B − P)^C )

For a field event, where a higher number is better:

Points = INT( A × (P − B)^C )

P is the performance. A, B and C are constants published for that specific event. INT means take the whole-number part and discard the rest, which is not a rounding: 883.49 becomes 883, and so does 883.99.

The constants for the men's decathlon are these.

Event	A	B	C	Units for P
100m	25.4347	18	1.81	seconds
Long jump	0.14354	220	1.40	centimetres
Shot put	51.39	1.5	1.05	metres
High jump	0.8465	75	1.42	centimetres
400m	1.53775	82	1.81	seconds
110m hurdles	5.74352	28.5	1.92	seconds
Discus	12.91	4	1.10	metres
Pole vault	0.2797	100	1.35	centimetres
Javelin	10.14	7	1.08	metres
1500m	0.03768	480	1.85	seconds

Two features of that table are worth stopping on before any arithmetic happens.

The units are inconsistent, and deliberately so. Jumps are entered in centimetres, throws in metres. A long jump of 7.40m goes into the formula as 740. A discus of 46.00m goes in as 46.00. There is no principle behind this beyond the historical fact that the tables were fitted separately for each event and the constants were left in whatever units the fitting used. Anybody computing a score by hand gets this wrong once and then never again.

And the exponent C is greater than one in all ten events, which is the single most consequential fact in the whole system. That is dealt with below, because it takes a section.

Run one performance through. A 100m in 10.90 seconds:

• B minus P is 18 − 10.90, which is 7.10.
• 7.10 raised to the power 1.81 is 34.7358.
• Multiplied by A, which is 25.4347, that is 883.4953.
• INT gives 883.

That is the whole calculation. Every score on a decathlon scoreboard is that sum, done ten times, with the ten results added.

• 10Events in the programme
• 2Consecutive days of competition
• 3Trials allowed in the long jump and each throw
• 30Minimum minutes between one event and the next

Set by Technical Rule 39. The thirty-minute interval is a minimum applied wherever possible, at the referee's discretion.

What B actually is: the performance worth nothing

The constant B is not arbitrary and it is not a scaling factor. It is the performance at which the athlete scores exactly zero, because that is the point where the bracket collapses to nothing.

Put 18.00 seconds into the 100m formula and the answer is zero. Put 480 seconds, which is eight minutes, into the 1500m formula and the answer is zero. The zero points on the decathlon tables are a 1.50m shot put, a 75cm high jump, a 220cm long jump, a 4.00m discus, a 100cm pole vault, a 7.00m javelin, an 82-second 400m and a 28.50-second 110m hurdles.

Those thresholds are set absurdly low on purpose. A functioning adult can clear 75 centimetres. The point of putting the zero so far below any competitive performance is that it keeps the whole competitive range on a smooth, well-behaved part of the curve, well away from the region where small differences in a poor performance would produce wild swings in points. The tables are not trying to score a beginner sensibly. They are trying to score the top few thousand people in the world sensibly, and they push the awkward end of the curve somewhere nobody competes.

There is a second consequence, and it is the one that bites. Because the score depends on the gap between the performance and B rather than on the performance itself, the same absolute improvement is worth different amounts at different points on the scale. That is not a quirk. That is the design.

Why C is greater than one, and what it costs the athlete who takes the obvious advice

An exponent above one makes a curve convex. In plain terms: the closer you get to the top, the more each additional increment is worth.

Take the 100m and hold everything else fixed.

Computed directly from the published constants for the 100m. The curve steepens as the times get faster, which is what an exponent above one means.

Show the numbers

What the 100m table pays, second by second

Item	Decathlon points
12.00	651
11.75	701
11.50	753
11.25	806
11.00	861
10.75	917
10.50	975
10.25	1035
10.00	1096

Going from 12.00 to 11.50 is worth 102 points. Going from 10.50 to 10.00, the identical half-second, is worth 121. The half-second is the same half-second. The tables say the second one is a fifth more valuable, because the athlete producing it is nearer the edge of what people can do.

The coaching consequence runs against the advice everybody gives. "Work on your weakest event" is intuitive, it is what a schoolteacher would say, and on these tables it is often wrong. An athlete who is already near a thousand points in the hurdles gains more from another tenth there than from the same relative gain in an event where they score seven hundred. The tables reward pressing an advantage, not patching a hole.

The exception is the athlete whose weak event is weak enough to be sitting on a genuinely flat stretch of curve, which in practice means a long way below competitive standard. Nobody at international level is in that position, which is why the strategy at the top of the sport looks like specialisation inside a ten-event competition rather than the balanced generalism the event is supposed to celebrate.

The steepness varies by event, and this is where the constants stop being an implementation detail. The 110m hurdles has the highest exponent at 1.92 and the shot put the lowest at 1.05. An exponent of 1.05 is very nearly linear, which is why the shot table looks like a ruler: 12m scores 606, 13m scores 667, 14m scores 728, 15m scores 790, and every further metre buys roughly the same sixty-odd points regardless of where you started. The hurdles table does nothing of the sort.

Where the points actually are

The useful question is not which event has the biggest exponent. It is how many points a decathlete gains from getting one per cent better at each event, measured from the same starting quality. That puts every event on one comparable scale, and the answer is not what most people expect.

100m24pts

400m23pts

Long jump19pts

High jump19pts

110m hurdles18pts

1500m18pts

Pole vault15pts

Javelin11pts

Shot put11pts

Discus10pts

Computed from the published constants. For each event the 900-point performance was solved for, improved by one per cent, and rescored. It is the fairest like-for-like comparison the tables permit.

Show the numbers

Points gained from a one per cent improvement, measured at the 900-point level

Item	Points gained
100m	24pts
400m	23pts
Long jump	19pts
High jump	19pts
110m hurdles	18pts
1500m	18pts
Pole vault	15pts
Javelin	11pts
Shot put	11pts
Discus	10pts

The sprints pay roughly twice what the throws do. A decathlete who improves his 100m by one per cent, which is about a tenth of a second at that level, banks 24 points. The same one per cent on the discus, about half a metre, banks 10.

This is the real answer to the old argument about whether the decathlon favours sprinters. It does, and the reason is arithmetic rather than prejudice. The events with the tightest human performance range relative to their distance from B are the ones where a small relative gain moves you a long way up the curve. Sprint times cluster; throw distances spread. The tables convert that spread into a flatter payoff.

It also explains a pattern anyone who watches combined events will recognise. The best decathletes tend to be athletes who could have made a living as sprinters or jumpers and learned to throw adequately, rather than throwers who learned to run. The tables were not written to produce that outcome, but they produce it reliably.

The 1500m sits in an interesting place. It pays 18 points per one per cent, which is mid-table rather than negligible, and one second at that level is worth about seven points. The event has a reputation for being where decathlons are won and lost, and the arithmetic partly supports it, though for a reason that has nothing to do with the table. The 1500m is last, everyone is exhausted, and the spread of performance on the second evening is enormous compared with the spread in an event contested fresh. The table does not favour the 1500m. Fatigue does.

Decathlon scoring explained through one athlete's ten marks

Here is a complete competition. The marks are invented, chosen as round numbers so the arithmetic stays legible, and no real athlete or competition is being described.

Event	Mark	Points
100m	10.90	883
Long jump	7.40m	910
Shot put	15.20m	802
High jump	2.00m	803
400m	48.50	885
110m hurdles	14.30	936
Discus	46.00m	787
Pole vault	4.80m	849
Javelin	62.00m	768
1500m	4:30.00	745
Total		8368

Every one of those point scores came out of the formula above. Nothing was looked up, adjusted or weighted afterwards. The 1500m mark went into the formula as 270 seconds, because the tables work in seconds and a decathlete's 1500m written as 4:30.00 has to be converted before it means anything.

Notice how flat the distribution is. The ten scores run from 745 to 936, a range of under two hundred points across events as different as a shot put and a fifteen-hundred. That flatness is the tables doing their job: they were calibrated so that comparable athletic quality produces comparable scores, whatever the discipline.

32%31%28%

• Sprints and hurdles2704
• Jumps2562
• Throws2357
• The 1500m745

The invented decathlon above, grouped by discipline. The four groups are three sprint and hurdle events, three jumps, three throws, and the 1500m on its own.

Show the numbers

Where the constructed 8,368 points came from

Item	Value
Sprints and hurdles	2704
Jumps	2562
Throws	2357
The 1500m	745

The four roundings, and all of them go the same way

Between the moment an athlete produces a performance and the moment a number appears on the scoreboard, the mark is rounded four separate times. Every one of them rounds against the athlete.

The mark is recorded conservatively. A track time from a photo finish system is converted to the next longer hundredth of a second, so 10.893 is recorded as 10.90 rather than 10.89. A horizontal jump or a throw is recorded to the nearest centimetre below the distance measured. A high jump or pole vault height is measured in whole centimetres.

The table lookup rounds down again. The tables are published as look-up documents rather than as formulas, and not every possible mark appears in them. The rule for a mark that falls between two listed entries is to use the score for the nearest lesser performance. The rulebook's own worked example concerns a women's javelin throw of 45.82m, for which no entry exists: the nearest shorter listed distance is 45.78m, and the athlete is credited with the 779 points attached to it.

The formula truncates. The INT in both formulas discards the fractional part rather than rounding it. An athlete whose performance computes to 883.99 receives 883, not 884.

And it happens ten times. Truncation alone costs on average about half a point per event, which across ten events is a few points on the total. That sounds trivial and it is the same order as the margin that has separated athletes on a podium.

None of this is a scandal. Consistency matters more than generosity in a scoring system, and rounding one way everywhere is defensible in a way that rounding to nearest sometimes and down other times would not be. It is worth knowing about because it explains why hand-computed scores from a stopwatch and a tape measure frequently come out a point or two above the official ones.

1. 1The performance happensA time, a distance or a height. Nothing about it is a score yet, and the athlete competing has no reason to know what it will convert to.
2. 2The mark is recorded to the official granularityTrack times are converted to the next longer hundredth of a second. Horizontal jumps and throws are recorded to the nearest centimetre below the measured distance. Vertical heights are measured in whole centimetres.
3. 3The mark is converted into the units the table usesSeconds for track, including the 1500m written out as a number of seconds rather than minutes. Centimetres for the jumps. Metres for the throws. This is the step people get wrong.
4. 4The gap from the zero constant is takenB minus the time for a track event, or the mark minus B for a field event. This is the quantity the score is actually built from.
5. 5The gap is raised to the power C and multiplied by AThe exponent is what makes the curve steepen towards the top of the range. The multiplier sets the scale so that a world-class mark lands near a thousand.
6. 6The result is truncated and added to the running totalThe whole-number part is taken and the fraction discarded. The rules require the score for each event and the cumulative total to be announced to every athlete after each event finishes.

The sequence set out in the competition and technical rules. The same six steps run ten times, and only the constants change.

A thousand points is a different mark in every event

The tables were calibrated so that a thousand points means roughly the same standard of athlete whatever event produced it. Solving each formula for exactly a thousand, then taking the nearest mark that can actually be recorded, gives this.

Event	Smallest recordable mark worth 1,000 points	Points it scores
100m	10.39	1001
Long jump	7.76m	1000
Shot put	18.40m	1000
High jump	2.21m	1002
400m	46.17	1000
110m hurdles	13.80	1000
Discus	56.17m	1000
Pole vault	5.29m	1001
Javelin	77.19m	1000
1500m	3:53.79	1000

Read that column and the scale of the event becomes obvious. Ten thousand points would require an athlete to produce all ten of those marks inside forty-eight hours, having also produced the other nine each time. It is a useful reference precisely because it is unreachable: the four-figure number is not a target, it is a yardstick that tells you how close to a specialist's standard a given decathlon mark is.

The world record for the decathlon stands at 9,126 points, set by Kevin Mayer of France at Talence in September 2018. Set that against the table above and the achievement resolves into something concrete: it is what happens when ten performances average a little over nine hundred points each.

The rules that make a decathlon different from ten separate competitions

The technical rules modify the individual event rules in a set of specific ways, and each modification exists to solve a scheduling problem created by putting ten events into two days.

Three trials only. In the long jump and in each of the three throws, every athlete gets three attempts and there is no final eight. In a standalone competition the leading eight advance to further trials. In a decathlon nobody does, which removes both the advantage of leading after three rounds and the chance to rescue a bad start.

The bar goes up by a fixed amount. The increment in the vertical jumps is uniform throughout: three centimetres in the high jump and ten in the pole vault, announced in advance and not negotiable. In an individual competition the increments can vary and the athlete who has won gets to choose the next height. A decathlete does not, because the score depends on the height and letting a leader pick heights would corrupt the arithmetic. The tactical layer that makes pole vault competitions and high jump competitions interesting in their own right is deliberately stripped out.

The clock is tighter at the end. The time allowed for a trial shortens as the field thins, and it shortens further in combined events than in individual ones. A single athlete left alone in the pole vault gets three minutes in a decathlon against five in a standalone competition, and two minutes against three in the high jump. Somebody has to keep the second day inside its timetable.

One false start per race. Combined events kept the older rule, so the first false start in a race is a warning rather than a disqualification, shown with a yellow and black card, and every athlete in the race is warned at the same time so nobody is in doubt. Anyone responsible for a further false start in that race is disqualified. The zero-tolerance rule that governs individual sprint races does not apply here, and this is the only corner of the sport where it does not.

No jump-off. The rule that settles a tie for first place in the vertical jumps with a jump-off is explicitly disapplied in combined events, because the tie in the high jump is not a tie for anything. Both athletes score the height they cleared and the competition moves on.

Thirty minutes, and ten hours. Wherever possible there is at least half an hour between the end of one event and the start of the next for any individual athlete, and at least ten hours between the last event of the first day and the first of the second. The half hour is measured from the end of the last trial of the previous event to the start of the first trial of the next, which in practice means an athlete walks straight from one arena to the warm-up for the following event and the interval is consumed by the walk.

And the heats are seeded by form. In every event except the last, athletes with similar performances are grouped together, with a preference for five or more per group and never fewer than three. In the final event the last heat is arranged to contain the leaders after nine events, which is why the 1500m at a major championship is a race between the medal contenders rather than a scattered field.

Fail to record a mark and you do not get a low score, you get no score

This is the rule that decides more decathlons than the tables do, and it is unforgiving.

An athlete who fails to attempt to start, or who fails to record a valid trial in any one of the ten events, is not permitted to take part in the subsequent events and is treated as having abandoned the competition. They do not appear in the final classification at all.

Three fouls in the discus, or three failures at the opening height in the pole vault, therefore do not cost an athlete seven hundred points. They cost the entire competition, including the nine other performances already produced. This is why decathletes open the pole vault far below their capability and why a thrower will send the first attempt out at a conservative distance rather than risk a foul. The downside is not a bad score in one event. It is the deletion of two days.

One consolation survives. A performance produced in an individual event inside a combined events competition can still be ratified as a record in its own right, whether or not the athlete goes on to complete the whole thing. An athlete who runs a world record 100m in the first event of a decathlon and then withdraws in the shot put has still run a world record.

A tie is a tie, and that is a change

Older versions of the rules settled equal totals with a count-back: the athlete who scored more points in a greater number of events, then the athlete with the highest single-event score, and so on.

That is no longer how it works. The current rule is one sentence long: if two or more athletes achieve an equal number of points for any place in the competition, it is determined as a tie. Both athletes hold the place. Two gold medals, or two fourths, and no further arithmetic.

It is a small thing that says something about the philosophy of the tables. A count-back implies that two identical totals conceal a real difference in quality that the tables somehow failed to capture. Declaring a tie says the opposite: the total is the measurement, and if two measurements are equal then so are the athletes. Given that the tables already round four times against everybody equally, that is the more honest position.

The wind rule applies to the average, not to any single mark

Three events in a men's decathlon have their wind measured: the 100m, the 110m hurdles and the long jump. For an individual event a following wind above two metres per second makes the mark wind-assisted and unusable for record purposes.

Combined events use a different test, and it is applied to the total rather than to any one performance. For a combined events world record, the average wind velocity across the wind-measured events, calculated as the algebraic sum of the readings divided by the number of those events, must not exceed plus two metres per second. Algebraic means the signs count: a headwind in the hurdles offsets a following wind in the long jump.

The practical effect is that a decathlete can produce a legally recorded 100m with a following wind above the individual limit and still have the total ratified, provided the other readings pull the average back. It also means an athlete can be denied a record because of the wind in an event they ran perfectly well. The reasoning behind the two metre per second threshold itself is the same in both cases; only the unit of measurement changes, from the single mark to the competition.

What the tables are not

They are not a physiological model. Nothing in the constants encodes the energy cost of a shot put or the neuromuscular demand of a hurdle. The tables were built by choosing benchmark performances at various levels for each event, deciding what those performances ought to be worth relative to each other, and fitting a three-parameter curve through the result. The current set has been in use since 2001, and it replaced earlier sets going back to the ones written when the event entered the Olympic programme in 1912.

So the tables are a convention with a value judgement inside it. Somebody decided that a 10.39 hundred metres and a 77.19 metre javelin are worth the same. That decision is defensible, it is stable, and it is not derived from anything more fundamental than expert judgement about relative difficulty at the time of fitting.

Which means the tables can go out of date without anybody changing them, because the sport moves underneath. When implement specifications change, or when footwear technology shifts what a given time represents, the relationship between a mark and the athletic quality behind it moves in some events and not others. A table fitted before such a shift is quietly scoring a slightly different sport from the one being contested. Revisions happen, and every revision is retrospective by definition.

There is one more distinction worth drawing, because it trips people up constantly. The combined events tables are not the same document as the general World Athletics scoring tables used to convert marks into points for ranking purposes. Both turn a performance into a number, both exist so that different events can be compared, and they produce different numbers for the same mark. If you are reading about how athletes are ranked and how a result score is calculated, that is the other set. The decathlon uses its own.

The heptathlon runs the same machinery with different constants

The women's heptathlon uses the identical pair of formulas, with seven events rather than ten and its own constants: the 100m hurdles, high jump, shot put and 200m on the first day, then the long jump, javelin and 800m on the second.

Event	A	B	C	Units for P
100m hurdles	9.23076	26.7	1.835	seconds
High jump	1.84523	75	1.348	centimetres
Shot put	56.0211	1.5	1.05	metres
200m	4.99087	42.5	1.81	seconds
Long jump	0.188807	210	1.41	centimetres
Javelin	15.9803	3.8	1.04	metres
800m	0.11193	254	1.88	seconds

The same properties hold. Every exponent is above one, so the curve steepens towards the top in exactly the same way. The shot put again has the flattest exponent and the running events the steepest, so the same bias towards speed applies. And the same three-figure yardstick works: a thousand points is 13.85 in the hurdles, 1.82m in the high jump, 17.07m in the shot, 23.80 in the 200m, 6.48m in the long jump, 57.18m in the javelin and 2:07.63 in the 800m.

The women's heptathlon world record of 7,291 points was set by Jackie Joyner-Kersee in 1988 and has stood ever since, which is a long time for any record in athletics and a very long time in an event where the tables themselves have been revised in the interval.

How to read a decathlon scoreboard

Once the arithmetic is in your head, the running score becomes readable in a way the raw marks are not.

Convert to per-event averages. Divide the total after n events by n. That number, compared against nine hundred, tells you immediately what class of decathlon is happening, and it works at any stage of the competition rather than only at the end.

Watch the gap in points, not the gap in marks. A two-metre advantage in the discus is worth about forty points. A tenth of a second in the 100m is worth about twenty-two. Two athletes who look far apart on the field can be within a few points of each other, and two who look level in the throws may not be.

Note who has banked their strengths. After five events you can see whether an athlete's remaining programme contains the disciplines they score best in. A leader whose good events are all behind them is not leading in any meaningful sense.

Do the 1500m sum before the race. Seven points a second at the top level, so a fifteen-second deficit going into the final event is roughly a hundred points, and a hundred points is a long way to make up over three and three-quarter minutes. Broadcasters usually put the required time on screen. It is more satisfying to have worked it out first.

And watch the opening heights. A decathlete's first pole vault attempt tells you how the competition is being played, because clearing it is worth nothing and failing three times at it ends everything. Conservative openers are a sign of an athlete protecting a good position. An aggressive one is a sign of somebody who has decided they need points more than they need safety.

The rest of the archive on this sport is built the same way: the rules and the formulas are published, they change slowly, and almost everything that looks like judgement on a scoreboard turns out to be arithmetic that somebody fixed a long time ago and nobody reads.