Why the Hybrid Score uses a harmonic mean

To measure hybrid fitness as one number you need two steps: grade strength and endurance on the same scale, then combine them in a way that doesn't let one half carry the other. The Hybrid Score does the second step with a harmonic mean, which is pulled toward the lower half. Strength 60 and engine 90 average 75, but their harmonic mean is 72. Strength 40 and engine 95 average 67.5; the harmonic mean is 56.3. That choice is ours. No published instrument validates combining strength and endurance this way.

Step one: put both halves on one scale#

You can't combine a squat and a VO2max until they're in the same units. So each half is graded against reference data for people like you.

Strength is your best estimated barbell squat, bench, deadlift and overhead press, divided by bodyweight and graded against sex-specific cut points. The kind of data those draw on is van den Hoek's set of 809,986 tested powerlifting entries, expressed exactly that way, as weight lifted over bodyweight.¹ Engine is your VO2max graded for your age and sex, with cut points that start from the FRIEND registry. That's 7,783 lab treadmill tests, where the median man in his twenties sat at 48.0 ml/kg/min and the median woman at 37.6.²

Both land on the same 0 to 100 ladder: untrained 20, novice 40, intermediate 60, advanced 80, elite 95. A 60 on strength and a 60 on engine mean the same thing, intermediate for someone of your sex, size and age. The cut points and the ladder are our choices too. How strong should a runner be has the strength table, and the science page lists which parts are published data and which are ours.

Step two: four ways to combine two numbers#

Once both halves are on one scale, there are a few obvious ways to make one number:

• the average, (S + E) ÷ 2;
• the geometric mean, the square root of S × E;
• the harmonic mean, 2 × S × E ÷ (S + E);
• the minimum, whichever half is lower.

For equal halves, all four give the same answer. As the halves pull apart, they don't. The harmonic mean is always at or below the geometric mean, which is always at or below the average. Here's what happens if one half stays at 95, elite, and the other falls.

One half at 95, the other falling

the lower half	Average (combined score)	Geometric mean (combined score)	Harmonic mean (combined score)
20	57.5	43.6	33
40	67.5	61.6	56.3
60	77.5	75.5	73.5
80	87.5	87.2	86.9
95	95	95	95

Computed from the formulas, with the higher half fixed at 95. The Hybrid Score uses the harmonic mean (src/lib/score-grading.ts harmonic()).

Read the left end. An elite lifter with an untrained engine, 95 and 20, averages 57.5, close to the intermediate line at 60. The harmonic mean puts them at 33. At the right end, with the halves 15 points apart, the three lines are within a point of each other. So the harmonic mean barely changes anything for a balanced athlete and changes a lot for a lopsided one, which is the point.

Every row averages 75. An average can't tell these four athletes apart. The harmonic mean ranks them in the order you'd probably rank them yourself if both halves matter to you.

If the harmonic mean sounds abstract, you've used one on a run. Cover 1 km at 10 km/h and the next 1 km at 15 km/h, and your average speed isn't 12.5 km/h. The first kilometre takes 6:00 and the second 4:00, so 2 km in 10 minutes is 12 km/h, the harmonic mean of the two speeds. The slow kilometre counts for more because you spent more time in it. The score works the same way: the weak half weighs more because it's where you're losing.

Why not the average, and why not the minimum#

The average is the one people expect, and it hides exactly the thing a hybrid athlete wants to know. A 95/40 athlete and a 67/68 athlete both average 67.5. One of them is a specialist with a gap. An average reports them as the same.

The minimum goes too far the other way. It ignores the stronger half completely. Under the minimum, a 60/90 athlete who adds ten points of engine sees no change at all, which is a strange thing to tell someone who just got fitter.

The harmonic mean sits between them. It credits improvement on both sides, but credits it more on the weaker one. The geometric mean also does that, more gently. Choosing harmonic over geometric is a choice about how hard to penalise the gap, and we picked the harder one. There's no published answer for which is right; it's a judgment.

The way I put it to lifters: a huge 1RM sitting next to a weak VO2max makes you half an athlete. The harmonic mean is that sentence written as a formula.

What one more point is worth#

The part that's actually useful for training is the slope. One more point of strength adds 2E² ÷ (S + E)² to the score, and one more point of engine adds 2S² ÷ (S + E)². In plain words, each half's point is worth more the bigger the other half is compared with it. So the lower half's points are always worth more.

At 60/90, a point of strength is worth 0.72 and a point of engine 0.32. Ten more points of strength would take the score from 72.0 to 78.75. Ten more points of engine would take it to 75.0. Same work on paper, more than twice the result on the weaker side. Under an average both would give 80.

That's why we think the harmonic mean is the right choice for the question this score exists to answer: is the way you're splitting your week making you a more complete athlete? The slope points at your weaker half without you having to ask. Strength-limited or engine-limited? works through the full point-value table and what it says about where to put your hours.

What the harmonic mean doesn't do#

A few things are worth saying plainly, because they're not what you'd guess from "harmonic mean".

Inside the strength half, the lifts are a plain average. A huge deadlift can make up for a weak squat within the Strength Index. The balance penalty only applies between strength and engine.

The two halves don't age the same way. Strength keeps your best logged lift with no time limit. Engine only counts runs from the last 90 days and watch VO2max readings from the last 120. So if you stop training, only the engine half falls. The harmonic mean then drags the score down with it, while the strength half holds still, because it keeps your best lift ever.

If one half has no data yet, it isn't treated as zero. It gets a starting estimate from the experience level you picked, between 22 and 65, so a new athlete never sees a score of zero. The score is marked as an estimate until both halves are measured.

And it isn't a health measure. It's a training metric graded against population data, nothing more.

My score at two points this year#

Going into my first HYROX in August, I was strength 74 and engine 80. The harmonic mean of that is 76.9, shown as 77. The average would have been 77.0. With halves that close, the choice of mean made no difference at all.

In late October I'm strength 74 and engine 57. The harmonic mean is 64.4, shown as 64; the average would be 65.5. Still not a big gap, because 17 points apart isn't that lopsided. The scoring model changed on 8 October, so those two scores don't compare directly. What they show is the same thing the chart does: the harmonic mean only bites as the halves pull apart.

A considered opinion, not a validated instrument#

Combining strength and endurance into one number isn't new, and we didn't invent it. What we can say about ours is what each part rests on. The halves are graded against published reference data. The way we blend them is engineering: a deliberate choice that a lopsided athlete should score below a balanced one with the same average. The science page says the same, in nearly the same words: the pillars are validated, and the blend is a considered opinion.

If you want to see it on your own numbers, the Hybrid Score calculator runs the same code, and the guide to reading your score shows where the app puts the lower half and what a point on each is worth. The definition of a hybrid athlete that falls out of all this, both halves at intermediate or better, is in what is a hybrid athlete.