Critical pace and running zones: Your threshold from everyday runs

Running zones are only as good as their anchor. Heart rate zones hang on a maximum heart rate that hardly anyone really knows. Pace zones hang on threshold pace, which classically comes from a lactate test in a lab, a 30-minute time trial or a fresh 10k race time. All three are rare, expensive or painful. Critical speed, usually called critical pace among runners, does without them: it can be computed from the hard stretches of perfectly ordinary training runs. How that works, what comes out of it and where the method stops is what this article is about.

What critical speed is

Plot the best speed a runner can hold over different durations against duration and you get a hyperbola: very fast for seconds, fast for minutes, then the curve flattens and approaches a pace that can be held for a long time. That pace is the critical speed (Hill 1925, Monod & Scherrer 1965). The curve fits in one line:

distance = D′ + CS × time

CS is the speed your aerobic metabolism can deliver in a steady state. Physiologically it marks the boundary between the "heavy" and the "severe" intensity domain (Jones & Vanhatalo 2017): below it, lactate and oxygen uptake eventually stabilise; above it, they climb until exhaustion. In practice CS is the pace well-trained runners can hold for roughly 30 to 45 minutes, usually a few seconds per kilometre faster than 60-minute pace.

D′ (say "D prime") is a distance in metres: the extra ground you can cover above CS before you have to stop. It is the running counterpart of W′ from the critical power curve in cycling: a reserve that drains above CS and refills below it.

A worked example

A runner has a CS of 4:00 min/km, which is 4.17 m/s, and a D′ of 200 m. For every distance, the equation predicts the best time:

• 1500 m: (1500 − 200) / 4.17 = 312 s, so 5:12 (3:28 min/km)
• 3000 m: (3000 − 200) / 4.17 = 672 s, so 11:12 (3:44 min/km)
• 5000 m: (5000 − 200) / 4.17 = 1152 s, so 19:12 (3:50 min/km)

With a D′ of 300 m the 1500 m time would drop to 4:48, the 5000 m time only to 18:48. That is how to read D′: it decides short distances and intervals, hardly the long ones.

D′ is even more useful as a time budget. If the runner goes ten percent faster than CS (4.58 m/s, 3:38 min/km), she spends 0.42 m/s × time of reserve; 200 m then last 480 seconds, eight minutes. At twenty percent above CS it is four minutes. That is exactly why 4 × 4 minutes at 3:20 is doable and 4 × 8 minutes at the same pace is not.

How trace derives critical pace from training runs

The road from training run to curve has four steps, and each one is a decision against a known error.

1. Grade-adjusted speed. Every run is first converted into a speed that accounts for what uphill and downhill cost (Minetti et al. 2002). Without this step, every downhill run sets a personal best that would never fall on the track, and the curve would be worthless.
2. The best-effort curve. From all runs of the past 90 days, the best average speed is taken for every duration. That is the running counterpart of the power curve on the bike.
3. The valid window. Only durations from 2 to 20 minutes enter the fit. Shorter is sprint-dominated; longer violates the model's assumption: the two-parameter model is validated for efforts of about 2 to 15 minutes and systematically overestimates outside that range (Jones & Vanhatalo 2017). trace requires at least three points from more than one activity. Two points always give a perfect line, with no way to check it.
4. Two fits of the same hyperbola. The equation can be linearised in two ways: distance against time (long durations weigh heavily) and speed against 1/time (short durations weigh heavily). trace computes both and takes the mean. The gap between the two CS values is a direct measure of reliability (Muniz-Pumares et al. 2019): if they differ by more than a few percent, the data is not good enough.

Before all that sits a filter you only understand once you have seen field data: best efforts from training are almost always submaximal. The true curve falls monotonically with duration, and a point that bulges the curve upward, because faster stretches sit to its left and right, is provably not a maximum. trace removes such points before fitting. And because sports watches occasionally file a bike ride as a run, a physiological ceiling of 2:13 min/km applies from five minutes onward; the 5k world record is 2:31 per kilometre, so real runners cannot fall out.

The result is a critical pace, a D′, a quality score and a list of caveats: too few points, too narrow a duration range, only one activity, data older than a few weeks, no hard effort. trace shows these flags instead of hiding them, because a CS marked "single activity" is a guess, not a threshold.

What you have to run for it

The model needs hard stretches of different lengths. Someone who only runs easy has no curve, and someone who only does 400 m repeats has no point in the valid window. Enough, spread over six to eight weeks: one session with intervals of three to five minutes, one tempo run of 15 to 20 minutes, and ideally a race or test run over 5 km. Those are the runs a training plan contains anyway. Critical pace falls out as a by-product, and it updates with every new hard run without you ever scheduling a test.

From threshold to running zones

With sufficient quality, the critical pace becomes the threshold pace from which trace derives the zones. If the curve is too thin, trace uses the threshold estimated from personal bests (Daniels' VDOT), and if you know your threshold from a test, you enter it yourself in the running settings. The zones are percentages of threshold pace, and because pace is counted in seconds per kilometre, a higher percentage is slower.

The bands sit close to Daniels: his interval pace is about 92 percent of threshold pace, his repetition pace about 84 percent, marathon pace around 108 percent. If you have trained with Daniels tables, you will recognise them; only the anchor now comes from your own runs.

Why pace zones and not just heart rate

Heart rate lags the effort by half a minute to a minute, climbs over the course of a session even at constant pace, and reacts to heat, caffeine and sleep. For a 3-minute interval it is therefore no usable target: by the time it reaches the zone, the interval is half over. Pace is immediate and exact. In return it knows nothing about wind, heat and surface, and on hills it is blind without grade adjustment. trace therefore shows both and computes a run's training load from grade-adjusted pace, not raw pace. On flat road you steer by pace; on trails and in the heat, heart rate helps as a second opinion.

How to use the zones in training

The distribution that studies of endurance athletes at every level keep showing is roughly 80 to 20: four fifths of the time in zones 1 and 2, one fifth in zone 4 and above (Seiler 2010). Zone 3 is not forbidden, but it is where recreational runners spend most of their time and gain the least: too hard to recover, too easy to be a stimulus. Concretely, per week:

• Most runs in zone 2, the long run included.
• One threshold session in zone 4: 2 × 15 minutes or 4 × 8 minutes with short rests.
• Every one to two weeks a VO₂max session in zone 5: 5 × 3 minutes or 4 × 4 minutes.
• Strides at the end of easy runs in zones 6 and 7, 15 to 20 seconds each.

D′ helps with rest length: an interval twenty percent above CS drains the reserve in four minutes; if you only refill half of it in the jog recovery, you will not get up to pace on the third rep. trace shows the D′ balance of a session as a curve, similar to W′ balance on the bike.

What critical pace says about races, and what it does not

It is tempting to compute a marathon time with the equation above. Please don't. The model holds for 2 to about 20 minutes; for 10 km it predicts 39:12 in the example, 3:55 min/km, only five seconds slower than CS itself. In reality CS is closer to 30- to 45-minute pace for most runners, and the marathon adds glycogen, muscle damage and durability, none of which the hyperbola knows about. trace therefore deliberately does not compute race predictions from CS but from your personal bests: with the Riegel model, whose fatigue exponent is fitted from your own results (between 1.02 for endurance-strong and 1.12 for speed-strong runners, instead of a flat 1.06), cross-checked with the Cameron formula and, from the half marathon up, corrected by your measured durability. CS and D′ stay what they do best: the threshold and the time budget above it.

Where the model reaches its limits

• GPS. Street canyons, forest and tunnels produce pace spikes that are not real. trace caps speeds above 12.5 m/s and discards downhill windows, but a noisy 3-minute stretch stays noisy. Track and open road give the cleanest points.
• D′ is sensitive. As the intercept of the line it reacts to every error in the short durations. Swings of 30 percent between two calculations are normal; CS is much more stable. Read D′ as an order of magnitude.
• The window is narrow. A runner whose hard stretches all sit between 3 and 5 minutes has a narrow duration range and therefore an uncertain slope. The flag "narrow duration range" means: run 15 to 20 minutes hard, once.
• Heat and altitude. Both lower the sustainable pace, and the curve does not know why. A summer of hot runs yields a lower CS that suddenly "rises" in autumn. That is not a change of form, it is weather.
• It ages. A CS from runs ten weeks ago describes the runner of back then. trace flags stale data and recomputes with every new hard run, but the zones are only ever as current as the last hard stimulus.
• Treadmill and trail. Without GPS there is no reliable pace, off-road no reliable grade adjustment. For both, heart rate and feel remain the better controls.

Bottom line

Critical pace replaces the threshold test with what you run anyway. It needs hard stretches of different lengths, clean GPS and a few weeks of patience; then it delivers a threshold that moves with you, and with D′ a time budget for everything above it. The zones are percentages of that threshold; stick to them and you train the right systems at the right time. For race times beyond 20 minutes the formula is not fit, and trace does not pretend it is. What critical pace, the D′ balance and running zones look like in trace is on the features page.

Sources

• Hill AV (1925): The physiological basis of athletic records. Nature.
• Monod H, Scherrer J (1965): The work capacity of a synergic muscular group. Ergonomics.
• Jones AM, Vanhatalo A (2017): The 'Critical Power' Concept: Applications to Sports Performance with a Focus on Intermittent High-Intensity Exercise. Sports Medicine.
• Muniz-Pumares D et al. (2019): Methodological Approaches and Related Challenges Associated With the Determination of Critical Power and Curvature Constant. Journal of Strength and Conditioning Research.
• Minetti AE et al. (2002): Energy cost of walking and running at extreme uphill and downhill slopes. Journal of Applied Physiology.
• Daniels J: Daniels' Running Formula. Human Kinetics.
• Seiler S (2010): What is best practice for training intensity and duration distribution in endurance athletes? International Journal of Sports Physiology and Performance.