critical speed

What assumptions are baked into your race prediction model?

After launching my power law calculator earlier this week I got a couple emails from readers who noticed some counter-intuitive behavior.

Suppose you have an athlete who has run 800m in 2:25 and 1600m in 5:10. The power law calculator predicts a 3200m performance of 11:03—pretty reasonable. 

Then suppose your athlete improves their 800m time to 2:20. Enter that into the calculator instead and you get a 3200m time of 11:26—which is slower than their predicted 3200m time before! This seems wrong: shouldn’t the runner now be able to run faster over 3200m as well?  

Now, this wouldn’t be the first time a reader spotted a subtle issue with one of my calculators, but in this case, the calculator is working correctly, under the assumptions baked into the model. Here’s the intuition: 

Suppose you had two different athletes: Fast-Twitch Frannie, who runs 1600m in 5:10 and 800m in 2:20, and Slow-Twitch Sally, who can also run 5:10 for 1600m, but can only run 800m in 2:25. If these two athletes race over 3200m, who will win? 

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New app for making power law predictions for race performance

I recently published a critical speed calculator app, which makes it super easy to use the critical speed model to estimate your steady-state max. However, the critical speed model is not the most accurate way to predict race performance at new distances—that honor belongs to power law models (sometimes also called Riegel models, after Pete Riegel who popularized their use in running). 

I covered the science behind power law models in this earlier article on power law models versus critical speed models for predicting race times. Thanks to the infrastructure I built for the critical speed model, it was super easy to swap out the statistical model for a power law model: so now I have a brand-new power law calculator too!

⏱️ Try my power law calculator here ⏱️

Power law models are great for extrapolating—for example, predicting your half marathon time from a 5k and a 10k, or predicting your 400m time from an 800m and a 1500m time. They perform much better at this task than the critical speed model, and my power law calculator also includes some useful features for prediction.

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New web app for calculating critical speed

When I published my detailed write-up on the science of critical speed for runners, I promised that I would code up a free calculator to calculate your critical speed (also known as “critical velocity” or CV) from a set of race performances. That calculator is now finished! 

⏱️ Try my critical speed calculator here! ⏱️

This free web app makes it super easy to implement the statistical calculations that give you critical speed—and its uncertainty bounds—given a set of race performances.  

Like all of my web apps, it’s designed to be mobile-friendly, and it includes cookie-based “memory” so you can come back to where you left off. This critical speed calculator is also super easy to use: you don’t have to convert race performances into seconds, and you can choose from a wide range of pre-set race distance options, or enter a custom distance.

This is the only critical speed calculator I know of that gives you statistically appropriate uncertainty estimates that you can use for physiologically based workouts. 

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Two workouts that aren’t in Marathon Excellence

A few weeks ago, I wrote about how I tested out the training plans for Marathon Excellence for Everyone with the help of a large group of “beta testers” from this very email list. Monitoring the training of these beta testers helped me fine-tune and improve the training plans in the book before it was released.

Today I want to showcase two workouts that I removed from the training plans after the beta testing rounds and explain why I cut them from the final schedules.

It’s not because they’re bad workouts—they’re great sessions! But I removed them because they were asking too much of the athlete early on in training. Not so much from a difficulty perspective, but in terms of psychological buy-in and in terms of precise pacing skills.

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New and improved threshold, CV, and VO2max pace calculator

I’ve made some major improvements to my threshold, CV, and VO2max pace calculator!

The latest update improves accuracy in longer events like the 5k and the 10k, adds data from master’s and adult runners, and provides better uncertainty ranges across a wide range of speeds. 

🎯 Check out the improved calculator here! 🚀

Below, I’ll cover some of the new features and lay out my roadmap for upcoming features.

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New app for calculating threshold, CV, and VO2max pace

I’m excited to share my latest web app: a calculator for threshold pace, CV pace, and VO2max pace! 

📱 Check out my new threshold, CV, and VO2max calculator here! 📱

This calculator allows you to predict physiological training paces from any race distance from 800m to 10 km. 

This app was developed by analyzing over 10,000 race performances using the critical speed model, the gold standard in physiology for determining metabolically stable and metabolically unstable paces. 

The app also includes uncertainty ranges so you can get an idea of the range of different physiological profiles that you might find among runners at the same level of performance.

Below the app, you’ll find a detailed write-up of how it works and what differences you’ll notice between this app and other CV pace, threshold pace, and VO2max pace calculators and tables that you might’ve used in the past. 

As with all of my apps, it is 100% free and open-source. If you find any bugs, have any suggestions for improvements, or spot something that doesn’t look right,  drop me an email. 

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Predicting threshold pace, CV pace, and VO2max pace from 5k times

Most serious runners do workouts at threshold pace, CV pace, and VO2max pace. But how can you know if you're running the right pace for your threshold, CV ("critical velocity," a.k.a. critical speed), or VO2max sessions? There are plenty of conversion charts online, but it's not always clear whether they're making predictions that are accurate for most runners.

This article introduces a simple framework for determining threshold, CV, and VO2max pace based off your current 5k fitness, using percentages of 5k pace to set workout paces. Below, I'll show how these three training paces can be derived from the critical speed model, and present an analysis on thousands of race performances that result in the following training guidelines:

Pace Estimate Meaning Also known as
Threshold 90% 5k Fastest pace that produces a metabolic steady-state SSmax, LT2, CS-, T pace
CV pace 96% 5k Boundary separating metabolically sustainable and unsustainable paces CS, critical speed
VO2max pace 100% 5k Slowest speed that produces metabolic instability and drives oxygen consumption to VO2max CS+

Don’t forget that I have a handy pace percentage calculator for quickly calculating pace percentages!

These predictions are accurate for >90% of runners ("accurate" here meaning "producing the intended physiological effects") and come from data on hundreds of runners with 5k PRs from 14:00 to 25:00. They'll probably work pretty well outside that range too.

Naturally, these predictions work great for full-spectrum percentage-based training, but they work just as well in other systems too.

Want to know where these calculations come from? Read on!

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Steady-state max (SSmax) for runners: The maximal metabolic steady state

Steady-state max is the single most important concept in exercise physiology. That’s a bold statement, but I’ve come to believe it.

The term “steady-state max” and its abbreviation “SSmax” (just pronounced “steady-state max”) refers to the highest metabolic power output that your body can achieve while maintaining a metabolic equilibrium—i.e. an internal state in your muscles and bloodstream that’s stable over time.

SSmax is connected to topics you’re probably familiar with, like lactate threshold (LT2, technically speaking) and critical speed, but they are not quite the same thing—metrics like LT2 and critical speed are ways of estimating SSmax, which is the actual underlying biological capability.

Understanding steady-state max is absolutely essential for building a modern, physiologically-based approach to training, so let’s dive in.

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The science of critical speed, critical velocity (CV), and critical power training for runners

Female athlete running in front of scientific graphic paper

Critical speed is the boundary that separates running speeds that can be sustained at a metabolic steady-state from speeds that cannot. Sometimes called critical velocity or “CV,” critical speed is known in the running world in partly due to its popularization by Tom “Tinman” Schwartz and his proteges, including Drew Hunter.[1]

Critical speed is increasingly becoming the gold standard among physiologists for identifying the limit of what runners would call “high-end aerobic” or “steady-state” running speeds, and is gaining traction as a training tool as well. The critical speed model explains the body’s response to different speeds better than older models based on the lactate threshold.

Among exercise physiologists, critical speed (or a semi-related concept, the maximum lactate steady state, which we’ll also discuss) is rapidly becoming the gold standard for capturing the aerobic fitness of athletes.

Critical speed has its roots in early work in the 1960s, 70s, and 80s, but didn’t really start to emerge as the strongest physiological model for intense exercise until the last 15 years or so.

In this article, we’ll take a detailed look at the critical speed phenomenon, understand how it works on a mathematical and physiological level, see some of the problems and controversies surrounding it, and learn how to apply the concept of critical speed in your own training.

⏱️ Reminder: I have a free critical speed calculator here ⏱️

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