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!
Mapping threshold, CV, and VO2max to the critical speed model
All three of these common training paces can be derived from the critical speed model, and related to one another via the concept of steady-state max (SSmax): the boundary that separates speeds that are metabolically sustainable—meaning those that produce levels of oxygen consumption, intramuscular acidity, blood lactate, etc., that are stable over time—from speeds that are metabolically unsustainable.
There’s just one problem with SSmax: the gold-standard tools for estimating it, like critical speed testing, are totally impractical for real training! Fortunately, it turns out that you can use 5k pace as a reasonably good predictor of threshold pace, CV pace, and VO2max pace by using the corresponding concepts from the critical speed model: CS- (for threshold pace), CS (for CV pace), and CS+ (for VO2max pace).
These predictions will be accurate (i.e. produce the intended physiological effect) for >90% of runners.
A quick summary of lactate threshold, SSmax, critical speed, and CV pace for runners
The single biggest determinant of your performance in long-distance events is your pace at your maximal metabolic steady-state, or SSmax (“steady-state max”)—the fastest pace that still allows you to maintain stable levels of key biomarkers like oxygen consumption (VO2), blood lactate, and intramuscular acidity.[1]
SSmax is the underlying biological phenomenon, but we need a measurement to estimate it. There are a number of possible ways to estimate SSmax; the one you’re probably most familiar with is LT2, the second lactate threshold. LT2 is so ubiquitous that runners often just call it “threshold pace.”[2]
LT2 testing, though, requires a lactate meter and can only estimate SSmax within about ten percent or so.
Another competing standard is maximal lactate steady-state (MLSS). MLSS involves doing several 30 minute continuous runs while repeatedly measuring blood lactate levels, and is more accurate, though still underestimates SSmax a bit (and still requires a lactate meter).
A better method to estimate SSmax comes from the critical speed model: the eponymous critical speed (CS) parameter from that model is a very accurate estimate of SSmax. Critical speed testing involves doing three to five all-out races or time trials over events lasting 2–20 minutes.[3]
This parameter is sometimes called “critical velocity” or “CV pace” in training systems inspired by Tom “Tinman” Schwartz’s approach.[4]
Critical speed incorporates uncertainty around your estimated SSmax
The critical speed model has another useful property, which is that it provides statistically-based estimates of the fastest metabolically stable pace, denoted CS-, and the slowest metabolically unsustainable pace, which is denoted CS+.
Here’s the rationale behind CS- and CS+: even the critical speed model can only provide an estimate of SSmax. If you run exactly at your critical speed, there’s a 50% chance you’ll be above SSmax and a 50% chance you’ll be below it. In other words, you’re teetering on a narrow ridge, with metabolic stability on one side and metabolic instability on the other.
If you want to be sure you are running in a metabolically sustainable fashion, you should run CS-: at that speed, there’s a very high chance you’ll be below SSmax.[5]
If you want to be sure you’re firmly at a metabolically unsustainable pace (for example, to stimulate adaptations to improve VO2max), you should run CS+: at that speed, there’s a very high chance you’re above SSmax.
Frequent critical speed testing is not practical for most runners
Critical speed is almost perfect—it’s the best estimate for SSmax, and requires no special equipment, but the need for all-out time trials is a real killer.
I expect to see improvements in fitness over the course of two to four weeks when an athlete is training well, and the idea that I’m going to have them do multiple time trials every few weeks to quantify that improvement is a non-starter.
The one place where critical speed is a viable strategy is when athletes are already doing frequent races that last 2–20 minutes. That means indoor and outdoor track at the high school and college levels.
The fact that we can use track times to get critical speed means we can also approximate critical speed—and therefore SSmax—using any common track race distance.
The 5k is an ideal reference distance, since it’s long enough to be pretty “aerobically loaded,” and also common enough that runners training for anything from the mile to the marathon have a pretty good idea of what kind of 5k shape they’re in (or, failing that, can hop in a road race or park run).
As a coach, I use percentages of 5k pace as the basis for base training for almost all of my athletes, then switch to race-specific percentages (e.g. %MP) during the race-supportive and race-specific phases. So, the 5k is the ideal event for getting an estimate of critical speed.
Predicting critical speed with 5k time
Most runners are familiar with “conversion charts” that predict race performance at one distance given your performance in another. The critical speed predictions are similar. The process works like this:
- Gather a large dataset of runners who competed in events lasting ~2–20 minutes (~800m to 5k) during the same season.
- For each season, find all the runners who recorded at least one time in three events from 800m–5k during that season, and who also raced at least one 5k.
- Fit a critical speed model to that runner’s performances, then calculate CS, CS+, and CS-.
- Remove any outliers with poorly fitted critical speed models, which might be the result of an athlete doing a race as a workout, running while sick, etc.[6]
Now, if we want to predict critical speed from a runner’s 5k time, we have the data we need to build a prediction model, using 5k time as the input, and CS, CS+, and CS- as the outputs. We just need a large dataset to fit our prediction models.
A large dataset of track times: The MIAC Honor Rolls (2000–2017)
There’s a very nice dataset that suits our requirements: the Minnesota Intercollegiate Athletic Conference (MIAC) honor rolls, which span 18 years of college competition.
Compared to a truly massive dataset (e.g. all of TFRRS), the MIAC lists have a few advantages. First, all schools are at sea level, so we don’t have to worry about altitude. Second, the MIAC dataset actually covers a longer timespan than TFRRS (so far). Third, since these are all D3 schools, there is a wider and “flatter” distribution of performances—5k times range from about 14:00 to 25:00.
The seasons are relatively short (mid-January to early March for indoor track; late March to early May for outdoor track) which makes it more likely that the runner’s best 5k performance actually reflects their critical speed at the time.
Another fringe benefit is that this dataset ends before the introduction of super spikes and the disruptions from the pandemic, both of which might introduce some systematic shifts in the data.
Starting from a total of over 45,000 season best performances from over 6,000 athletes, applying the criteria above (3 different events from 800m–5k) yields 2,690 critical speed estimates from 1389 unique athletes. Filtering down to athletes who had 3 different events including a 5k brings it down to 1,394 critical speed estimates from 792 athletes (50.5% male, 49.5% female).
Here's what the data look like:
There’s an obvious caveat here, which is that by definition, everyone in this dataset is ready to run a 5k, since successfully completing one was a criteria for inclusion in the dataset.
There are a ton of interesting insights in this dataset, including how athletes progress throughout their career and how performances have evolved over time, but I’ll leave that topic for another article.
The real question we’re after is how well can you predict critical speed or CV from your 5k time? And the answer is—pretty well.
Threshold, critical speed / CV, and VO2max pace as percentages of 5k pace
The fastest and easiest method is to just express CS-, CS, and CS+ as percentages of 5k pace then look at the distribution across individuals. Here’s what that looks like:
Notice how there’s a decent amount of variability, even as a percentage of 5k pace. That variability is the result of runners being more “fast-twitch” or “slow-twitch,” i.e. oriented towards shorter versus longer events.[7]
We actually don’t want to just take the average of these distributions. Instead, drawing inspiration from CS- and CS+, we want to find the paces that result in a very high chance of being on the correct side of SSmax.
Threshold pace: 90% 5k pace (or slower)
If you want a very high chance of being at a metabolically stable pace—which is the whole idea behind threshold workouts—you should run at a pace that would result in almost all runners being at or below CS-.
In our data, the 10th percentile value (so, correct for 9/10 runners in terms of creating the desired metabolic effect) is 90.3% 5k pace. Rounding off and leaning conservative, we can confidently say that threshold pace is 90% 5k pace or slower.
While a reasonable uncertainty range (10th/90th percentiles) spans 90.3% to 95.4% 5k pace, you don't know where you are in this range, so to get the desired effect—a metabolic steady-state—you should run on the slow end of the range.
You might run slower, e.g. 88% 5k pace, for “sub-threshold” repeats, or a fast continuous run at 85% 5k pace. Both would be expected to be metabolically stable paces for virtually all runners.
Critical speed / CV pace: 96% 5k pace
For runners who are trying to ride the line right at critical speed / CV pace, it does make sense to take the median. The 50th percentile value for CS in our dataset comes out to 95.6% 5k pace. So, a good estimate of critical speed / CV pace is 96% 5k pace.
The 10th/90th percentiles are 94.2–96.9% 5k pace, but since you don't know where you are in that range, in this case you should just take a value right in the middle.
VO2max / metabolically unsustainable paces: 100% 5k pace (or faster)
When running workouts that target VO2max, you want the slowest speed where there's a very high chance you'll be in a metabolically unsustainable situation. That pace (CS+ in the critical speed model) works out to 100.0% 5k pace. So, a good estimate of VO2max pace is 100% 5k pace.
Faster paces will also work, in the sense of producing a metabolically unsustainable situation inside your body. However, you won’t be able to rack up as much overall workout volume at faster paces.
Notably, using 100% 5k pace will give you a VO2max pace that is is slower than most calculators would predict for “vVO2max,” but vVO2max is a misleading concept anyways. Any speed faster than your steady-state max (SSmax) will eventually bring you to VO2max; it’s merely a question of how long it takes.
Again, the full 10th to 90th percentile range is 96.1–100%, but since you don't know where you are within this range, it makes sense to run on the upper end to be sure you are getting the desired outcome: a metabolically unsustainable state.
A sneak preview: Improving predictions with a regression model
Our 5k pace percentages work pretty well, but we can get slightly more accurate predictions by fitting an explicit regression model that predicts critical speed given 5k pace. The results are a lot cleaner when both critical speed and 5k pace (well, 5k speed) are converted to meters per second.
Here’s what the results look like for CS+, CS, and CS-:
Now, this is just a preview of another project I'm working on with the same project: an app to calculate threshold pace, CV pace / critical speed, and VO2max pace from any race distance.
It's a bit more complicated than the analysis here, but I'm making good progress on it and I'll post it as soon as it's finished (join my email list if you want to be among the first to find out!).
📱 UPDATE: Calculator is done! Check it out here.
Recap
The critical speed model is a great way to estimate SSmax. Unfortunately, doing time trials or races all the time just isn’t workable for real-world training.
Fortunately, you can use 5k pace as a reasonably accurate estimate for critical speed, and therefore get all of the relevant training paces that come out of the critical speed model: threshold pace, CV pace, and VO2max pace (or CS-, CS, and CS+ if you prefer the technical terms.
The following guidelines work quite well:
- Threshold workouts: 90% 5k pace
- CV workouts: 96% 5k pace
- VO2max workouts: 100% 5k pace
Remember that can calculate these paces easily with my pace percentage calculator.
Learn more about physiology-based training
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Footnotes
[1] Technically there is a narrow window where it may be possible to sustain a steady-state with a stable VO2 but gradually increasing blood lactate levels. It’s super interesting and nobody knows why it happens! Check out my article on SSmax for more on this strange phenomenon. Trying to replicate and understand this phenomenon would make a great topic for an exercise science PhD or Master’s thesis.
[2] Confusingly, when physiologists say “lactate threshold” they typically mean LT1, the first lactate threshold.
[3] Some physiologists prefer to use time to exhaustion at a constant speed (on a treadmill), because it ensures that the metabolic demand of the exercise is constant. I think they also like it because they can do it in their lab, as most labs do not have an indoor track suitable for time trialing. I don’t like time to exhaustion rests because they are highly “motivationally loaded,” and show much greater variability from day to day compared with a time trial over a set distance.
[4] Physiologists switched to calling it “critical speed” a while back after being hounded by biomechanists who insisted that a “velocity” must have both a magnitude and a direction.
[5] In the critical speed literature the usual method is to do 1.96± the standard error of the estimated CS, which in theory gives a 95% confidence interval around CS (i.e. CS+ / CS- are the upper/lower 95% CIs, but technically it’s more complicated than that—it is not quite correct to use normal distribution z-scores for linear regression models with only 3–5 data points, but when you do the “correct” thing and use t-scores you get comically wide confidence intervals. The right approach would probably be to use Bayesian methods, but nobody has published a paper on that yet! For this analysis I used the Z-scores for 90% confidence intervals, partly because our model will be “better” than expected: we use the best performances from an athlete each season, as opposed to all of them.
[6] The literature on critical speed offers some guidelines on coefficient of variation relative to model coefficients to determine whether a particular critical speed model is a “good fit”
[7] I tend to shy away from the terms “fast-twitch runner” and “slow-twitch runner” to refer to a runner because I suspect that muscle fiber composition only explains part of why some runners tend to do better or worse over longer distances.
[8] By “correct” here I mean “correctly predicting which side of SSmax you’ll be on.”
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Thank you John for such great writeup.
I have a question regarding the VO2 Max training. Here's a brief intro of my background.
26M, zero athletic, xc and track experience back in school and just start running one year ago. My 5k and HM pb is 17:26 and 1:18:02, which seems to indicate that I underperform my 5k(hmp = 96% 5kp). I want to be a well-round runner, but whenever I do those classic VO2 Max workout on track such as 12 x 400m, 5 x 1000 @3-5k pace, I felt trashed and slower to recover comparing to workout like 10 x 1k @15kP or 5 x 2k @HMP. I am afraid of doing more 5k specific training will leads to bad quality on other important sessions. I started thinking of replacing those speed session with hill workout but haven't put in practice.
So my question is
1. Does doing 200m hill repeat @5k effort reduces the mechanical load on my leg while eliciting similar VO2 Max benefit
2. Do I need to care about the exact pace when doing hill repeat? Or just need to focus on the effort considering the incline rate might differ a lot.
Yes, I actually think this is a great application of hill repeats - you can get that VO2max-type stimulus with, probably, less damage to your legs vs. doing a session of the same intensity on the track. A few other "aerobic power" sessions you can consider incorporating:
(1) longer reps at 8k-10k pace through hills, e.g. 4 x 2 km at 8k-10k pace w/ 3-4min rest through cross-country terrain (rolling hills, maybe soft surfaces but not super rugged trails)
(2) 4-6 km continuous through rolling hills or cross-country terrain, or on a treadmill ascending at a steady 3-5% grade, at 95-98% of 5k pace (e.g. 4k at 98% or 6k at 95%) - can use GAP to adjust if on treadmill
(3) Progression runs of 8-10 km where you start easy and work down to ~15k pace by about 2k to go, then push the pace significantly faster for the last 1-2 km, with the last couple minutes being "all out minus a kick," i.e. getting to the finish as if you are ramping up for your final 400m kick in a race.
All of these put you in a metabolically unsustainable situation for a decent amount of time, but are not as hard on your body as traditional hard intervals on the track.
For hills, unless you're on a treadmill I usually recommend just going by effort, since it's really hard to know (especially for short hills) exactly how steep the hill is!
This is really interesting! I’ve had trouble in the past determining some of these speeds based on my own race times, since I’m pretty slow (just set a sub-36 minute 5k PB at the turkey trot). For CV, for example, people/calculators will say it’s “30–40 minute race pace, or 8k/10k pace,” which is obviously 5k pace for me, and it’s never clear which model I should follow. Same with LT2 or VO2Max, as you can imagine. So I’m curious. How accurate do you think your calculation is far outside of the 14-25min 5k range? Should I stick with percentages of 5k pace or do some napkin math with an estimated 25min race effort?
If you're attempting to predict threshold pace or CV pace, I think the percentages of 5k pace will probably start falling apart above ~28-30 minutes or so. I do have a more sophisticated calculator in the works that should generalize better to slower (and faster) 5k times though! And even if 90% 5k pace is no longer a good predictor of threshold pace at 36:00 in the 5k, that doesn't mean that 90% 5k pace isn't a useful pace to run in training. I have 10k runners do long fast runs at 90% 10k pace all the time, so "90% of race pace for a ~36 minute race" is clearly a useful pace to train at!
Hi John,
A very interesting read - as per usual.
I've usually used VDOT tables and/or Tinman's calculator for training paces. I've read elsewhere that these tend to be quite aggressive, but hadn't realised quite how aggressive after comparing your percentages above to what the calculators (especially Jack Daniels' one) are producing.
For example, a recent 19min 5K puts my Tinman Threshold pace at 4:04-4:11/k and my Jack Daniels T Pace at 4:04/k. 90% of that race pace puts me at an estimated 4:11/k Threshold.
Obviously at the lower end of Tinman's number and actually quite a way off Jack Daniels' one (even my HM pace according to his calculator is 4:08/k - superhuman if going by the 5K*90% method you outline.
I like to err towards the "safe" side of things in training so have no qualms slowing down. Further I believe the method you outline above is in some ways much more transparent than the calculators.
However it has got me thinking about the tables and paces I, and I'm sure plenty of others, have been using.
Generally, what's your view on the calculators (especially VDOT) in terms of estimating race and training paces? Do they have a place in modern training or are they outdated and perhaps even risky given their over-aggressive recommendations?
Thanks! I think traditional calculators have a place in training, though I also find that they tend to be "aggressive" and are not quite clear in what they are trying to predict, and what data they used to formulate the model. I'm pretty sure that most traditional calculators predict AVERAGE values, for example the AVERAGE threshold pace across a group of 19:00 5k runners...but that means you'll get a value that is too fast for 50% of 19:00 5k runners! If the whole point of running threshold is to be at a metabolic steady-state, then you definitely want more than 50% certainty that you'll be below your critical speed. So, I think at the very least if you're trying to get a physiologically reliable result out of a workout you do need a more modern approach. Calculators can still be handy if you need a rough estimate of, say, 15k to 10k race performance conversions -- though even then, I'm often finding myself wishing that those had uncertainty estimates too. If someone runs 19:00 for 5k, I'd prefer a calculator that says "10k: 39:55, range 39:30-40:25" vs. one that just spits out "39:55." I've got building one of those on my to-do list though!
Hey John! Thanks for the analysis, great stuff!
I work with a lot of HS athletes and have done the 20min time trial along with a 3min time trial to predict CS but (like you've mentioned) taking time away from training to do this, is less than ideal. It's also hard to get some HS athletes to go all out for 20min or getting 30 of them to have a decent enough day to make confident predictions of their CS.
In saying that, I was wondering if you think it's too much of a stretch to use 3200m times as a predictor of CS? Our boys team races 5k for XC so I have a decent data set (although making CS predictions from XC isn't my favorite) Our girls team, on the other hand, races 2mi so it would be nice to be able to make accurate predictions from their race results.
The percentage ranges that seem close to me are as follows. What do you think?:
Threshold - 84-86%
CS - 90-91%
VO2 max/5kpace - 95-96%
Glad you found it useful! I think those numbers seem pretty reasonable, and you'll definitely enjoy my next project...I'm working on a calculator that can predict threshold/cs/vo2max paces for any distance from 800m to 10k! I'm hoping that will be done before the new year.
You're right! I would enjoy that haha. Currently, I use a self created app for CS and D' that uses the standard 2-5 parameter model.
I'm curious about how you plan to mitigate some of the issues that arise from single parameter models? And if you think accurate predictions can be made for both CS and D' based on a single race result.
If you don't have the time to go in to all of that right now, I'm sure I can read all about it once you complete the project and write up.
Once again, thanks for all you do!