Brief thoughts: Calculating percentages of race pace

A few days ago, I received an email from my high school coach asking me about the "correct" way to calculate percentages of a given pace.  This is a question that I am asked fairly frequently, and the answer has a few interesting angles, so I have decided to make a post about the details.

Many different training programs are predicated on doing workouts, easy runs, and interval sessions at various percentages of a particular pace, whether this is race pace or threshold pace or VO2 max pace.  But if you ask a group of people how to calculate, say, 85% of 5:00 mile pace, you'll get two different answers.  The first camp will say, "Simple, just multiply 5:00 per mile by  1.15, which gives you 5:45 per mile."  The second will say, "No, you have to divide 5:00 by 0.85, which gives you 5:53."  Who is correct?

In some sense, they are both correct.  To break down what each of these particular strategies actually mean, mathematically speaking, it helps to compare and contrast the result for a variety of percentages.  So, sticking with our example of 5:00 mile pace, let's do the math on a few various paces, both faster and slower than 5min-miles.  To make things simple, let's call one variant—85% = 5 x 1.15— the "multiplication method" and the other—85% = 5 / 0.85— the "division method."

Injury Series: Plantar fasciitis in runners as a degenerative overuse injury

Plantar fasciitis is a vexing, persistent, and fairly common injury to the plantar fascia, the thick, fibrous band that runs along the bottom of your foot.  While it accounts for around  8% of running injuries,¹ it is also quite common in the general population.²  Unlike many running injuries, it is slightly biased towards men; one study found that, of 158 runners diagnosed with plantar fasciitis at a sports medicine clinic, 54% were men.¹  Plantar fasciitis is by far the most common cause of "heel pain," and a quick internet search for that term will turn up a slew of podiatry websites which specialize in treating plantar fasciitis, both in athletes and in sedentary people.  While not technically correct, plantar fasciitis is often referred to as having "heel spurs."  Ironically, despite its commonality in both active and inactive people, and despite the fact that it makes up a huge percentage of the patients at podiatry offices across the country, plantar fasciitis is a poorly-understood injury with no solid slam-dunk treatment or even a firm theoretical underpinning of the mechanism of injury.  Regardless, we'll dive into the wealth of research on it to learn what we can and inform our treatment and prevention approach. 

Terminology

As is often the case, there are some terms we need to clarify before we go into the bulk of the article.  Plantar fasciitis is another unfortunately named injury, as the -itis suffix implies an inflammatory cause, which we'll soon see is not the case.  The plantar fascia is also sometimes referred to as the plantar aponeurosis; medically speaking, an aponeurosis is a flat band of tissue that closely resembles a tendon and connects either bone or muscle to each other, while a fascia is a band of connective tissue that encapsulates muscles.  Because "plantar fascia" is the more common term, and because the injury is still most often referred to as "plantar fasciitis," those are the terms I'll be using in this article.  While "heel pain" and "heel spurs" are commonly used to refer to plantar fasciitis, neither are correct: while it is indeed the most common cause of heel pain, there are other injuries, like a calcaneal stress fracture, that can cause pain at the heel.  And a heel spur—a small bony growth extending from the heel bone along the plantar fascia—is neither a definitive cause nor indicator of plantar fasciitis.³

Anatomy and function

The plantar fascia as a whole is comprised of several bands of connective tissue that run along the sole of the foot, anchoring the metatarsal heads to the calcaneus (the heel bone).  While there are several separate bands, the most important is the central aponeurtoic band.  It runs from the medial side of the heelbone, fanning out as it attaches to each of the five metatarsal heads.  At the heel, the center band of the plantar fascia is thick and has a triangular cross-section.  The central band handles the bulk of the strain on the plantar fascia, and as such is the part most susceptible to injury.  Some sources describe the entire collection of plantar bands as the "plantar fascia," while others refer to it as the "plantar aponeurosis" and the central band as the "plantar fascia."

On a microscopic level, the plantar fascia is much like other tendons and ligaments of the body: small, wavy proteins called collagen fibers make up the structure of the fascia, giving it strength and stiffness.  The plantar fascia is stronger and stiffer than the small tendons of the body, though it is weaker and more stretchy than the patellar or Achilles tendons, which handle high loads at the knee and ankle, respectively.  With a stiffness of about 200 N/mm,⁴ the plantar fascia isn't something you could "stretch" like a rubber band, but it's also springy enough to store and release energy elastically during the gait cycle.⁵

Microscopic image of a healthy plantar fascia.  From Lemont et al.

 The plantar fascia's main function seems to be supporting the arch of the foot during standing, walking, and running.  It has been likened to a "tie-bar" which prevents the arch from flattening, though it is not the only contributor to arch stiffness.  Even when the plantar fascia is severed, the arch retains 65% of its stiffness in static stance—the rest of the structural integrity being associated with the joint capsules and bone geometry of the foot.^{6, 7}  

The plantar fascia acts like a tie bar, helping to support the arch of the foot when it is loaded.