Every zone scheme is a set of percentages of some anchor, and the anchor is the whole argument. One runner, three published schemes: the ceiling of easy aerobic work lands at 131, 141 or 150 bpm. And if the anchor is 220 minus age, a two-standard-deviation error moves one boundary by 30 bpm.
50/11 means nothing until you attach a wheel. Gear inches and metres of development, derived and converted, a full table for a real 12-speed drivetrain, and why the gear step between two sprockets decides whether you can hold a cadence.
xG is the fitted probability that a shot with a given set of features becomes a goal — a model output, not an observation. A worked match, the binomial arithmetic that says one game is far too few shots, and the limits nobody quotes.
French, YDS, UIAA, V-scale and Font are ordinal scales with no underlying unit. A conversion table is a negotiated alignment between climbing communities — and published tables disagree by half a grade at the top and by four letter-grades at the bottom of the boulder scales.
A strike scores ten plus your next two balls, a spare ten plus your next one. That bonus chain is the entire game — it is why a perfect game is 300 and why alternating strikes and spares scores 200, not the 250 almost everyone guesses.
Running pace is time per kilometre or mile. Here's how to work it out from any run, convert between units, and use it to pace a race without blowing up.
ERA measures what happened, FIP measures only what the pitcher controls without his fielders, WHIP measures traffic allowed. Two pitchers can swap places entirely between them — and the gap between ERA and FIP is a forecast, not a verdict.
OPS adds two fractions with different denominators, which as arithmetic is indefensible. It survives because it tracks run scoring far better than batting average and costs nothing to compute — but it underpays on-base ability, and OPS+ does not fix that.
Field goal percentage counts a three-pointer and a layup as the same event and ignores free throws entirely. eFG% fixes the first problem, TS% fixes both — and the ranking of three players changes at every step.
Turning jump height into take-off velocity is exact physics. Turning it into watts is a regression fitted on somebody else's athletes — and the three common formulas disagree by thousands of watts on the same jump.
BMI weighs you and divides by your height squared. It cannot tell muscle from fat, which is why lean athletes get classed overweight. FFMI removes the fat first — and inherits every error in the body-fat estimate it is built on.
Epley, Brzycki, Lombardi, O'Conner and Wathan are five curves through the same data. They agree within a few pounds at low reps and disagree by a quarter at fifteen — which is exactly how you know when an estimate is worth having.
SWOLF adds seconds to strokes, which is dimensionally indefensible and useful anyway. The catch is what it rewards: it prices one stroke at exactly one second, so it can improve while you get slower — and it is not comparable between pools of different lengths.
Rolling resistance grows with speed, air resistance grows with its square, and power grows with its cube. Work the equation and the crossover falls at 10 mph — after which almost everything you pay for is air, and a headwind costs more than the same tailwind returns.
Naismith's 1892 rule times a route in two lines of arithmetic. It also ignores descent completely and assumes a fit walker with no pack. Here is the rule, Langmuir's fix, and Tobler's continuous alternative — whose fastest speed is on a downhill, not on the flat.
Maximal aerobic speed is the slowest speed at which you reach your VO2max. Because it is a speed and not a heart rate, every training zone becomes a percentage of something you can measure on a track — and the whole week falls out of one test.
Heart rate zones split your effort into five bands, from easy to all-out. Here's what each does, how to estimate your zones, and how to train with them.