How your percentile is calculated

Every lift is compared only with the same exercise, the same gender, and the same weight class. We call that combination a group. Your weight class is set from the bodyweight on your profile.

Each lift is logged for your right or left arm. The two arms have separate leaderboards, and each arm keeps its own current lift per exercise. Both arms start from the same chart; the live-data part of the blend uses only lifts from the same arm, so left and right standards separate as lifts are logged. Two-handed exercises (such as the EZ bar curl) aren't left or right: they're logged as both arms and ranked on their own.

A new group has few lifts, so a published strength chart sets what normal looks like. Each lift logged in the group shifts the result toward real data. At 30 lifts, the chart and the logged lifts count equally. Past that, logged lifts count more.

Your rank is the highest one your percentile reaches. The percentile is the share of your group you out-lift.

Beginner's chart column sits at the 5th percentile, but everyone below Novice counts as Beginner. Lifts far above normal (z above 3, about the top 0.13%) are held for review before they count, so the very top of Anomaly appears once an admin approves them.

For each exercise we store a chart with rows by bodyweight: 155, 175, 200, 220, 240, 265 and 310+ lb for the armwrestling lifts, and every 10 lb from 110 to 310 lb for the curls (shown below at the same bodyweights as the others). Each row lists five ranks, Beginner to Elite, each at a fixed percentile (see Ranks above). Anomaly isn't on any chart: it comes from the same bell curve as your percentile (step 4), so it sharpens as lifts are logged.

Everyone in a weight class shares one standard, like a weigh-in: a 96 kg and a 105 kg Light Heavyweight are ranked against the same line, and so are a 300 lb and a 350 lb Super Heavyweight. That line is read at the class's weigh-in limit (Light Heavyweight at 105 kg); the open classes use 125 kg for men and 90 kg for women.

A class limit rarely lands exactly on a chart row, so we take the two nearest rows and blend them in a straight line. Above a chart's last row, that row is used.

Below a chart's first row, standards are estimated (under 155 lb for the armwrestling lifts, under 110 lb for the curls). We scale the first row down by bodyweight. How fast it scales comes from the chart itself: we fit strength ∝ bodyweight^k across all of that exercise's rows. Every rank is scaled by the same factor, so the ranks stay in order.

Men's light classes have a floor on the armwrestling lifts (not the curls). The charts drop off quickly below about 170 lb, so each rank's standard is at least a share of the Welterweight standard: 90% at Featherweight, 95% at Lightweight, rising smoothly to 100% at about 179 lb. The floor only raises standards, never lowers them.

Those five numbers are then turned into a bell curve. We draw the straight line that best fits "rank value vs. z-score" (least squares), and that line gives us the chart's average (μ_standard) and spread (σ_standard):

value ≈ μ_standard + σ_standard · z

μ_standard = (B + N + I + A + E) / 5
σ_standard = Σ zᵢ·valueᵢ / Σ zᵢ²

We take every non-flagged lift in your group and compute its average (μ_actual) and standard deviation (σ_actual). n is the number of those lifts. A standard deviation needs at least two lifts, so with fewer than two the live σ is left out.

The two are combined as a weighted average. The chart counts as if it were n₀ = 30 lifters, and the real data counts as n lifters:

μ_blended = (n₀ · μ_standard + n · μ_actual) / (n₀ + n)
σ_blended = (n₀ · σ_standard + n · σ_actual) / (n₀ + n)

n₀ = 30

Your lift is placed on the blended bell curve. Φ is the standard normal cumulative distribution function. It gives the share of the curve that falls below your z-score:

z = (weight_lifted − μ_blended) / σ_blended

percentile = Φ(z) × 100

A percentile of 90 means your lift beats about 90% of its group: the top 10%. Your rank is the highest rank your percentile reaches.

A new lift is flagged for review if either is true:

• it reaches Anomaly, the top 1% of its group (a z-score of 2.33 or more against the group's blended curve), or
• the weight lifted is more than 5× bodyweight.

Flagged lifts need proof (a video link, notes, or a video emailed to us) and are excluded from percentiles and leaderboards until an admin reviews them. Your own flagged lifts show on My Results as "Under review".

armstats uses the East vs West (EVW) weight classes. Your class comes from the bodyweight on your profile.