How to Fix a Poor-Fit Load-Velocity Regression When R² Is Low

You pull up the session's load-velocity chart and the dots don't line up into anything like a line — they scatter across the plot like buckshot. The software still returns an R² value and spits out a 1RM estimate anyway, so you use the number because it has to come from somewhere. Then the athlete tells you the prescribed warm-up felt twenty kilos off, and now you're stuck deciding whether the sensor is broken, the athlete had an off day, or the session was a waste.

None of those, usually. A poor-fit load-velocity regression almost always traces back to one of three fixable problems: the load span was too narrow, too few valid trials were collected (or the wrong rep got picked from each set), or one or two outliers are dragging the line off course. This guide walks through how to tell which one is wrecking your R², with the numbers and rebuild protocol to get back to a regression you can actually use.

What a Poor-Fit Regression Actually Looks Like

In a properly executed load-velocity test on a bilateral barbell lift, García-Ramos, Pestaña-Melero, Pérez-Castilla, Rojas, & Haff (2018, International Journal of Sports Physiology and Performance, 13(3), 326–331) tested 30 trained men across four bench press variants and found linear r² values above .96 for pooled group data and above .98 for individual regressions. That's the benchmark. If your athlete's individual regression comes back at r² = 0.85, or worse, 0.71, something in the data collection broke down — it isn't ordinary individual variation.

A poor fit tends to show up in one of three patterns. The scatter pattern: points that don't approximate a line at any load, usually caused by mixed submaximal effort across the session. The bent-line pattern: points that form two distinct slopes joined at a break, usually caused by a load span that crossed from one lifting strategy to another — ballistic throws at light loads mixed with grinding reps at heavy loads. The single-outlier pattern: five clean points and one that sits well off the line, almost always one bad rep rather than a systemic problem.

Knowing which pattern you're looking at tells you which fix to reach for first.

The Three Causes Behind a Low R²

Every poor-fit regression falls into one of three buckets, and they stack — a single session can carry two or three at once, which is why the fix works better as a checklist than a single silver bullet.

Load span problems and trial count problems often travel together, because a coach short on time both limits the number of test loads and clusters them around the athlete's usual training zone. Outliers are a separate, session-specific issue — they can show up even inside an otherwise well-designed test.

Fix 1: Widen the Load Span

The single most common cause of a poor fit is a load span that doesn't actually span anything. A coach testing three loads at 70%, 78%, and 85% 1RM has produced three points crammed into a 15-percentage-point window — and any measurement noise in bar velocity (IMU and linear-position-transducer sensors carry roughly ±0.02–0.05 m/s of inherent noise) gets massively amplified once that narrow line is extrapolated out to V0 or the minimum velocity threshold.

Cuevas-Aburto, Ulloa-Díaz, Barboza-González, Chirosa-Ríos, & García-Ramos (2018, PeerJ, 6:e5835) tested this directly on the bench press. Comparing a 4-load protocol (29–59 kg, a narrow high-load span) against a 6-load protocol that added two very light loads (roughly 1 kg and 8 kg), the between-session coefficient of variation for the regression slope dropped from 14.5% to 6.72% — more than a twofold improvement — and the CV for V0 dropped from 10.4% to 5.05%. Widening the tested range, not just adding more points at the same loads, stabilized the line. Their stated limitation: even the wide-span version started at 29 kg, heavier than the 17–20 kg minimums used elsewhere, so the true benefit of going lighter may be larger than what they measured.

The practical target: span at least 45–50 percentage points of 1RM, anchored by one point at or below 30% 1RM and one at or above 85%. If your training zone is 70–90% 1RM, that means deliberately adding lighter loads you'd never program in a real session — an empty bar or a bar plus small plates — purely to stabilize the line.

Fix 2: Fix Trial Count and Rep Selection

Four data points is the accepted floor for a linear regression; five to seven is the practical target. But the more common error isn't the number of loads tested — it's which rep at each load actually gets fed into the regression.

Inside a fatiguing set, velocity drops rep to rep. If a coach records the mean velocity across a 5-rep set at 60% 1RM instead of the single best rep, that data point blends fresh and fatigued output instead of reflecting the maximal-intent velocity the regression assumes. The result sits below where it should fall on the line — statistically indistinguishable from an outlier, except it's a methodology error repeated at every load in the session.

Pestaña-Melero, Haff, Rojas, Pérez-Castilla, & García-Ramos (2018, Journal of Applied Biomechanics, 34(3), 184–190) compared linear and polynomial regression models for predicting %1RM from velocity and found intraclass correlation coefficients of 0.73–0.78 for the velocity attained at a given %1RM across individuals — moderate-to-high but clearly athlete-specific. Their conclusion: pooled or population-average equations carry real error for any single athlete, and linear models performed comparably to polynomial ones while staying simpler to compute. The limitation they flagged: the comparison used bench press data only, so the linear-versus-polynomial conclusion doesn't automatically transfer to lifts with more curvilinear relationships, like some Olympic lift variants.

The practical fix: use 1–3 reps per load, not high-rep sets, and always extract the single fastest rep from each load — never the set average.

Fix 3: Find and Remove Outliers

Once span and trial count are solid, a single bad rep is usually what's left. Common causes: a spotter braced the bar on a near-maximal attempt, the athlete's grip shifted mid-rep, the bar path drifted off the sensor's axis, or the athlete simply didn't commit to maximal intent on that rep — most often the very first warm-up set, before they've mentally locked in.

A worked example from a pattern that shows up often: six loads tested at 30%, 45%, 60%, 70%, 80%, and 90% 1RM produced MCVs of 1.32, 1.10, 0.95, 0.63, 0.55, and 0.30 m/s. The initial linear fit returned r² = 0.71 — poor by any standard. Plotting the residuals showed the 70% point sitting 0.15 m/s below where the line predicted (around 0.78 m/s based on the surrounding points); video review confirmed a spotter had braced the bar mid-rep. Removing that one point and refitting the remaining five produced r² = 0.97.

The residual threshold worth using as a cutoff: any point more than 0.08 m/s off the fitted line is a candidate for removal, provided you can identify a plausible reason — technical break, assistance, distraction — rather than removing it purely because it improves the number. Never drop a point solely to chase a higher r². If you can't explain why a rep was invalid, keep it in and add another test load nearby instead.

The Full Rebuild Protocol, Step by Step

1. Select 6 target loads spanning at least 45–50 percentage points of 1RM: roughly 20–30%, 40%, 55%, 70%, 80%, and 90%. Include the sub-30% anchor even though you'd never train there — it stabilizes the low-load end of the line.
2. Warm up normally, then test each load with 1–3 reps, resting 2–4 minutes between loads (longer as load increases).
3. Record every rep's MCV and take the single fastest rep at each load as that load's data point — discard the rest of the set.
4. Fit the linear regression and calculate r². If it's below 0.95, calculate the residual for every point.
5. Flag any point more than 0.08 m/s off the fitted line. Review video or session notes for a plausible cause before removing it.
6. Refit with the remaining points. You need a minimum of 4 valid points after exclusions — below that, retest the missing load rather than accepting a thin regression.
7. Confirm r² ≥ 0.95 before trusting the profile for daily 1RM estimation.

Budget 20–25 minutes for the full rebuild, including warm-up — roughly the same time cost as a single heavy 1RM attempt, with none of the fatigue penalty.

How to Confirm the Fix Actually Worked

A high r² alone isn't proof the profile is trustworthy — it's possible to inflate r² by over-trimming points until only the cleanest three remain, which technically fits a line through almost anything. Check three things together before signing off:

• r² of 0.95 or higher, calculated on at least 4 remaining valid points, not fewer.
• V0 within the published normative range for the exercise — for the back squat, roughly 1.2–1.8 m/s; a V0 wildly outside that range even with a high r² suggests a sensor or setup error, not just a data-cleaning issue.
• Estimated 1RM from the line matches the athlete's known training numbers within about 5%. If the regression says 165 kg and the athlete has comfortably worked with 155 kg for triples recently, something is still off.

If all three check out, the profile is ready for daily 1RM estimation. Rebuild it on the same schedule as any load-velocity profile — every 6–8 weeks, or immediately after a session where the daily estimate and the athlete's subjective effort disagree by more than 5%.