Gear
Wide tape, narrow tape
A wide tape averages over a tapering shaft and lies less flat around a curve; a narrow tape follows the site more precisely and is the better girth instrument.
A tape's width is not a cosmetic detail. A wide tape covers more of the shaft's length while it is wrapped around a single girth site, and because the shaft is not a uniform cylinder, that width can quietly average two different circumferences into one number.
Why width interacts with taper
Girth is defined at a specific site, conventionally the midpoint of the shaft. A shaft is rarely a perfect cylinder over any real span - it commonly tapers or bulges somewhat along its length - which means the circumference a centimetre above the midpoint and a centimetre below it can genuinely differ. A narrow tape, laid flat at the midpoint, reads close to the true circumference at that specific point. A wide tape covering, say, a centimetre or more of shaft length is not reading one circumference; it is lying across a small range of them, and the number it gives is some blend of the site you intended and the tissue immediately above and below it.
The direction of the error depends on which way the shaft tapers at that point, which is exactly the problem - it is not a consistent bias you can correct for, because it depends on individual anatomy.
Curvature is the second reason
A wide tape also lies less flat when the surface it is wrapping is not perfectly straight along the tape's own width, which is the case anywhere the shaft has any natural curve. A narrow tape conforms to a shorter span of surface and sits flatter against it, tracing the actual circumference more faithfully. A wide tape bridges over small irregularities the way a wide plank bridges over a dip in the ground, and the bridging shows up as a slightly different reading than a tape that follows the surface more closely.
What "narrow" means in practice
Sewing and tailor's tapes commonly run from about 6 mm to 13 mm wide, and the narrower end of that range is the better choice here, for the reasons above. This is a small, second-order effect next to the larger ones - technique, site selection, and tension dominate the overall error, as the instrument comparison against technique already establishes - but among tapes that are otherwise similar, narrower is the correct default rather than a matter of preference. It is worth choosing deliberately if you are buying a tape specifically for this, rather than reaching for whatever wide dressmaking tape happens to be in a drawer.
A quick way to see the effect yourself
Wrap a wide tape around a tapered household object, such as a wine bottle near its shoulder, and take a reading. Then wrap a narrow tape or a folded strip of paper at exactly the same point and compare. On a strongly tapered object the two readings can differ by a visible amount, because the wide tape is genuinely spanning a range of different circumferences while the narrow one is not; on a near-cylindrical object the two will agree closely, because there is nothing for the width to average over. This is the same reason comparing two instruments on one object before using either on yourself is worth the two minutes it takes - it isolates what the instrument itself is doing from what your technique is doing. It also demonstrates why the effect is real rather than theoretical: it takes two minutes with objects already in a kitchen to see a wide tape and a narrow tape disagree on the same tapered surface, which is a more convincing check than taking the claim on faith.
What this does not replace
Tape width does not substitute for correct site selection. A narrow tape wrapped at the wrong point on the shaft is still measuring the wrong thing, precisely; where the midpoint actually is has to be right first, and a narrow tape only makes that correct site selection pay off more fully once it is.
None of this bears on a rating from a photograph, where no tape of any width is involved. Rate Cock scores an image rather than wrapping anything, and the same is true of a photo-based tool, a human judge's impression, and an AI model's read of a picture - a wide or narrow tape is not a variable in any of those, because none of them touches the shaft at all.