NTILE(n) deals rows into n buckets as evenly as it can — when counts do not divide, the leading buckets get the extra rows, so labels sit on unequal populations.

NTILE answers 'deal these rows into n hands' — a row-count operation, not a value-distribution one. Two consequences surprise: bucket sizes differ by one (extra rows go to the leading buckets — misleading when bucket 1's average is compared to bucket 3's on different denominators), and equal values can land in different buckets because the deal cuts by position. For value thresholds, use percentiles or explicit range buckets.

SELECT
  w,
  NTILE (3) OVER (
    ORDER BY
      w,
      id
  ) AS bucket
FROM
  castings
ORDER BY
  id;

SELECT
  w,
  CASE
    WHEN w < 40 THEN 1
    WHEN w < 70 THEN 2
    ELSE 3
  END AS bucket
FROM
  castings
ORDER BY
  id;

NTILE put the two equal 30-weight castings in different buckets — it deals rows by position, not value, and over 7 rows the buckets are 3·2·2; a value-range CASE keeps equal weights together.

NTILE for row-splits (sizes acknowledged); PERCENT_RANK/percentiles or CASE ranges for value semantics; a deterministic ORDER BY under all.