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BLEU is a reference-based metric for evaluating machine translation. It combines modified n-gram precision at several lengths using a geometric mean, then applies a brevity penalty to discourage very short outputs. Kishore Papineni and colleagues introduced it as a way to make repeated translation evaluation less costly than repeatedly collecting human judgments.^[ref]

For each candidate n-gram, count matches only up to its maximum occurrence count in a single reference. Sum these clipped matches across the corpus and divide by the total number of candidate n-grams of that length to obtain $p_n$. This clipping prevents repeated use of a common word from earning unlimited matches. Corpus aggregation uses counts, rather than simply averaging independently calculated sentence scores.^[ref]

With candidate length $c$, effective reference length $r$ and weights summing to one,The original baseline uses $N=4$ and $w_n=1/4$. Effective reference length sums the closest reference sentence lengths for the candidates.^[ref]

For a synthetic one-pair calculation, take reference the cat is on the mat and candidate the cat is on mat. The clipped precisions areHere $c=5$, $r=6$ and the precision product is $1/4$, givingThis is about $57.893$ on a scale multiplied by one hundred; it is not $57.893\%$ translation accuracy.

The unsmoothed score becomes zero when a required precision is zero. Short sentences make this particularly conspicuous, while legitimate rephrasing can reduce overlap. State tokenization, casing, reference set, smoothing and scale when comparing results. The example illustrates the arithmetic; the paper emphasizes corpus-level use rather than treating each sentence score as an independent human-quality judgment.^[ref]

By Kishore Papineni.

ACL 2002, pp.311–318; DOI10.3115/1073083.1073135. Section2.1 clipped n-gram precision, section2.1.1 corpus aggregation, sections2.2.2–2.3 brevity penalty and four-order geometric combination. Original paper title and byline verified; other authors are Salim Roukos, Todd Ward and Wei-Jing Zhu. Prepared example counts are independently derived.

Kishore Papineni is a machine translation researcher who coauthored the 2002 paper introducing BLEU. Its original byline places the authors at IBM's research center. The method supplied an automatic way to compare machine output with human reference translations, making repeated evaluation less dependent on commissioning a fresh human assessment for every system change.^[ref]

One key idea is modified n-gram precision. Repeating a common word cannot earn unlimited matching credit, because the candidate's matched counts are clipped by the counts available in the references. This connects a cheap string-counting procedure with an explicit defense against a trivial way to inflate ordinary overlap.^[ref]

For an original unigram example, let the candidate be red red red blue and the reference be red blue green white. Both candidate word types appear in the reference, but clipping permits only one occurrence of red and one of blue, giving $p_1=2/4=1/2$. This is only the unigram component: the full BLEU calculation also combines higher-order n-gram precisions through a geometric mean and applies a brevity penalty.

The original method aggregates counts over a corpus. It is not simply the arithmetic mean of independently scored sentences, and a short example explaining one component should not be presented as the complete metric. Its usefulness as an automatic comparison also does not turn word-sequence overlap into a direct proof that every sentence conveys the correct meaning.^[ref]