On trips across five or more time zones, jet lag was rated about 40% lower on melatonin than on placebo, on average, across four early trials.
The pooled scores come from four small trials of 17 to 52 people, published from 1987 to 1992. Two later trials that found no benefit, one of them the largest at 257 people, were left out of that pool. A re-analysis that counts them finds about half the effect of a pooling that leaves them out. Ratings varied so much between people that their spread often exceeded 90% of the average score, so the 40% is a gap between group averages, not what each traveller felt. Scores were compared after the flight, not as change from how each person felt before it.