There has often been some fuzziness in the way the results of the Iowa caucuses were calculated and reported. But this is the first year that Iowa Democrats released raw vote counts. The transparency provided the public with its first opportunity to check the complex math that determines which candidates get the delegates they need to win the Democratic nomination.

And in many cases, the math did not check out. In such a close race — Pete Buttigieg, the former mayor of South Bend, Ind., is leading Senator Bernie Sanders of Vermont by a tenth of a percentage point — even small mistakes can add up.