One of the properties of an elo rating system is that the sum of all elo changes is zero. When calculating the new FIDE elo ratings, the elo changes are added to the old ratings and the new ratings are rounded. However, doesn't the last step create rating points?
Say, player A has 110 ratings points more than player B and both players have a K-factor of 10. When player A wins against player B, he gains 3.5 points, while player B loses 3.5 points (see FIDE elo calculator). But after adding the elo changes and rounding the new ratings, player A will gain 4 points and player B will lose only 3. As a result, the zero-sum property is violated.
Am I overlooking something? If not, has this been noticed and pointed out before?
Wouldn't it be more correct if the elo changes are rounded first, before adding them to the old rating? (In the example, -3.5 would be rounded to -4.)
Or is this effect so small that it can be neglected, compared to other effects like the inflow of new players, different K-factors, etc...?