Wang and Sitters' 11/6-approximation for graph balancing (each job allowed on at most two machines) is not one algorithm but a set of permitted executions. Step 1 may return any feasible solution of the fractional relaxation. Step 3 may match remaining jobs to the rounding's slots in many ways. We determine exactly what that latitude permits: ratios arbitrarily close to 11/6, none reaching it, so 11/6 is the least constant bounding every permitted run. We then determine the worst-case guarantee, against the optimum itself, as a function of the big-job threshold beta, the fractional share at or above which Step 2 assigns a job. On Wang and Sitters' own range 1/2 < beta < 1 the guarantee is exactly max{3/2 + beta/2, 5/2 - beta}. We extend the same eligibility rule to 0 < beta <= 1/2, outside the range they state. There a big job's two shares can both reach the threshold, so Step 2 acquires a third choice. We determine it too: exactly 3/2 + (1-beta)floor(1/beta), hence unbounded as beta falls. The worst-case ratio is therefore known at every threshold in (0,1), and attained at none. Consequently 2/3 is the unique optimal threshold, and the guarantee jumps at one half and again at every threshold 1/k below it, rather than degrading smoothly. A companion note examines changes that leave the constant unchanged.

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