  We study the classical, randomized Ranking algorithm which is known to be $(1
- \frac{1}{e})$-competitive in expectation for the Online Bipartite Matching
Problem. We give a tail inequality bound, namely that Ranking is $(1 -
\frac{1}{e} - \alpha)$-competitive with probability at least $1 - e^{-2
\alpha^2 n}$ where $n$ is the size of the maximum matching in the instance.
Building on this, we show similar concentration results for the Fully Online
Matching Problem and for the Online Vertex-Weighted Bipartite Matching Problem.
