  Backoff algorithms are used in many distributed systems where multiple
devices contend for a shared resource. For the classic balls-into-bins problem,
the number of singletons -- those bins with a single ball -- is important to
the analysis of several backoff algorithms; however, existing analyses employ
advanced probabilistic tools to obtain concentration bounds. Here, we show that
standard Chernoff bounds can be used instead, and the simplicity of this
approach is illustrated by re-analyzing some well-known backoff algorithms.
