Solving an optimization problem \emph{online} means serving a sequence of requests
one after the other without knowing future requests.
The performance of an online algorithm is measured by the \emph{competitive ratio},
the quotient of its solution and an optimal solution computed off\-line.
This ratio can be quite high in the worst case.
The problem to minimize cache misses for a sequence of data requests is a
typical example, where a simple adversary can force a ratio up to to the cache size.
However, the performance of caching algorithms like LRU seems to be much better
in real life.
We have made an approach to explain this phenomenon by a smoothed analysis
and present some results.
We will also discuss how to measure performance ratios in a probabilistic setting.