  We explore connections between an operator's matrix element distribution and
its entanglement generation. Operators with matrix element distributions
similar to those of random matrices generate states of high multi-partite
entanglement. This occurs even when other statistical properties of the
operators do not conincide with random matrices. Similarly, operators with some
statistical properties of random matrices may not exhibit random matrix element
distributions and will not produce states with high levels of multi-partite
entanglement. Finally, we show that operators with similar matrix element
distributions generate similar amounts of entanglement.
