Spatial filtering is the fundamental characteristic of microphone array based signal acquisition which plays an important role in applications such as speech enhancement and distant speech recognition. In the array processing literature, this property is formulated upon beam-pattern steering and it is characterized for narrowband signals. This paper proposes to characterize the microphone array broadband beam-pattern based on the average output of a steered beamformer for a broadband spectrum. Relying on this characterization, we derive the directivity beam-pattern of delay-and-sum and superdirective beamformers for a linear as well as a circular microphone array. We further investigate how the broadband beam-pattern is linked to speech recognition feature extraction; hence, it can be used to evaluate distant speech recognition performance. The proposed theory is demonstrated with experiments on real data recordings.