We present a small polaron picture and show that finite bandwidth effects a
re important to understand colossal magnetoresistance. Besides the polaron
size parameter, we show that there is another parameter (adiabaticity param
eter) that is relevant to studying magnetoresistance. We find that for fixe
d values of the polaron size parameter an increase in the adiabaticity para
meter increases the magnetoresistance. The magnetic transition is studied w
ithin a mean-field approach. We point out important oversights in the liter
ature. We find that for the reported values of the bandwidth (based on band
-structure calculations) and for experimentally determined values of activa
tion energy and Debye frequency, the calculated values of the magnetoresist
ance compare favorably with experimental ones. We calculate the optical con
ductivity too and find that there is reasonable agreement with experiment.