The modified soil-adjusted vegetation index (MSAVI) and its later revision, MSAVI2, are soil adjusted vegetation indices that seek to address some of the limitation of NDVI when applied to areas with a high degree of exposed soil surface. The problem with the original soil-adjusted vegetation index (SAVI) is that it required specifying the soil-brightness correction factor (L) through trial-and-error based on the amount of vegetation in the study area. Not only did this lead to the majority of people just using the default L value of 0.5, but it also created a circular logic problem of needing to know what the vegetation amount/cover was before you could apply SAVI which was supposed to give you information on how much vegetation there was. Qi et al. (1994a) developed the MSAVI, and later the MSAVI2 (Qi et al. 1994b) to more reliably and simply calculate a soil brightness correction factor.
The formula for calculating MSAVI itself is the same as the formula for calculating SAVI: