Which method of depreciation involves analyzing the physical deterioration of property?

The engineering breakdown method is the correct choice because it specifically focuses on assessing the physical deterioration of property through a detailed analysis. This method involves examining the structure and components of a property to identify wear and tear, obsolescence, and other forms of physical decline that can affect its overall value. By collecting data on the condition of various elements of the property, the appraiser can estimate the extent of depreciation caused by physical factors.

In contrast, other methods like the market comparison method and the sales comparison method primarily focus on external market influences and comparable sales rather than the physical condition or deterioration of the property itself. The cost method, while it may consider some physical aspects when calculating depreciation based on replacement costs, does not target physical deterioration in the same explicit, analytical manner as the engineering breakdown method does.