One of the most widely used index to quantify the drought events is the standardized precipitation index (SPI) and it is actually based on precipitation time series only.
The index is used, among others, also by the NOAA.
I'll borrow the description of the index from a scientific article (Farinosi et al 2018)
Standardized precipitation Index (McKee et al., 1993)
The index is a measure expressed in standard deviation units of the
variation of the precipitation of a specific number of months respect
to the long run average (WMO, 2012). The number of months based on
which the SPI could be calculated usually varies between 3 and 48
months. Shorter time scales SPI is considered a good indicator of
variations of soil moisture, while on longer scales (up to 24 months),
it could be associated with groundwater or reservoir levels variation
(WMO, 2012). That for, a shorter SPI (3 months) is often utilized to
detect meteorological droughts; a medium SPI (6 months) is usually
associated with agricultural droughts; a longer SPI (12–24 months) is
associated with hydrological droughts. SPI was calculated using the R
package SPEI (Beguería and Vicente-Serrano, 2014).
Usually the minimum requirements to have a robust estimation of the SPI is to have a precipitation time series of at least 30 years.
You could use the SPI to quantify the number of "droughts" (choosing a threshold under which you define the event - for instance see this) in a period for your area of interest and then aggregate the number of "meteorological", "agricultural", and "hydrological" droughts.