Measuring seasonality effect I am working on a research problem related to time series analysis. Now, I have STL decomposition and FB Prophet to decompose my data into trend, seasonality and residual. I struggle with measuring the strength of my seasonality component. In the book Forecasting: Principles and Practice, there is a formula which is the ratio of var(residual) to var(residual + seasonality) (takes 0 if negative). Yet, it's very difficult to build an intuition behind it, on repeated trials it shows that daily seasonality is pretty much zero (though my algorithms suggest that there is one.) I would appreciate any hints and suggestions as to measuring the strength of seasonality. Thank you!
 A: 
on repeated trials it shows that daily seasonality is pretty much zero (though my algorithms suggest that there is one.)

I am not sure about Prophet, but STL will fit a seasonal component whether or not one is present. This may account for your observation.
I personally would fit seasonal and non-seasonal models to your data and assess forecast accuracy on a holdout sample for both models. Then you can quantify by how much including seasonality reduces your MSE. (And whether it does so at all.)
A: Are you dealing with simple or complex seasonality in your data? For example, monthly data may show monthly seasonality whereas hourly data may show daily and weekly seasonality. 
I think your decomposition would need to reflect whether the seasonality in your data is simple or complex. Simple seasonality would produce a single seasonal component when decomposing the time series into its component parts, whereas multiple seasonality would produce multiple seasonal components.  For an example of the latter, see https://otexts.com/fpp2/complexseasonality.html. 
One way to retrieve the long term trend and seasonal component(s) in your time series would be using a GAM model.  For this type of model, you can report an adjusted R squared and keep track of improvements in adjusted R squared associated with introducing additional systematic components to the model.
