Standardized Mean Difference in PROC PSMATCH

[wfan]

I am puzzled by how PROC PSMATCH calculates the standardized mean differences for matched observations. According to the SAS document (https://documentation.sas.com/doc/en/statug/15.2/statug_psmatch_details25.htm), the standardized deviation for matched observation is pooled (before matching) instead of the matched (after matching). Why does SAS use the before-matching standardized deviation to calculate the after-matching standardized mean differences? This question also applies to weighting.

As an example, the table below is from the SAS document example (https://documentation.sas.com/doc/en/statug/15.2/statug_psmatch_examples01.htm). The same standard deviation is used for all observations and weighted observations. Shouldn't the standard deviations be different?

Many thanks