TL;DR
The GroupSummary() function only takes two parameters. The field name, and a Mode of 0 or 1. Mode 0 is a formatted output and shows "avg", "total" etc as part of the output. Mode 1 just outputs the number. It can't take expressions as a parameter.
Create a calculated field that doesn't have a bracket ")" at the end of the name. GroupSummary() can't handle the trailing bracket. I used the field name [LPEcalc].
Give this new calculated field the expression "Math(Now()-[Last played, 0])&datatype=[number]".
Create an Expression Column in an Album View with the expression "GroupSummary(LPEcalc)" as a test. It should give you a formatted average time since [Last Played] for all selected files, taking into account only those files that have a value in [Last Played]. For example, the output might be "223.68 avg".
As you want to see this in the Tag Window, add an Expression item to the Tag Window, name it something like "Avg days since play", and give it the expression of "GroupSummary(LPEcalc)".
Done. See image for what I built.
PS: If you want to show the same data in an Expression Column in a View, but want MC to show the average time since played independently for each Album, use the expression "GroupSummaryQuery(Album,LPEcalc)".
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Ah yes, I had forgotten about that nice little summary at the top of the old Tag window.
The good news is that you can still use that version of the Tag window. Just hold the Shift key when you click "Tag" in the Action Window. That will toggle use to the old version of the window, and MC will keep using that until you Shift+Click again.
The bad news is that the old Tag window will probably go away at some stage, and may not be updated as time goes on. In fact, I don't think it has had any updates for some time.
Let's just look at the components of that information.
1. "1:17:26 total" is just the [Duration] field.
2. "333 MB total" is just the [File Size] field.
3. "70 plays total" is just the [Number Plays] field.
4. "207.5 days ago" is just "Math(trunc(Now()-[Last played, 0], 1)) days ago".
But all the above have had the MC magic of summarisation to a total because a group of files is selected. This magic of summarisation is not available for fields shown in the Tag window. MC will just show [Varies] there when multiple files are selected.
The equivalents using GroupSummary are.
1. GroupSummary(Duration)
2. GroupSummary(File Size)
3. GroupSummary(Number Plays)
4... So finally to your actual question. I've been playing with these functions and documenting as a went, so forgive the unnecessary discussion.
GroupSummary takes a field name as its only parameter. As in the above cases, the field names need to be "bare", with no [] brackets around them. It looks like you have created a new calculated field called "Last Played (Elapsed)" using the expression "FormatDate([Last Played,0],Elapsed)", which would mean that when used in GroupSummary the expression would be;
GroupSummary(Last Played (elapsed))
But that isn't going to work, as GroupSummary doesn't handle the field name ending with a ")" bracket.
Renaming the field to "Last Played elapsed" and using the expression GroupSummary(Last Played elapsed) doesn't work either, as it just results in the output of [Varies]. Not helpful. It isn't the spaces in the field names that is the issue either. Using a field named [LPE] and the expression GroupSummary(LPE) also gives the output of [Varies].
So it looks like maybe the GroupSummary function doesn't like using a custom field. But maybe it is the expression being used. Nope. Changing the expression to explicitly calculate the time since the files were last played using the expression "Math(Now()-[Last played, 0])" rather than the formatting in the expression "FormatDate([Last Played,0],Elapsed)" still gives an output of [Varies].
However, changing the field [LPE] so that it is no longer a calculated field, and then just setting its value to "=Math(Now()-[Last played, 0])" by editing the field, makes the expression GroupSummary(LPE) work correctly, outputting the average number of days since any tracks that have a value in [Last Played] have been played. The output was in the format "223.5 avg".
Note that the LPE field must be a Decimal or Integer field for this to work. This is a big hint.
So an idea formed. I created a calculated field called [LPEcalc] and gave it the expression "Math(Now()-[Last played, 0])", then changed the [LPE] field to just expression to just "=[LPE]" and "=[LPE, 0], trying to get it to just copy across the value of LPEcalc. But GroupSummary(LPE) still gave the result of [Varies]. I also tried all of the above using GroupSummaryQuery(Album, LPE), with the same results as GroupSummary(LPE).
But then, success! As documented at the top of this post.