You need to code a case condition in your calculated field
case [Dimension parameter]
when 'Ship Mode' then [Ship Mode]
when 'Segment' then [Segment]
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I may not understand your data completely, but here's a couple of suggestions.
First, you might try creating a calculated field called "Show Item" that would look something like this:
CASE [Parameters].[Race Distances]
WHEN "Half" THEN IF [Half]="Half" THEN 1 ELSE 0 END
WHEN "M&H" THEN IF [M&H]="M&H" THEN 1 ELSE 0 END
WHEN "Marathon" THEN IF [Marathon]="Marathon" THEN 1 ELSE 0 END
WHEN "Relay" THEN IF [Relay]="Relay" THEN 1 ELSE 0 END
WHEN "Wheel" THEN IF [Wheelchair]="Wheel" THEN 1 ELSE 0 END
WHEN "Other" THEN IF [Other]="Other" THEN 1 ELSE 0 END
WHEN "All" THEN 1
And convert it to a "Discrete" item, and to a "Dimension", and then place it on your Filter shelf, and check only the box next to 1 (so you are only showing the items that have a 1 not the the 0). Then right click your Race Distances parameter, and select "Show Parameter Control." Now when you change the item in the parameter control, the map should update.
Another solution would be to create a single column in your data-source to indicate the type of race, rather than having a seperate column for each type of race. If it's possible to change your data-source, then I think I would prefer this alternative, but either way it should work.