display lowest 4 values from 6

If you have blanks in the "Placings" column, B2:B24 in my example, change formula in F2 to

=SMALL(IF($A$2:$A$24=$D2,IF ($B$2:$B$24<>"",$B$2:$B$24)),COLUMNS($F2:F2))

...also if you want to prevent errors in the scenario where a team has less than 4 placings make a further change to

=IF(COLUMNS($F2:F2)>SUM(($A$2:$A$24=$D2)*(ISNUMBER($B$2:$B$24))),"",SMALL(IF($A$2:$A$24=$D2,IF($B$2:$B$24<>"",$B$2:$B$24)), COLUMNS($F2:F2)))

This is brilliant - excatly what I am looking for. However there is one more item that needs to be figured out. I have another forumla which is giving the values in both columns A & B, so some of them are 'empty' and showing #N/A. So those formulae seem to be given a value of zero in a set of data with #N/A is present. Is there a way to tell the formulae to ignore #N/A entries?

It would probably be easier to change the formulas in columns A and B to return blanks rather than #N/A, what formulas do you have returning #N/A?

Yes, I guess you are right. Right now I have:

=LOOKUP(A29,Entries!$A$4:$E$387)

Which takes values from a database on another tab/sheet

What's in A29? That formula can give a "closest match" result even if A29 isn't found in Entries!$A$4:$A$387. If you only want an exact match, without #N/A try

=IF(LOOKUP(A29,Entries!$A$4:$A$387)=A29,LOOKUP(A29,Entries!$A$4:$E$387),"")