Yup, they're pretty hideous formula.
The #VALUE error is because my formula assumes that the scores will always contain a "-", which delimited the home team's score from the away team's score. If that isn't there then things go a bit haywire.
You can try changing the formula in D3 to:
=SUMPRODUCT(--(ISNUMBER(FIND(B3 & " vs",Predictions!$A$4:$A$7))),--(VALUE(LEFT(Predictions!$B$4:$B$7,IFERROR(FIND("-",Predictions!$B$4:$B$7)-1,0)))>VALUE(MID(Predictions!$B$4:$B$7,IFERROR(FIND("-",Predictions!$B$4:$B$7)+1,0),255))))+ SUMPRODUCT(--(ISNUMBER(FIND("vs " & B3,Predictions!$A$4:$A$7))),--(VALUE(LEFT(Predictions!$B$4:$B$7,IFERROR(FIND("-",Predictions!$B$4:$B$7)-1,0)))<VALUE(MID(Predictions!$B$4:$B$7,IFERROR(FIND("-",Predictions!$B$4:$B$7)+1,0),255))))
But this is an array formula and must be entered using Ctrl-Shift-Enter, not just Enter.
Obviously the formula in columns E & F would require similar modification.
I think it's probably time for some VB as well. This might be a useful start:
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