Python 2, 96 91 bytes

lambda x,a,b,c,d:(x+((100*sum((a==b,a==c,a==d,b==c,b==d,c==d)))or 10)+177*(a==b==c==d))/100

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Python 2, 96 91 89 bytes

-2 bytes thanks to @Kevin Cruijssen

lambda x,a,b,c,d:(x+(100*sum((a==b,a==c,a==d,b==c,b==d,c==d))or 10)+177*(a==b==c==d))/100

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Python 2, 96 bytes

lambda x,a,b,c,d:(x+(100*((a==b)+(a==c)+(a==d)+(b==c)+(b==d)+(c==d))or .1)+177*(a==b==c==d))/100

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This version outputs excess decimals on zeros (e.g. 0.95 instead of just 0). If that is incorrect, an alternate solution for 98 bytes is:

lambda x,a,b,c,d:(x+(100*(((a==b)+(a==c)+(a==d)+(b==c)+(b==d)+(c==d)))or 10)+177*(a==b==c==d))/100

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Python 2, 96 91 bytes

lambda x,a,b,c,d:(x+((100*sum((a==b,a==c,a==d,b==c,b==d,c==d)))or 10)+177*(a==b==c==d))/100

Try it online!

Python 2, 83 bytes

lambda x,a,b,c,d:(x+177*(a==b==c==d))/100+(a==b)+(a==c)+(a==d)+(b==c)+(b==d)+(c==d)

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Takes literally anything for the icons as long as they compare equal to themselves.

Python 2, 96 bytes

lambda x,a,b,c,d:(x+(100*((a==b)+(a==c)+(a==d)+(b==c)+(b==d)+(c==d))or .1)+177*(a==b==c==d))/100

Try it online!

This version outputs excess decimals on zeros (e.g. 0.95 instead of just 0). If that is incorrect, an alternate solution for 98 bytes is:

lambda x,a,b,c,d:(x+(100*(((a==b)+(a==c)+(a==d)+(b==c)+(b==d)+(c==d)))or 10)+177*(a==b==c==d))/100

Try it online!