Lead your team to win the wrestlers world championship!
Python 2, 59 57 bytes
-2 bytes thanks to @dingledooper!

lambda a,b:sum(b.sort()&lt;b&lt;[x]&gt;b.pop(0)for x in sorted(a))

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A function that takes 2 lists as arguments, and returns the maximum number of matches that can be won.
Approach
For each opponent (from weakest to strongest), match that opponent with the weakest available member of my team that can win.
For example, let's say the strength of 2 teams (sorted) are as follow:
No.       1  2  3  4  5
Me       [2, 2, 4, 5, 8]
Opponent [3, 6, 7, 7, 9]


The 1st opponent has strength 3, so we need to match that with our 3rd team member.
The 2nd opponent has strength 6, so we match that with our 5th.

We cannot win any more match. So in total we can win at most 2 matches.
Ungolfed code
a,b=map(sorted,input())  # sorted strength of my team and opponent team
s = 0                    # number of matches that can be won
for x in a:              # loop through my team, in order of increasing strength
  if x &gt; b[0]:             # if current member can beat the weakest opponent left
    s += 1                   # then match those two
    b.pop(0)                 # and remove the weakest opponent
                           # (otherwise, current member is useless)
print s