Try setting $/ = ""; before you start to read in data. This will cause each <INPUT> to grab one paragraph of data, rather than one line. See perlvar.

Note that each paragraph will include the blank line at the end.

So you could say:

$/ = "";
$players1 = <INPUT>;
$totals1  = <INPUT>;
$players2 = <INPUT>;
$totals2  = <INPUT>;
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... to grab your data in chunks. You could split each chunk on "\n" characters to get the individual players.

Update: I should mention that this presumes your blank lines are really blank, with no whitespace!

buckaduck