Well, the main problem is that you declare a new instance of the handN variables inside your if{} blocks, and so the values of those variables die when they go out of scope (once the if block ends). Then you revert back to the previous (undefined) value of $hand1, $hand2, etc.

Update: Notice also that the warnings you received were pretty good clues to the source of the problem:

Use of uninitialized value in addition (+) at ./test.pl line N, <> lin
+e M.
[download]

my $teamhand=$hand1 + $hand2 + $hand3 + $hand4;
[download]

So it is saying that you are adding up variables that you have never initialized. Sure enough, when you originally declared them, you didn't set them to zero or anything. But surely you updated their value along the way, didn't you? Ah, no, that's when I noticed the new 'my' declaration of each of the $hand1, $hand2, $hand3 and $hand4 variables.

As others have pointed out you've got problems with scopeing. This sort of thing just crys out for arrays and loops though.

use strict;
use warnings;

my @bowlers;
my $team_handicap;

for my $bowler (1..4) {
    print 'Please enter Bowler ',$bowler,"'s 3 scores:\n";
    for (0..2)  {
        print '::';
        my $score = <>;
        chomp $score;
        $bowlers[$bowler]{avg} += $score;
    }
    $bowlers[$bowler]{avg} = int ( $bowlers[$bowler]{avg} / 3 );
    
    $bowlers[$bowler]{handicap} = 
      ($bowlers[$bowler]{avg} >= 200) ?
      int( (200 - $bowlers[$bowler]{avg} ) * .85) :
      0;
      
    $team_handicap += $bowlers[$bowler]{handicap};
}

print "\n\n";

for my $bowler (1..4) {
  print 'Bowler ',$bowler,"'s Average Score:  ",$bowlers[$bowler]{avg}
+;
  print "\tBowler ",$bowler,"'s Handicap:  ",$bowlers[$bowler]{handica
+p},"\n";
}
print "The team's handicap is:    $team_handicap";
[download]

You repeat "my" for the $hand1-4 variables when you assign to them, but in the separate scope of each if statement. Thus, when you do the addition to $teamhand, you get the original, uninitialized $hand1-4 variables.

For kicks I converted this into Perl6. Below is a fairly direct transaltion, though I think i'm going to try a rewrite without looking at the p5 version to see what i end up with.

#!/usr/bin/pugs

my @bowlers;
my $team_handicap;

for (1..2) -> my $bowler {
  say "Please enter Bowler $bowler's scores:";
  for (0..2) {
      print "Score $_:";
      my $score = =$*IN;
      @bowlers[$bowler].<average> += $score;
  }
  @bowlers[$bowler].<average> = int(@bowlers[$bowler].<average> / 3);
  @bowlers[$bowler].<handicap> = int( (200 - @bowlers[$bowler].<averag
+e> ) * .85);
  $team_handicap += @bowlers[$bowler].<handicap>;
}
say;
for (1..2) -> $bowler {
  say "Bowler $bowler's Average Score:", @bowlers[$bowler].<average>,
      "\t Handicap: ", @bowlers[$bowler].<handicap>;
}
      
say;

say "The team's handicap $team_handicap";
[download]

You can see it is very similar to Perl5 though definitly not the same, comment, improvments are welcome. Or get a committer bit and update it yourself. Link to the live version: http://svn.perl.org/perl6/pugs/trunk/examples/games/bowling.p6

for (1..2) -> my $bowler {

for 1..2 -> my $bowler {

say;

Probably tries to print $_, which is undef. Expect a warning.

Juerd # { site => 'juerd.nl', plp_site => 'plp.juerd.nl', do_not_use => 'spamtrap' }

A slightly more perl6 ish version.

#!/usr/bin/pugs

#http://svn.perl.org/perl6/pugs/trunk/examples/games/bowling2.p6
use v6;

print "How many bowlers are on your team?";
my $bowlers = =$*IN;
print "How many games would you like to average?";
my $games   = =$*IN;

my @bowlers;

for (1 .. $bowlers) {
    my $bowler;
    say "Enter scores for bowler $_:";
    for (1.. $games) {
      print "game $_ score:";
      my $score = =$*IN;
      $bowler<games>.push( $score );      
    }
    $bowler<id>       = $_;
    $bowler<total>    = [+] @{$bowler<games>};  
    $bowler<avg>      = $bowler<total> / $games;
    $bowler<handicap> = int ( (200 - $bowler<avg>) * .8);
    @bowlers.push($bowler);
}

for @bowlers -> $bowler {
  say "Bowler $bowler<id>'s average is $bowler<avg>\tHandicap: $bowler
+<handicap>"; 
}

my $team_handicap = [+] @bowlers.map:{ $_.<handicap> };
say "Team handicap is: $team_handicap";
[download]


___________
Eric Hodges