+1 user field after comment is made
It's worth noting the comment table has a 'uid' column so you could potentially query that to get the comment count for a user.

e.g:

$user_comment_count = db_select('comment', 'c')
-&gt;condition('uid', $account-&gt;uid)
-&gt;countQuery()
-&gt;execute()
-&gt;fetchField();


However, if you want to increment a field on comment insert, you could use Rules or hook_comment_insert

e.g: Rules export (Increment field_comment_count for current logged in user on comment insert)

{ "rules_increment_comment_count" : {
    "LABEL" : "increment_comment_count",
    "PLUGIN" : "reaction rule",
    "OWNER" : "rules",
    "REQUIRES" : [ "rules", "comment" ],
    "ON" : { "comment_insert" : [] },
    "IF" : [
      { "entity_has_field" : { "entity" : [ "site:current-user" ], "field" : "field_comment_count" } }
    ],
    "DO" : [
      { "data_calc" : {
          "USING" : { "input_1" : [ "site:current-user:field-comment-count" ], "op" : "+", "input_2" : "1" },
          "PROVIDE" : { "result" : { "result" : "Calculation result" } }
        }
      },
      { "data_set" : {
          "data" : [ "site:current-user:field-comment-count" ],
          "value" : "[result:value]"
        }
      }
    ]
  }
}


You'll need to tweak the Rule to match your conf, but something like that should work.