It certainly does. Strength if you are a mage affects the strength of your hit. Not as much as a high magic lvl, but still alot.
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obviously combat, because of strength!
Your attack stats don't but look at you Magic bonus on attack, that does.
Cooking is a minor skill which does not increase combat level; only Attack, Strength, Defence, Magic, and Range will increase your combat level. As a result of the Evolution of Combat update, Summoning, Prayer and Constitution no longer affect combat level.
Levels that effect combat level are constitution, attack, strength, defense, prayer, magic, ranged, and summoning.
to go up in combat level you need to go up levels in strength, attack, defence, hitpoints, prayer and summoning.NOTE: Magic ,range ,and and slayer do put up your combat level but it takes much higher lvls for them to affect it, no other skills do affect combat lvl.The highest combat level you can get is 138, this is when you have level 99 in all strength, attack, defence, hit points, prayer and summoning