How?
Magic Missile is 5 shots of 3-5 damage each, or 20 total. If you have Super Potency I and Force IV (a really unpopular enhancement) then it's multiplied by 1.9, coming to 38. Without metamagic that costs 10 sp, so 3.8 dpm (damage per mana).
Instead if I use Chain Lightning, that's one shot of 16*5 damage, which is 80 or 40 on a successful save. Super Pot VI and Energy IV bring it to 40 * 1.9 = 76. 76 damage for 35 mana is 2.2 dpm. I'll add Empower for 15 - 6 enhancement - 2 thelis = 7 sp. Then I add Maximize for 25 - 6 enh - 2 glove = 14 sp.
So for 35+7+14=56 sp that does 76 * 3 = 228 hp, or 228/56 = 4.1 dpm.
So even if Arraetrikos always saves, 952 sp of Chain Lightning will be 3900 damage, while 950 sp of Magic Missile is 3610 damage. The more saves he fails, the more Chain Lightning wins.
And as for Polar Ray: 16*5 = 80 damage. With only normal Glaciation (20) instead of Superior (50), the multiplier is 80 * 1.6 * 2 * 1.5 = 384. The cost is 45+7+14 = 66 sp, giving 5.8 dpm. (Actually a little less, because Arraetrikos has some cold resist). Chain Lightning would beat that if he failed the saves enough, but his reflex is good.