Statistical calculations of what Yogg will do on average isn't worth it anyways, logic is sufficient to tell you that it's a good card to play. Many things can prove without having to have you run the math.
1) Given that all spells originate from you, you have a much higher chance of wiping his board than wiping yours (although with just Yogg on board, chance are you're gonna kill him too). Most AoE in the game targets your opponent exclusively.
2) Given that all secrets in the game cast by you target you, then Yogg will always give you the beneficial effect of a secret and not your opponent.
3) Given that all summoning spells (eg, force of nature and the like) will be cast by you summon minions for you, if you cast a summon spell it will give you minions and not him.
4) Given that the majority of draw cards target you, then most draw spells will be beneficial to you (unless you don't want to draw cards, then, well, SOL I guess).
5) That really only leaves healing spells, direct damage spells, and other targeted effects (like buffs and debuffs) as possible negative effects. And since the majority of those are more likely to hit your opponent than you (since you cast Yogg under optimal conditions), then the only drawback to casting Yogg is that he might heal/buff your opponents minions more than it would heal/buff your own minions. But, the amount of heal/buff spells in the game are dwarfed by the amount of damage spells in the game. So, targeted effects are more likely to harm your opponent than it is to harm you.
