If you are comparing how much you would spend not on the plan vs on the plan, then yes to break even with the dining plan then yes you need to spend at least $38 a day to make it worth your while.
I really don't know of any counter service restaraunt where you would be spending $15 for your meal though. A better breakdown would likely be, if I am doing a sit down for $25, a counter service for $10 and a snack for $4 a day normally when I go to Disney, then I will break even on the dining plan.
When I was trying to figure out if it was worth it for us to get it, I looked at the menus on allears and priced out what hubby and I would normally eat if not on the plan, which for our original 8 night trip was 4 sit down meals and the rest counter service. Adding up the costs it was actually more expensive (by about $10) with the 4 sit down meals and the 12 counter service meals plus snacks then it would have been on the dining plan with 8 sit down meals and 8 counter service meals plus snacks including adding in an extra $100 for out of pocket expenses. So for us it was a no brainer to go for the dining plan. We like to eat well when we do sit down restaraunts though, so for someone that may eat more modestly their costs may be different.
Honestly to break even on the plan you need to average $38 a night for however many nights you are at Disney, so if one day you end up eating $30 worth of food as long as the next night you end up eating $50 worth of food you are still breaking even on the plan.
