I've been looking to scale up the CR of a few Ancient dragons for one of my settings, so I've been figuring out the offensive and defensive CR of each dragon to determine how my scaled-up dragons should compare. The thing is, by my calculations, most of these dragons (virtually all that are young or older) end up with a higher CR than is listed in the Monster Manual.

For example, a Young Red Dragon, listed at CR 10. By my calculations, its effective AC and HP come out to 22 and 356, respectively, making its defensive CR 21. Its average damage over 3 rounds is about 68, with an attack bonus of +10 and a DC of 17, giving it an offensive CR of 10 or 11. Regardless, its CR comes out as around 16. Ignoring the fire immunity and either rounding down or ignoring the fly speed (or the saving throw bonuses) gives a CR of 10, as written, but I can't figure out how exactly they arrived at their result.