At my son’s very atypical elite public HS, the admit success rates for Yale were about 20% early and just under 15% regular with a total of 6-12 admits and 5-9 enrolling each year. For comparison, Harvard was very different, with an EA admit rate of close to 50% vs a Regular admit rate of under 10% with the same 6-12 admits and 5-9 attending each year.
For kids applying to both - like my son did - the smart by-the-numbers play was apply early Harvard, regular Yale.
I have no idea whether this has any relevance to experiences of other applicants from other HSs, but I would recommend taking a close look at the Naviance data available at your school and carefully strategizing where you are likely to get the biggest boost from an early application. This is even more important if you are thinking of applying early to any schools which - unlike Yale, Harvard, etc. - have binding early applications.
FYI, son was accepted Harvard early, Yale regular. We found having the financial package from Harvard very helpful when requesting an improved award from Yale.