Co-Founder/CTO of PiggyBackr [AngelPad S12]. Hacking stuff since 4. Constantly making new mistakes, never repeating them. Would be good to call for: ideation, brainstorming, entrepreneurship, coding, tech questions, accelerators, problem interviews, product feedback
Each accelerator is going to be different so there's no typical wait time, but here's some basic advice:
1. You can't count on getting in, so you must continue growing your business as you would without the accelerator.
2. Ask your other entrepreneur friends who applied at the same time if they heard back yet. If so, definitely follow up with your contacts at those accelerators
There's not really much else you can do to improve your chances now that your applications are all in. You can try some "stunts" like sending 500 cupcakes or something else to grab attention of the partners (you can find stories of stuff like this working for people), but in my opinion these are more of a distraction. Just focus on your business.
Are you first-time entrepreneurs? If not, you might not even need an accelerator. Pitching accelerators is essentially pitching investors, so getting interest from three accelerators is an indication that you might be ready to raise.
If you are first-time entrepreneurs, an accelerator could be beneficial, as it has the potential to greatly accelerate your first raise. Choose the accelerator with the best network. This is the single most important factor. Consider their history with companies similar to yours. The mentors and founder network are good PERKS, but you can build those relationships yourself. What's most valuable is the time saved in building INVESTOR relationships, and a good accelerator can open a lot of doors quickly.