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Checks sent by email, rather than mail. The idea works as follows:
Note that this start-up could charge the payee 20 cents per check (it's less than 50% of the cost of a stamp) and have a higher successful delivery rate than snail mail (easy to beat!)
The analytic part of this business model is in the security component to prevent fraud from happening. To a lesser extent, there are also analytics involved to guarantee that email get delivered to the payee at least 99.99% of the time. Information must travel safely through the Internet, and in particular, the email sent to payees must contain encrypted information in the URL used to print the check.
Paypal already offers this type of functionality (online payments), but not the check printing feature. For some people or some businesses, a physical check is still necessary. I believe checks will eventually disappear, so I'm not sure if such a startup would have a bright future.
Read related article (other analytic start-up ideas)