There are no stats that letters of intent (LOI) do or don't work. (Programs do not tend to be transparent about how their ranking processes are handled.) However, because many programs do not want to go far down their rank list (mostly for reasons related to ego), they are eager to highly rank candidates who want to be at their programs. So I advise my clients to do whatever they can, including a LOI, to let a program know it is their first.
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