Friend, this is completely the wrong math on so many levels!
I don't even know where to start... these numbers are not even remotely representative of anything about the larger prison population.
The IP reported receiving 65,600 letters for
assistance, so around ~0.4% of all requests
for help were later proven to be wrongful convictions.
[...]
Assuming the ~0.4% wrongful conviction rate is
representative for this population
For this to be even remotely representative of the overall wrongful conviction rate, this would mean that the IP thoroughly investigated and pursued all 65,600 cases and that new and completely fair trials were conducted in all 65,600 cases.
- The 251 exonerations were obtained by pursuing only a small fraction of those 65,600 cases. Presumably ones where they felt most certain of overturning the conviction.
- The 65,600 letter-writers are surely not representative of the overall prison population; this is a subset of convicts who have the resources to know about the IP and get a letter to them, with some kind of self-belief in their own innocence
- While apparently not true in this case the standards for death sentences tend to be higher than those for other convictions because they are so likely to be appealed, so the percentage of wrongfully convicted people on Death Row is likely to be different than that of the general convict population
- etc etc etc
I don't think your numbers are correct even as a back-of-the-envelope Fermi equation sort of estimate...