Using guessimation, x would be the numer of people that confessed that were innocent, so 91.25 < x < 182.5, and that, alone, was the principally driving force (assumptive, I'm aware) to convict them - and these are the numbers that we're aware of because of the overturned convictions.
Whilst I can understand the reprieve it must give police and the district attorneys in the efforts of building a case, it almost seems as if they just kind of give up applying any further scrutiny, once any confession is had - whether the person actually committed the crime or not.
I'm not sure why this breakdown, for lack of a better vernacular at present, occurs though.
Is it antipathy? Is it because numbers are more important than anything else (e.g.: for elected positions such as Sheriffs)? Is it because we ply the path of least of resistance to the investigating demeanor?
I'm sure a lot of the convictions in the past are biased for varying other degrees but this seems to infer that even without those other degrees of influence, we have a high margin of error for putting innocent people away.
Add those varying degrees referenced above into the equation and I'm not so sure that the deflection, "It's not a perfect system but it works," is really applicable, anymore.