And those are conservative numbers according to Judge Jed Rakoff, 
who has written a compelling piece explaining that innocent people are pleading guilty to crimes that they have not committed.  There is a lot to blame for this phenomenon but he offers this solution:
What can we do about it? If there were the political 
will to do so, we could eliminate mandatory minimums, eliminate 
sentencing guidelines, and dramatically reduce the severity of our 
sentencing regimes in general. But even during the second Obama 
administration, the very modest steps taken by Attorney General Eric 
Holder to moderate sentences have been met by stiff opposition, some 
from within his own department. For example, the attorney general’s 
public support for a bipartisan bill that would reduce mandatory 
minimums for certain narcotics offenses prompted the National 
Association of Assistant US Attorneys to send an “open letter” of 
opposition, while a similar letter denouncing the bill was signed by two
 former attorney generals, three former chiefs of the Drug Enforcement 
Administration, and eighteen former US attorneys.
Reflecting, 
perhaps, the religious origins of our country, Americans are notoriously
 prone to making moral judgments. Often this serves salutary purposes; 
but a by-product of this moralizing tendency is a punitiveness that I 
think is not likely to change in the near future. Indeed, on those 
occasions when Americans read that someone accused of a very serious 
crime has been permitted to plea bargain to a considerably reduced 
offense, their typical reaction is one of suspicion or outrage, and 
sometimes not without reason. Rarely, however, do they contemplate the 
possibility that the defendant may be totally innocent of any charge but
 is being coerced into pleading to a lesser offense because the 
consequences of going to trial and losing are too severe to take the 
risk.
I am driven, in the end, to advocate what a few 
jurisdictions, notably Connecticut and Florida, have begun experimenting
 with: involving judges in the plea-bargaining process. At present, this
 is forbidden in the federal courts, and with good reason: for a judge 
to involve herself runs the risk of compromising her objectivity if no 
bargain is reached. For similar reasons, many federal judges (including 
this one) refuse to involve themselves in settlement negotiations in 
civil cases, even though, unlike the criminal plea bargain situation, 
there is no legal impediment to doing so. But the problem is solved in 
civil cases by referring the settlement negotiations to magistrates or 
special masters who do not report the results to the judges who handle 
the subsequent proceedings. If the federal rule were changed, the same 
could be done in the criminal plea bargain situation.
As I 
envision it, shortly after an indictment is returned (or perhaps even 
earlier if an arrest has occurred and the defendant is jailed), a 
magistrate would meet separately with the prosecutor and the defense 
counsel, in proceedings that would be recorded but placed under seal, 
and all present would be provided with the particulars regarding the 
evidence and issues in the case. In certain circumstances, the 
magistrate might interview witnesses or examine other evidence, again 
under seal so as not to compromise any party’s strategy. He might even 
interview the defendant, under an arrangement where it would not 
constitute a waiver of the defendant’s Fifth Amendment privilege against
 self-incrimination.
The prosecutor would, in the meantime, be 
precluded from making any plea bargain offer (or threat) while the 
magistrate was studying the case. Once the magistrate was ready, he 
would then meet separately with both sides and, if appropriate, make a 
recommendation, such as to dismiss the case (if he thought the proof was
 weak), to proceed to trial (if he thought there was no reasonable plea 
bargain available), or to enter into a plea bargain along lines the 
magistrate might suggest. No party would be required to follow the 
magistrate’s suggestions. Their force, if any, would come from the fact 
that they were being suggested by a neutral third party, who, moreover, 
was a judicial officer that the prosecutors and the defense lawyers 
would have to appear before in many other cases.
Would a plan 
structured along these lines wholly eliminate false guilty pleas? 
Probably not, but it likely would reduce their number. Would it present 
new, unforeseeable problems of its own? Undoubtedly, which is why I 
would recommend that it first be tried as a pilot program. Even given 
the current federal rules prohibiting judges from involving themselves 
in the plea-bargaining process, I think something like this could be 
undertaken, since most such rules can be waived and the relevant parties
 could here agree to waive them for the limited purposes of a pilot 
program.
I am under no illusions that this suggested involvement 
of judges in the plea-bargaining process is a panacea. But would not any
 program that helps to reduce the shame of sending innocent people to 
prison be worth trying?