For reference, here in the UK people (typically) get 33% off their sentence if they plead guilty. There was a push in 2011 to make it 50%, but that was rejected.

However the people being prosecuted don't know in advance what sentence they will receive exactly. Sentencing is carried out after the verdict (sometime quite a while after if "pre-sentence reports" need to be compiled). There are sentencing guidelines, so they have a reasonable idea or starting point, but there is much variation in these due to many different mitigation or aggravating factors.

Particularly at the "low" end, a person may not know whether they will be getting 33% off a community order or 33% off a jail sentence.

Still, there are very, very few occasions where it is reported that innocent people plead guilty due to the reduction in risk. That may also be due to the reasonable lengths of the starting sentences.

The majority that go through the courts, that is those who are actually guilty, plead guilty. They get a small "reward" for not tying up the courts unnecessarily.

My personal opinion is that in an ideal world we wouldn't offer any plea deals, but we don't live in that world. Yet.

"Still, there are very, very few occasions where it is reported that innocent people plead guilty due to the reduction in risk."

Is part of the plea bargain deal not discussing your innocence? In other words, how do we know whether people taking plea bargains are innocent?

No. It's not a deal thats "made" per-se, there are no conditions to be haggled over, its simply that Judges will automatically award the reduced penalty at the sentencing stage if the defendant pleads guilty.