Judge/juries sentencing question

Anyone know of any studies done that show that in cases where the defendant is found guilty in cases where the evidence is not a slam dunk…they receive lighter sentences?

Or at least in murder cases are more likely not to receive a death sentence?

Just anecdotally, in watching real-life crime shows, it seems in cases where I didn’t think ‘beyond a reasonable doubt’ had been achieved , rarely is a sentence of death given.