If juror ignorance about the meaning of "beyond reasonable doubt" had the effect of causing too many acquittals, you can be sure something would be done to improve judicial directions on the point.
The New South Wales Bureau of Crime Statistics and Research, in Bulletin No 119 (September 2008) "Juror Understanding of Judicial Instructions in Criminal Trials" by Lily Trimboli, concludes on this topic:
"The problems in juror understanding ... do not all stem from the way judges give instructions. It is assumed at common law that the phrase 'beyond reasonable doubt' requires no explanation and is readily understood by most ordinary people. Appeal courts have, for this reason, repeatedly warned trial court judges (see Green v The Queen (1971) 126 CLR 28, 32-33) not to attempt to clarify the phrase when explaining its importance to juries. The present study shows, however, that there is considerable divergence among jurors about the meaning of 'beyond reasonable doubt'. Around half (55.4%) of the jurors surveyed, believed that the phrase 'beyond reasonable doubt' means 'sure [that] the person is guilty'; 22.9 per cent believed that the phrase means 'almost sure' the person is guilty; 11.6 per cent believed that it meant 'very likely' the person is guilty; and 10.1 per cent believed it meant 'pretty likely' the person is guilty. This is quite a wide spread of opinion and it suggests that some clarification of the threshold for convicting a person would be of assistance to juries. While statutory clarification of the phrase 'beyond reasonable doubt' may be controversial, one relatively simple change that could be made to improve current practice would be to provide written materials to the jury to assist in their deliberations."
A perfectly sensible suggestion, but what should a written instruction say?
In discussing R v Wanhalla (25 August 2006) I noted the Court of Appeal's reluctance to mathematise the concept of proof beyond reasonable doubt by expressing it as a probability of guilt. I suppose that people vary in their understanding of "sure", "almost sure" and "very likely". The survey does not seem to have attempted to establish a way of ranking those words against a common reference, other than the phrase beyond reasonable doubt itself. If the jurors in the survey had been asked to express "sure", "almost sure", "very likely" and "pretty likely" as probabilities a recommendation could have been made as to the usefulness of directing juries in terms of probabilities.
The question in the survey was put as "In your view, does the phrase 'beyond reasonable doubt' mean pretty likely the person is guilty/very likely the person is guilty/almost sure the person is guilty/sure the person is guilty?"
What is clear is that there are likely to be too many convictions because of juror misunderstanding of the standard of proof. Progress in rectifying this seems to be painfully slow; such dragging of the feet by officialdom (I use this awful word to avoid using another awful word) would not occur if there were too many acquittals.
See also on this, Jeremy Gans ....