Captain obvious : by reducing time to market and defects on releases.
To extend on this one liner, the usual pitfall is being an organization change without any reference.
Engaging a culture or organization change implies some expense to train and introduce people to this new method, this have a cost in training but also imply a loss in productivity as people in a train session won't produce anything. This is the investment part of the cultural change.
To measure a ROI you have to first find some relevant metrics which should be improved (understand costly, either expensive or source of loss of profit). This could be a shorter time to market, less patch after each release, a better customer engagement within your product. Relevant metrics will be highly dependent of your product(s).
Measuring a ROI (how fast you have covered the training expense) implies that you can factually present an evolution on those metrics, so before engaging any change you must have defined those metrics and measured them in an objective way.
Once you have a real evolution to show you can tell if you did improve something in a way which has covered the training expense and become more profitable than it was before.
The usual pitfall is to engage the change before having defined any metrics and thus evaluating the ROI on a feeling and not on factual datas.
Productivity can be a metric, but its measurement is usually very hard to do in an objective fashion and should not be a first class metric for this kind of study.