Just some more thoughts on this. The “unit cost” is a better metric, as described here: Is there a beeminder term for … “pay per unit”?. For example, suppose one averages 3 exercise sessions on their at home stationary cycle per week for 52 weeks, 156 sessions, and one paid Beeminder $5, $10, $30, $30 in derailments, that’s $75/156 or about $0.50 per exercise session.
The problem with the unit cost metric is that it doesn’t quite determine the cost if one doesn’t derail. Suppose one has 156 sessions over a year and no derailments? There is still a cost in both the time of managing one’s beeminder and “money at risk”. That’s where some economic mathematical model might come in handy. Also, this type of cost analysis could be factored in along with unit cost.