This post is completely boring for outsiders. I am just writing this down so that I do not forget.
In my department, we earn one sabbatical credit for each quarter we work more than 50% of time. And of course we can spend our accumulated sabbatical credits to take sabbatical leaves.
Now there are two types of sabbatical leaves, regular and “sabbatical in residence”. The latter requires fewer sabbatical credits but you have to stay in the San Diego area.
Here are how things work. Suppose your teaching duty is \(x\) courses per year. Then if you take the regular sabbatical, you need to spend 9 sabbatical credits and your teaching duty is reduced by \(x/3\). (The idea is that spending 9 sabbatical credits gives you one free quarter, and since there are three quarters per academic year, your teaching duty is reduced by one third.) On the other hand, if you take a sabbatical in residence, you need to spend 6 sabbatical credits and your teaching duty is reduced by \(2x/9\). In addition, to enforce you to stay in the San Diego area, you need to teach at least 0.5 courses while taking sabbatical in residence.
Notice that the conversion rate from sabbatical credit to teaching reduction is \((x/3)/9=x/27\) with regular sabbatical, while it is \((2x/9)/6=x/27\) with sabbatical in residence, so they are identical. However, the regular sabbatical is slightly more advantageous due to the smaller opportunity cost: note that if we take the sabbatical in residence, because it requires spending fewer sabbatical credits, we would take it more often, and therefore we would accumulate fewer sabbatical credits (because you do not earn sabbatical credits during sabbatical). This argument shows that the only reason we would be interested in taking the sabbatical in residence is to spend sabbatical credits before permanently leaving the university.