Therefore, the odds are defined as follows:

Note that exp(βi(Xi + 1)) = exp(βiXi) exp(βi). This shows that if Xi changes by a unit amount, the odds is multiplied by exp(βi), which we label the unit odds ratio. As Xi changes over its whole range, the odds are multiplied by exp((Xhigh - Xlow)βi), which we label the range odds ratio. For binary responses, the log odds ratio for flipped response levels involves only changing the sign of the parameter. Therefore, you might want the reciprocal of the reported value to focus on the last response level instead of the first.