Elo rate

When a postdoctoral candidate receives multiple offers, they typically accept one and decline the others.

We regard such outcomes as a form of competition among offers, or among institutions when the offers are institution-specific, and apply the Elo-rating or Bradley-Terry model .

In the Elo-rating framework, the probability that institution \(i\) is chosen over institution \(j\) is modeled as

Here, \(R_i\) and \(R_j\) are the Elo ratings of institutions \(i\) and \(j\). If the two ratings are equal, the probability is 50%. If institution \(i\) has a 400-point rating advantage, it is chosen with probability approximately 91%.

We set the rating of DESY to 1000 as the baseline and apply maximum likelihood estimation to the Bradley-Terry model using data from 2006 to 2026.