In my Handbook of Writing for the Mathematical Sciences I described the spotlight factor, originally introduced by Tompa in 1989. The spotlight factor is defined for the first author of a paper in which there are authors listed alphabetically, and it is assumed that the paper is from a community where it is the custom to order authors alphabetically.
The spotlight factor is the probability that if coauthors are chosen independently at random they will all have surnames later in the alphabet than the first author. This definition is not precise, since it is not clear what is the sample space of all possible names, so it is better to regard the spotlight factor as being defined by the formula given by Tompa, which is implemented in the MATLAB function below.
The smallest spotlight factor I have found is the value 0.0244 for Zielinski, for the paper
Pawel Zielinski and Krystyna Zietak, The Polar Decomposition—Properties, Applications and Algorithms, Applied Mathematics, Ann. Pol. Math. Soc. 38, 23-49, 1995
This beats the best factor of 0.0251 reported by Tompa in a 1990 follow-up paper.
Can you do better?
Here is a MATLAB M-file to compute the spotlight factor, preceded by an example of its usage:
>> spotlight('zielinski',1) ans = 2.4414e-02
function s = spotlight(x, k) %SPOTLIGHT Tompa's spotlight factor of authorship. % SPOTLIGHT(X, K) is the spotlight factor for the author whose % last name is specified in the string X, with K coauthors. % Mixed upper and lower case can be used. % Smaller spotlight factors correspond to rarer events. % Reference: % Martin Tompa, Figures of Merit, SIGACT News 20 (1), 62-71, 1989 if ~ischar(x), error('First argument must be a string.'), end if nargin < 2, error('Must give two arguments.'), end x = double(upper(x)) - double('A') + 1; x( find(x < 0 | x > 26) ) = 0; % Handle punctuation and spaces. s = 0; % Ideally use Horner's rule, but the following is clearer. for i=1:length(x) t = x(i); s = s + t/27^i; end s = (1 - s)^k;