For the 20 groups in 2015-2016 (8 in the Champions League and 12 in the Europa League), I gathered each club's points, club coefficient for five seasons like UEFA does, and club coefficient just for the previous season, 2014-2015. I calculated the sum for each group and what percent of the sum belonged to each club. I calculated the correlation between percent of points and five season coefficient and compared it to the correlation between percent of points and one season coefficient. Here are the results by group, with 1SC meaning one season coefficient and 5SC meaning five season coefficient, and the higher value was the better predictor of Group Stage performance: Champions League A: 1SC = .8617, 5SC = .8363 Champions League B: 1SC = .4478, 5SC = -.3377 Champions League C: 1SC = .9200, 5SC = .9359 Champions League D: 1SC = .1953, 5SC = .7688 Champions League E: 1SC = .9363, 5SC = .9426 Champions League F: 1SC = .9258, 5SC = .9383 Champions League G: 1SC = .9113, 5SC = .8633 Champions League H: 1SC = .7990, 5SC = -.0739 Europa League A: 1SC = -.5290, 5SC = -.5371 Europa League B: 1SC = .6188, 5SC = -.0375 Europa League C: 1SC = .5335, 5SC = .3586 Europa League D: 1SC = .5839, 5SC = .8381 Europa League E: 1SC = .4098, 5SC = .2226 Europa League F: 1SC = .6225, 5SC = .9494 Europa League G: 1SC = .0026, 5SC = .6018 Europa League H: 1SC = .5405, 5SC = .6933 Europa League I: 1SC = .8276, 5SC = .9889 Europa League J: 1SC = .0001, 5SC = .9764 Europa League K: 1SC = .7764, 5SC = .7075 Europa League L: 1SC = .8451, 5SC = .1182 The one season coefficients had an average correlation of .5615 and the five season coefficients had an average correlation of .5377, so the one season coefficients did a slightly better job at predicting Group Stage performance. Each method was better than the other method for half of the Champions League groups and half of the Europa League groups.
It could be argued that the UEFA Coefficient should be a 4-year weighted (40%, 30%, 20%, 10%) cycle, but I do prefer the five-year unweighted model.