Looks interesting. The discussion ended over 4 years ago. On google I do not find much for Endurance Index nor Endurance Parameter Ratio. The paper from which the concept is taken and referenced in the discussion was behind a pay wall :-(
To your knowledge, is the EI (or endurance parameter ratio) used and to what purpose from a practical point of view (certainly not widely, please correct if I am wrong)?
From a modeling side it seems a bit fragile and only valuable if your data contains enough maximal efforts to estimate CP and W' correctly.
For estimating CP I understand that maximal efforts between 3 and 12 minutes (or 2 and 20) are crucial (taken frequently, e. g. every 4-6 weeks).
For W' exhaustive tests over which durations are recommended (certainly such that you are working above CP, so is 3 min maximal already enough or would adding tests of 1 min, 90 Sek, 2 min. add to more robust estimates)?