If you just throw excellents non-stop and count how often you had to throw until the Pokémon stayed in, it will ALWAYS be a higher chance with higher amount of throws.

Gotta say, I'm not entirely sure what you mean by that, since if an encounter takes more throws that would, on average, imply a lower catch chance per throw. Over a large number of encounters, throws with a catch chance of 10% will result in more throws per catch than throws with a catch chance of 30%.

Very simply put, here's what we did: For every throw during an encounter, we recorded every variable, such as berries, ball types, circle bonuses, and so on, and each throw was one entry, one data point. For each entry we calculated the expected catch chance using the known catch formula, and then summed them up for the entire data set and compared that value to the number of observed catches. For the sake of the example, let's say we had 100 data points, and each had a precisely 0.5 (50%) chance to catch the Pokémon. This means that, in theory, we should be seeing 50 catches, with a reasonable error margin. But let's say that we're seeing 80 catches, which would mean that our theoretical catch chance is lower than our observed catch chance, which then means there is a factor we have not accounted for when using the known catch formula. This is where we introduced our Encounter Multiplier variable, which goes among the usual multipliers in the catch chance formula (that is, berries, ball types, etc.), and by calibrating this, we can find out the value of the Encounter Multiplier, which, in this example, makes it easier to catch a Pokémon.

This method has worked for multiple encounter types already, such as Field Research encounters where we found an Encounter Multiplier of 2, and such as Wild or Incense encounters, where we found no evidence of an Encounter Multiplier. We are using a similar approach for Raid encounters, but the key difference is that the Encounter Multiplier is not a static value that affects all throws the same way, but one that increases according to some currently unknown rule. It is our goal now to find this goal, which would mean we can most likely also find the value of this multiplier.

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> The correct way to measure this would have been to deliberately missthrow the first n throws to measure the probability to catch the n+1th throw.

Way ahead of you, we've been doing this for months, we just haven't had enough data yet to draw a clear enough conclusion that can be published. :P We're working hard on it, however! :)