Ok, let's break it down:
I really don't remember what DoD says about the location of the object, but I have no reasons to doubt what you say. So I agree with you, your observation makes the Atlas V hypothesis less probable that it was before your observation is taken into account. I could agree that we can expect the Dod statement with 75% probability if the Gimbal was inside the test range (then it was no Atlas) and 25% otherwise, because there are many reasons why DoD says what it says (ie.: they may simply be wrong). It's 3:1 odds against the Atlas (75% divided by 25%).
Accuracy on position of the UAP
Why 75%? Where does that number come from? Is it what you expect, based on what?
AFAIK, the DOD has not made public any analysis at all on their 144 UAP events that served as basis for the UAPTF report (which was only a summary of reports they have so far). I personally (subjectively) think that when they refer to "incursions in test ranges" is only a description of the apparent event. But to objectively know if the objects were or not actually where they apparently were, an analysis should be done all the cases and determine if that's right or not. Only then you can calculate a probability on the accuracy of that statement.
I simply don't know what value to assign, so for me this value is
unknown, could be anything between 0 and 100%.
But just for fun, my experience tells me that in UFO reports basic estimations like distances, angles, speeds, and so on are usually wrong. But distances measured by devices are often right, unless there is a malfunction. So I am going to say
50%. (I know, this goes in favor of the Atlas V hipothesis.)
But the Atlas V hypothesis starts with very high probabilities: we're 1) 100% sure it was launched in a timeframe consistent with what we know about the video,
Timeframe coincidence
The launch was on Jan 20th, at 20:04 ET. (Jan 21st, 01:04 UTC)
The Navy confirmed the gimbal video was taken on Jan 21st (see post #22).
So, this fact would make the probability of a coincidence 0%.
But, on post #23,
@Edward Current suggested the exercise date could be in UTC and someone forgot to put it back to ET, so maybe the dates do actually have a window of coincidence.
So, what probability do we assign to the Navy answering a question in UTC rather than in local time? Do we have any precedents to obtain a reality-based probability? For me this is again unknown, but if we want to play to this game, I am going to say that is unusual, so let's make it
10%.
Anway, let's assume there is in fact a window of coincidence. How long is that window?
Should we take a 1-day window coincidence? Then we have a probability of 100%, as you say, that the plane was on the air the same day the launch happened.
But, how long does a fighter stay in the air during this exercises? mmm... I'm going to take a 1-hour window. As the day has 24 hours, the probability of the fighter flying in an specific 1-hour time window is
1/24 ~ 4.1%. So that number in combination with the
10% of Navy reporting a date in UTC rather than local, is my timeframe probability.
2) I think we can be pretty confident the F-18 FLIR would have seen a glare if pointed to the Atlas V engines even if the distance was large, and 3) we can be pretty confident that IR glare in the FLIR appears as the Gimbal object does. I'd give an 80% probability to assumption 2) being true, but let's say from 80 down to 30%. For assumption 3) I'd say 100%, but let's say 100-50% instead.
IR flare
I would ask for justification of those numbers, but anyway, I can go with them.
So with my preferred numbers the probability of Atlas V being the Gimbal is 80%, with the lowest numbers I can possible conceive with the data I have the probability is 15%. The next hypothesis on the list is... uh.. what is it? this is already a difficult question... another F-18 or another nearby jetplane? This looks the best candidate to me and it has long be discussed and apparently refuted (not that I remember the details), do you agree on a probability of 1% that the Gimbal was another nearby jetplane?
I would say you should do the same exercise of breaking down all the probabilities for the jet solution that lead to that 1%, instead of assigning it directly.
I don't know what my made-up numbers finally result compared to yours. In fact, I don't think it matters, I won't even try to defend these numbers.
These numbers are simply reflecting our own biases. It's like the Drake equation, where you can plug in any numbers you like and get radically different results. These calculations only makes sense if you can objectively determine those probabilities. Otherwise it is numerology
It would me more productive to obtain such basic data like the date and time. Has anyone been able to contact the pilot/WSO who recorded the video? Is it possible to find (via FOIA, I guess) the deck logs of the ships where the planes took off from, and check the date and time the exercise took place?
Or to find
go/no-go proofs to discard hypothesis (was the video taken in daylight? Was the plane heading towards the Atlas V?...)