I am not sure what type of proof for line movement you (all) want, but if you have read what I stated previously, then here is the detailed summary.



explanation:
DPS - the difference between closer and opener, from the standpoint of a home team (+2 means the home team was more favored - meaning the line moving in this direction - from the opener to the closer, eg went from -5 to -7 or from +8 to +6, while -2 means away team was more favored from op to clos)

N - number of instances

p-value is the probability value derived from two-tailed binomial distribution and is the probability that the result is due to a chance


As you can see from the table, the winning % ag openers increased along with the magnitude of line movement for EVERY single bracket, meaning that if one could correctly predict line movement, he/she would do very well in terms of win%, eg for line movements bigger than 2 (2,5 and more) you would achieve 56% ATS, fading movements smaller than -1 you would go 55%, smaller than -2 57% and smaller than -3 almost 64%. Of course noone is able to predict every line movement, but this is the definite proof that betting good numbers before they move and assuming you correctly predict the direction (and perhaps magnitude) of the movement you will end up with a huge profit.

As for the closers, it can be seen that for every line movement magnitude, the 'bias' from openers was removed (not a single win% is significantly diff from 50%) and in this regard the closing numbers are coin flips, the value has gone. This is the proof of market efficiency for closing lines as well. If it was not true than you would not see signif differences in openers and closers win%, or even worse, you could see the inverse relation (meaning the line moves in the wrong direction and closers are biased). Evidently, the latter is not the case. If you want you can replace openers and closers with the line before and after it has moved, respectively (I hav had only data on openers and closers, but the logic is the same here)

Now, I am not stating anything about early / late movements caused by public / sharp / bookies playing around or whoever. I have not researched it and do not claim to know the reason for those movements. Of course I have heard and read a lot of theories regarding those (such as greek being one of the sharpest books, betting% theories and huge bets moving lines, RLM and so on), but I havent had sufficient data to examine this. What I have examined is the efficiency of the NBA PS market. The result you see is an exerpt from my thesis and it was a fully academic research, so was the methodology (mainly economic and econometric journals, as well as one book about sportsbetting). I also examined teams records and simple betting strategies, among others, but as far as line movement is concerned, i think this is enough proof for validity of it (of course the way I - and other reasearchers - defined it)