If it was random, you would know it. Hawk-eye has almost* always been accurate.
*Although once in NZ it didn't function probably and gave something completely ridiculous. But that just happened once and was very obvious.
If the ball has already pitched, hawk-eye continues the path after it hits the pad. This takes into account everything, including: Amount of Spin, Amount of Swing, Bounce etc etc
The only thing it can not predict is newly developing swing AFTER contact, but neither can the human eye can it? Since it has never happened.
I can give you other instances of hawk eye being inaccurate. In the 2nd test 4th innings 2010 RSA vs India at Durban. Boucher was judged lbw from Zaheer but hawk eye showed it to completely miss the off stump and so a lot of south africans unjustifiably felt hard done by. A sky sports commentator picked this up, the ball had in fact reversed in and was most probably going to hit off stump but hawk eye carried the ball along its original trajectory. The south african media being selectively analytical jumped all over this and blamed the umpire when in fact it was hawk eye's fault.
Also in the Perth test Aus vs India 3rd test 2008, Kumble trapped Symonds plumb lbw but hawk eye said it was going over and so a lot of aussie fans claimed that this equated to the 8 obvious blunders that Bucknor made during the 2nd SCG test to hand the aussies the match. There have been many other instances when hawk eye has made an apparent blunder, I see it all the time. You may think im chatting a pile of crap? But Adam Gilchrist agrees with me...and so does Mark Taylor judging by how he's laughing.
YouTube - Adam Gilchrist Commentary on 20.20 1:35
The way hawk eye works is that it takes frames of video footage from multiple cameras and uses each frame to assess the flight pattern e.g. from frame 1 to frame to frame 2 its turned 2mm, from frame 2 to frame 3 its turned 1 mm etc and thus we can predict how much it will turn. Therein lies the problem with hawk eye. If we are using it to predict turn after pitching it is severely limited. For example if Harbhajan bowls a ball and it strikes a batsmen on the pad immediately after it pitches, it is almost impossible to assess the amount of turn because there will simply not be enough footage to take enough frames of footage and hence accurately depict the ball's later path. Same applies to bounce if the ball strikes the pad very soon after pitching. Hawk eye is even more inaccurate when the ball strikes the pad very soon after bouncing when bowlers bowl dooras, googlies, topspinners etc as it will probably not even be able to register the fact that the ball was doing something different to all the other balls in the over. Hawk eye only becomes accurate to predict turn bounce etc when there is considerable time between the ball pitching and striking the pad (which will only really applies to exaggerate back foot shots). In such instances the decision becomes so obvious, that even the naked eye will be able to make a judgement...to the point that if you sat a 100 ppl in a room and got them to watch the footage that at least 90 off them would reach a consensus of out/not out. Hence hawk eye is a redundant technology.
In such instances where there is little time between the ball pitching and striking the pad, I believe benefit of the doubt should be given to batsmen as the original lbw rule required that the ball be quite obviously striking the stumps. That is the whole point of lbw. It was not designed to give batsmen out based on a statistical calculation of probabilities based on limited data. If it was then all games back in the day would have been required issac newton to stand as umpire.
Another way of saying what I'm saying is: we should not make such definitive judgments on batsmen's wickets when using a predictive model.
Also another problem with the current UDRS is that the very same decision can be given out/not out based on the original umpires verdict. How is that fair? It removes fairness and equality from the decision making process and just further accentuates the subjectivity of umpires. If you are going to use a crap system at least let both teams benefit/suffer from it equally.
Finally I'd like to finish by saying that a peer reviewed journal did a study on hawk eye in 2008 and concluded that one of the biggest problems with its use is that followers of the sport seem to treat its judgment as the "unchallengeable truth" and do not understand its limitations. Are you listening south africans who feel that ab de villiers was given wrongly out to harbhajan (durban 2010) because hawk eye showed it going over the top and australians who feel symonds was given wrong out to kumble (perth 2009) ? Compare the strength of that evidence to when symonds was given not out by bucknor who blatantly edged ishant do dhoni and the whole stadium noticed it.