I suspect that the last couple of paragraphs of your post are ultimately about the Laxman non-out that occurred earlier in the day. The fieldsmen thought that it was out, the umpire gave it not out, the batting side called for a review, and the Hot Spot did not show anything, so the umpire was quite correctly not overruled, although Shane Warne (commentating) said that he had a hunch the batsman had actually hit it. The controversy occurred when “Snicko” was run on the same ball by the television company a few minutes later, which showed that Laxman had clearly hit it.

So India gained one and lost one over the day, I suppose.

With respect to reviews of LBWs, l have no problem with technology being used to find out what happened. There are four factors that are taken into account when deciding if a batsman is out LBW. Firstly, where did the ball bounce. (Did it pitch outside the leg stump, in line with the stumps, or outside the off stump?). Secondly where did the ball hit the batsman? (Once again, leg, off, or in front?). Thirdly, did the batsman hit the ball before it hit the pad? Fourthly, was the ball going to hit the stumps? Replays should be used to check on the first three, so Harbhadjan Singh should have been given not out. But as you say, his team did not want this kind of review.

However, I do have problems with using computer software to predict the path of the ball and using this in decisions, for reasons I have stated elsewhere. This shouldn’t prevent replays being used for the uncontroversial bits, though.

If by “ultimately” you mean that was what I was “ultimately” thinking about, no.  I missed all that.  I did not pay exclusive attention to the cricket either in the later afternoon (see the posting) or earlier.

The heart of it is that a snick is more likely to be missed than invented, either by an umpire or by technology, but especially by technology.

And you seem to agree:

Umpire: Laxman not out
Hot Spot: Laxman not out
Snicko: Laxman out
Jennings: Laxman out

You score it out by one vote to two (a bit like Thatcher outvoting everybody else on spending cuts).  I.e. you say that if anyone or anything spots a snick, it should be out. I pretty much agree.  Snicko would not make it up, is the basis of the argument that Laxman was indeed out.

Although, I do think an umpire often does see a snick that didn’t happen.  More to the point: hear.  Which is why I prefer technology for caught behinds, if technology says out.

Also, has there ever been a case where Snicko said not out, but Hot Spot said definitely out?

Re Harbhajan, did Hot Spot agree with the slomo cameras that Harbhajan was definitely not out?  I presume so.

And am I correct in assuming that the problem with Snicko for reviewing is that it is, for the moment anyway, too slow in yielding its results?

I think everybody was entirely correct in the Laxman decision. The onfield umpire had to give the batsman the benefit of the doubt as he could not see the edge, and neither the replay nor Hotspot gave a reason for the onfield umpire to overrule him. Entirely correct in terms of process and no person made a mistake, but none the less the wrong decision in terms of what likely happened, which we know because there was more technology that was not used in the decision. (I think that it is a “length of time taken” reason why snicko is not used, so perhaps that can be fixed at some point. It is not beyond belief that people will find some way to game that one, too).

With the Harbhajan decision, it was trickier because the umpire made a clear mistake of a kind that a good umpire is not supposed to mistake and that a review system is supposed to overrule. Once again, though, a situation where all available technology was not ruled, and we likely got a wrong decision.

If Laxman had hit it, been given out, and then the pictures and Hotspot had not shown an edge, then the on field umpire would have been overruled, as I understand the rules. This is less likely to happen, though, as a batsman who knows he is out and who has been given out is unlikely to ask for a review, particularly given that this is likely to be seen as unsporting if the review confirms the decision. So in the case of catches, the fact that Hotspot is prone to false negatives is less of an issue. (Except, inevitably, someone in a crucial situation will ask the question anyway, particularly if Hotspot is known to make mistakes).

And of course in the case of an LBW, the question of whether the batsman hit it can have the opposite effect. Edge = not out. No edge = out. So if Hotspot is prone to false negatives, then it is going to give batsmen out when they are not out in LBW situations. You can have different rules for Hotspot in LBW than catch situations, but things are then getting complicated.

I think the problem is that the players have learned to game Hotspot, probably due to this business with the Vaseline. I think it either needs to be fixed, replaced or supplemented with something else, or removed from the decision process.