"Virtually certain"

Now even in this example - if an opponent hit this shot and claimed his ball must be in the water I'd say no - sorry. May seem likely it is in the ditch/burn but tough. Am I wrong?

I think so , maybe not in the letter of the rules but for the reason Bob mentions below ..

I know its not your job to find my ball , but in the situation mentioned , where else can it be ?

If that was me who hit the shot and you disagreed, I would ask you where you think ball is if not in the hazard.
 
If that was me who hit the shot and you disagreed, I would ask you where you think ball is if not in the hazard.

Surely it's not for me to say where the ball is? It could be anywhere as it disappeared out of sight. What if I didn't think it was quite as 'straight down the middle' as my playing partner/opponent claimed it was?

This is why I thought you had to see the ball entering the water or actually heading into it as a matter of fact. In the case of an out of sight ditch/burn neither applies as I have no sight-line to the water hazard.

A similar scenario has happened to me in a match and I said no. I was apologetic and said it would seem that the ball could well have gone in the water - but neither of us saw it go in. The situation was one where there was a shallow 12ft high transverse hedge with ditch/water hazard at it's base to the left of the fairway - the rough was cut back from the ditch about three feet both sides. My opponents tee shot was pulled left and looked to be clearing the hedge but then seemed to hit the hedge about half way up. We hunted high and low both sides of hedge and ditch, and in ditch but couldn't find it. He claimed it must be in the water in the ditch - I said no as I didn't see it go into the ditch and it wasn't heading into the ditch when it hit the hedge. Tough. But thems the rules - I said.
 
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Surely it's not for me to say where the ball is? It could be anywhere as it disappeared out of sight. What if I didn't think it was quite as 'straight down the middle' as my playing partner/opponent claimed it was?

This is why I thought you had to see the ball entering the water or actually heading into it as a matter of fact. In the case of an out of sight ditch/burn neither applies as I have no sight-line to the water hazard.

A similar scenario has happened to me in a match and I said no. I was apologetic and said it would seem that the ball could well have gone in the water - but neither of us saw it go in. The situation was one where there was a shallow 12ft high transverse hedge with ditch/water hazard at it's base to the left of the fairway - the rough was cut back from the ditch about three feet both sides. My opponents tee shot was pulled left and looked to be clearing the hedge but then seemed to hit the hedge about half way up. We hunted high and low both sides of hedge and ditch, and in ditch but couldn't find it. He claimed it must be in the water in the ditch - I said no as I didn't see it go into the ditch and it wasn't heading into the ditch when it hit the hedge. Tough. But thems the rules - I said.

I think it's easiest to look at it this way -

It's relatively easy to put together a scenario whereby you don't see the ball enter a water hazard, but you are all absolutely certain that it's in it; 80 yd wide fairway with a clean cut small pond right in the middle, just over a slight brow, B&W marker post in the centre of the pond and another 200 yds of fairway beyond it. Player's ball flies straight for the marker post as it disapears over the brow...both players expect the ball to be in the pond, and sure enough when they get to the area the ball isn't to be seen anywhere.

So we establish the principle that it's 'only' virtually certain that the ball is in the water, but that that's sufficient for the purpose of 26-1.

How far you come away from the above situation, through the other examples you have written and back to the origional question, is a matter that can only really be dealt with on the evidence available at the time. I agree with those who raised concerns based on the variables involved in any ball hitting any tree in the case of the original post as an example; without being there you can't really rule.
In the case of the hedge, a similar situation arises; you have a ball seen entering a hedge halfway up - from that point I would want positive evidence that the ball was in the water to rule that 26 applied, unless the hedge was in the middle of a huge water hazard and part of the hazard!

Finally, you will see in various places in the rules situations where a player has correctly, in the eyes of the rules, proceeded under 26-1 on the basis of virtual certainty and the origional ball is subsequently found outside the water hazard. It is accepted that this can happen, and the status of the original ball remains as lost in the water hazard and play continues with the dropped ball.

Virtual certainty is a practical solution to a number of issues within the rules in the absence of absolute facts, no more and no less.

Finally, I would also point out that a number of balls clearly seen to land in a water hazard, only to be subsequently found outside as a result of bouncing out again (sometimes you can predict and see it bounce, other times it's more a case of 'unbelievable!') - so seeing it in isn't the answer either.
 
A lost ball and a ball lost in a hazard are 2 different things hence the virtually certain rule. Same penalty but replayed differently ie from original position for lost ball and at the hazard/DZ for being there.

You are quite right to pick me up on a careless use of "lost" in the context, but the tongue in cheek question as to how you identify a lost ball equally applies to a ball "not found". It wasn't a serious comment though.

The obvious reason for the "ball not found" procedure in Rule 26-1 is fairness. If a player puts his ball in a water hazard and it is known etc to have gone into it but can't be found, it is only fair that he is allowed to proceed in the same way and under the same penalty as the player whose ball goes into the water hazard where it can be seen and identified.

We might note that R26-1 does not mention a "lost ball" but a ball "not found". It's an important distinction. If you know your ball is in the water hazard but you can't find it, it is not "lost" in terms of the Rules and Rule 26-1 applies; if you think it is in water hazard and after consideration decide you are virtually certain it is there, again it isn't "lost" and 26-1 applies; but if after consideration you decide you can't be virtually certain it is in the water hazard, the ball is "lost" (after 5 minutes searching etc etc) and Rule 27-1 applies. In Rules terminology, you can never "lose" a ball in a water hazard - which is small comfort when your brand new shiny golf ball has just drowned in a pond.

This is why I thought you had to see the ball entering the water or actually heading into it as a matter of fact. In the case of an out of sight ditch/burn neither applies as I have no sight-line to the water hazard.

Not necessarily. My illustration of a situation where there is just nowhere else your ball might be than in a water hazard that was out of sight when you played is sound. I don't claim much originality for it since if you take a look at Decision 26-1/1.3 you will find a remarkable similarity. ;).

It is a clear day, with good visibility. A player's ball is struck towards a water hazard, which has closely mown grass extending right up to its margin. The ball is observed to fall out of sight as it approaches the water hazard but is not seen actually to enter it. From a distance, it can be seen that there is no golf ball lying on the closely mown grass outside the hazard and, from both prior experience and a reasonable evaluation of current course conditions, it is known that the contour of the ground surrounding the hazard causes balls to enter the hazard. In such circumstances, it is reasonable for the conclusion to be reached from a distance that the ball must be in the water hazard.
 
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