Understanding the statistics of probability is a complex thing, because in essence you have to look at it from both ends at the same time - that a 1-in-1000 chance is both as likely as any of the other 1-in-1000 chances, and also can be overlooked just as equally.
The 10 minute delay before a character goes to work one morning MIGHT change the world, but 999-in-1000 chances that it won't. But it might, and could.
If Aleksandr II is not assassinated, a knock-on effect down the line could be that his grandson Georg does not get tuberculosis - it may well not be the case, but it could.
What an understanding of the statistics of probability does is free the author of a timeline to make choices and decisions. A timeline is not an intellectual exercise in determining what WOULD have happened.. It can be an intellectual exercise, if you wish, but at the same time it is an entertaining exploration into the possible. Most of the time the author is going to be faced with options of equal likelihood, and will choose one.
Choice is a curious idea to some alternate historians - ie not to the writers, but to the critics. Some people are always, and only, critics. They will argue that a choice is that - a choice. They think that there should be no choice, but that somehow alternate history is a discipline and that there is an answer to "what next", not a choice of answers but AN ANSWER.
But there isn't - there can't be. How can we know the future? How can we know the ALTERNATE future? We can guess, we can hypothesise - and writing the timeline, we can CHOOSE.
If we accept that the author's choice is important, that it is necessary, then we accept that 1-in-1000 is always the probability, for any option. That it may be 1-in-1000, or 1-in-100 or 1-in-10,000 is not relevant - it becomes equal to the other realistic options. We can choose that butterflies are working overtime and that leaving the house 10 minutes late one morning changes the world. Or we can choose that chance plays it down the middle and that Tsar Aleksandr II living into old age means that his grandchildren have a different life, in different places, and that Georg never gets TB. Or we can choose that he still does, and that maybe if Aleksandr II lives longer then one of his grandchildren end up assassinated. As long as its rational and realistic, its an equally acceptable choice as any other.
Realism and rationality obviously do matter - we are talking about equal probabilities, not a set of 1-in-100 choices on the one hand, and a 1-in-1,000,000 choice on the other. The wildly unlikely is by definition far, far less likely than the choice of an option from a set of equally probable choices, even if each of those choices is also equally unlikely.
Shake a dice - let us for the sake of argument give it 20 sides. You may get any number, but the statistics of probability are that there is a 19-in-20 chance that you won't get any number that you choose beforehand. That sounds bad - but if there are twenty of you, and you all choose a different number, then that 1-in-20 chance is a certainty for somebody.
Rick Robinson taught me this valuable rule for alternate history - that what seems unlikely may be only as unlikely as every other option. Having Winston Churchill be the same even if his parents met in different circumstances seems unlikely, but it is no less likely than any of the other options.
But having Winston Churchill grow up to become a drop-out and anarchist assassin IS less likely than other options, and would need to be justified. That justification would take the form of other changes to the timeline (chosen by the author from a set of equally likely outcomes, echoing forward) that mean that the dropout anarchist Churchill ends up with an equal probability of occurring as other likely reasons.
That's an important point - the apparently unlikely can happen if the changes to the timeline leading to it have led to it becoming an equal probability. Hitler is not explained by his being a 1-in-1,000,000 chance (which it would have seemed in 1914) but by the sequence of events in Germany that led to his being an equal probability by 1933.
The interesting thing about understanding probabilities is that it answers questions from both directions. To those who say that X is not going to happen, you can answer that it is as likely as any of the alternatives. To those who say that Y is going to happen, you can answer that the alternatives are as likely, or as unlikely, as Y is.
A proper understanding of statistical probabilities is important to being able to write interesting and believable timelines.