I think it's important to know your odds on every shot...what do you think?
You may want to start trying to "see it." Knowing your own abilities and limitations will definitely help your game.
Also, you may not get to shoot a shot 10 times in a row, but you definitely get to shoot a shot many times over the course of competing. Lets say for example, you are playing in a hill hill game in the tournament finals, you come across a shot you've been practicing, but still are having issues with, you know you miss this shot as much or more than you make it. So, would you still take this shot since with your theory you only have to make it this one time? (obviously if no easier safety is available, you shoot)
If you would still shoot this shot, you need to take some time to practice away from the table. Practice mentally making yourself learn to think about other options before you just go firing away.
I see players do this in 1p a lot. They see a shot high level players would shoot routinely but its not yet in their arsenal. They shoot the shot and either miss and sell out, or they get the cue ball position wrong, don't block the ball, and their opponent just knocks the ball up table. If they knew their own capabilities, they could have picked a better shot, and save this one for the practice table.
This is akin to some bad poker player saying "every hand is 50/50, I either win or I lose." Those players generally go home broke, and your theory is the pool equivalent.
The missing variable in your equation is whether a safety is available, and if so the odds of executing the safety vs. the odds of making the shot + position for next ball.
-roger
A player needs to see all the options he / she got on the table and then compare which one is the best to take. If a dead lock safety is easier than making the shot then trying to make the shot is a silly mistake. Everyone seems what they have on the table differently. The power to see comes from how well a player understand the game and their ability and calculating odds are a part of that analysis.
IMO the only way a player is going to be good at calculating odds if they understand their "true potential" on the pool table. But, how many players except for pro's / top amateurs have that ?
Calculating odds also depends on the type of game you play. When you are playing straight pool / 1- pocket and if you take a low percentage shot that might change the whole game. The same can be said for rotation when you get close to finishing the game. If you have a tough 9 ball shot (60% chance of making it) and virtually no good safe, what are you going to do ? play a "safety" and give your opponent a chance to go for it ? I would rather shoot the 9 ball then trying to play a phony safe.
At the end of the day the only thing that matters in pool is making the shot. That will make you win. Sometimes you'll have to "go" for a shot no matter what and sometimes thinking about your other options is better.
I think there is a thin line between being fearless and being stupid on the pool table. The funny thing is most of the time you will loose a game not because you missed a tough shot but cuz you missed an easy one (the one you can make all day long). And at that moment of time when you missed it all this talk about calculating odds goes right out the window.
I think it is good to have at least a rough idea of your chances. For those who didn't follow the description above, here is a diagram of a 75-degree cut shot off the foot spot from about the center of the table. I doubt that most players would be willing to give up 10-1 money odds on the shot, even top players.I run into situations very often when someone thinks that a particular shot should be made 90% of the time. Etc.
The shot that came up recently was like the 9 on the break spot, and cue ball around the middle of the table...only it was a sharper cut than that...say, 70-80 degree cut into the corner. A friend I was playing said "I can't believe you missed that shot...that's a basic shot...you should make that every time"
I explained that its a 70% shot...he insisted that its a 90% shot. I bet some cash on it,
When I set the shot up and challenge him to shoot it 10 times, he made it 7 out of the 10... And then blamed boredom and fatigue.
It's amazing to me how many times folks over-estimate the real odds of a given shot.
I think it's important to know your odds on every shot...what do you think?

You need to have a good idea of your shotmaking percentages with all levels of your game, from best to worst performances. Knowing these is what dictates how you play; safe, all out shot or 2 way shot, along with so much more.
If you face 4 shots where you should make each ball 90% of the time , you likelihood of making all 4 is only %65.
If you face 4 shots where you should make each ball 85% of the time the odds of making all 4 drops to 52%.
With 4 shots at 80% potting percentage, a runout occurs only 41% of the time.
You need to be aware of the effect of poor position play and how any shot with a 80% or less chance of being made really hurts runout percentages.
Yes most peoiple overestimate their shotmaking percentages ...and then wonder why they don't win. These are often the middle of the road players that always seem to pass on winning safetys, even when balls are tied up later in the rack.
Okay so what if you're faced with 4 shots and three of them are 100% and one of them is 10%, what are your odds?
Let's be clear. Nobody actually is calculating any odds in pool. This isn't like poker on EPSN where the odds of winning are clearly displayed. This is pure judgement and the only question you should ask yourself is, "Which way will get me the win the easiest?" That's the only question that matters. All this talk about players calculating stuff is silly.
10%, right? You multiply the probability of (independent) events to get the probability that they will all happen, and 1 * 1 * 1 *.10 = 10%.
I think a lot of players (OK, I'm talking about myself) make the mistake of shooting a 70% shot and then a 90% shot (.7 * .9 = 63%) rather than just taking the easier 90% shot first and settling for a little bit harder 80% shot on the second ball (.9 * .8 = 72%).
Most people I'm sure don't attach numbers to shots - though it may not be a bad idea - but don't you think most people have a feeling about their chance of making various shots? And doesn't that figure in to their shot choice and strategy?
I developed a "Shot Matrix" analysis tool (in the Safety Toolbox) to determine what to do in common playing situations and when to go on offense or defense.
Key is the realistic evaluation on success based on 10 attempts of the shot.
On days when everything is dropping - you can attempt lower percentage shots. But when your game disappears, shorten up on your confidence level - a lot.
For example - on average, you can make a shot 50% of the time. On good days, this can be 80%. On bad days, it will be less than 30%. Make your playing decisions based on your shooting at that time, not some memorable experience where you couldn't miss blindfolded.
I think it is good to have at least a rough idea of your chances. For those who didn't follow the description above, here is a diagram of a 75-degree cut shot off the foot spot from about the center of the table. I doubt that most players would be willing to give up 10-1 money odds on the shot, even top players.
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One way to learn your percentages for a particular shot that is faster than just shooting a shot over and over is to use a technique called "progressive practice". This works for shots that can be made harder or easier by varying something like distance. In the simplest form, it gives you your 50% point for some kind of shot (such as shots off the spot with cut angle as the variable). See item 4 under http://sfbilliards.com/misc.htm for more explanation of how this works.