I honestly can't tell if you're arguing against me or with me or whatnot.
Not sure if you're talking to me or SA. If you're talking to me. It's a matter of what you're trying to figure out. However, I will say I agree with you, that on an individual basis you're not ever due. Your failures on the first 9 PPs will not mean that your chances are better on the 10th. That's obviously including straight probability and not including psychological factors and factors of luck. It's possible that psychologically, by the 10th PP the players "grip their sticks tighter". However, let's not include that because that's not something that you can in any way shape or form gauge. Here are three questions that can be asked:
If the question is:
1) If you didn't score on the first 9 PPs, are you more likely to score on the 10th?
The answer is a resounding NO! Each event is independent (although that's not necessarily true in sports, but is for this example for simplicity purposes). You have the same exact chance. So if your PP sucks and you have a 10% chance every time to score. Then on the 10th PP you have a 10% chance to score. So in that sense, I believe this is what you're talking about. You're not ever "due" to score. The chances of you scoring aren't higher in this instance.
2) Does a team have a better chance to score if they get 10 PPs than if they get 9?
The answer is YES. 0.9 to the power to 10 (chances you go 0 for 10) is lower than 0.9 to the power of 9 (chances you go 0 for 9).
3) Does a team have a good chance to go 0 for 10 on a PP in general?
This depends on what the probability of success and failure on each PP is. If probability of failure is absurdly high like 99%, then the chances of failure are still absurdly high. 0.99 to the power of 10 is still about 90%. However, if it's not absurdly high and you drop it just to 90%, (which is still really high), you get 0.9 to the power of 10. That's about 35%. So even if your PP blows chunks, you have a 35% of going 0 for 10. Now that's still the highest possible individual outcome. As I said there are 1,024 outcomes (2 to the power of 10). Each of the other 1,023 outcomes are less likely to happen. However, if you take all of the other 1,023 outcomes you get 65% (and that's significant, each likely outcome isn't).