Quote:

>>When observing top players at play (Accu Stats) one can notice

>>that the incoming player more oftenly opts for a shot rather that

>>for a pass. It's a steady tendency. All I'm saying is that it is wise

>>to take that into account. It is wiser to leave a little more difficult

>>shot (or safety) on pushout.

>>When my oponent is 50% shooting and 50% passing,

>>THEN I know I am pushing out just right. It's not a matter of rating the

>>shot, it's a matter of rating the oponent.

>This is not an accurate assessment. You only know the shot/pass

>percentage, but not the difficulty of the shot the opponent left. If you

>know that the average shot left is a 50:50, then you can make this

>assessment. But, if the average shot left is more or less than 50:50,

>you have to reevaluate.

I agree. I'm surprised that there is controversy over this, but perhaps

different people are thinking about slightly different situations. Here

is the way that I'm thinking about it:

Suppose that you are playing an opponent who does not evaluate situations

accurately, and you leave him a situation in which if he takes the shot he

will win, say, 30% of the time, and if he passes the shot he will win 70%

of the time. If he were smart, he would pass, and you would lose more

often than you would win. But if he takes the shot half of the time and

passes the other half of the time, then he will shoot and win 30%/2=15% of

the time, and he will pass and win 70%/2=35% of the time, for an overall

winning fraction of 15%+35%=50%. It doesn't matter what the shot

difficulty is (50:50, 30:70, 10:90), as long as the player picks the good

choice just as often as the bad choice, he will end up at 50%. So from

this point of view, the "right" types of shots to leave him are not ones

where he passes as often as he shoots.

I guess what you would really like is to leave a 30%:70% situation where

the player consistently picks the 30% choice. This is what I was calling

a "cowboy" if the 30% choice involves shooting, or a "dunce" if he always

seemed to choose the wrong option. But the problem with leaving the

30%:70% situation is that he might choose the 70% option; even if he is a

cowboy, you can't _force_ him to take the 30% choice. You don't want that

to happen in a hill-hill game, for example. That is why I said that the

optimal strategy for a push out, assuming you aren't playing a dunce, is

to leave a 50%:50% situation. That way, you can't get hurt more than

50%. Even if you are playing a dunce, but one that is smart enough to

flip a coin to see which choice to take, you can't force him to give you

any advantage over 50% with a pushout.

If there is a skill mismatch, in your favor say, then you also can push to

advantage. In this case you can leave a situation that the opponent can

shoot and win, say, 20% of the time, and he can pass and win, say, 40% of

the time. The best that he can do is the 40%. But the fact that these

two fractions don't add up to 100% is not due to the pushout itself, it is

due to the skill mismatch. The pushout exploits the existing skill

mismatch, but it does not really create a new bias towards one player or

the other. If you are the weaker player in this situation, then again the

50%:50% situation should be your goal; you can do worse for yourself, but

you can't do better.

Another interesting pushout possibility is when one player has a wild

money ball that the other doesn't. In addition to the skill mismatch

bias, there can also be biases due to this asymmetry that can more than

compensate for the skill mismatch (assuming here that the weaker player is

the one with the extra money ball ;-).

Quote:

>Also, just because a shot is 50:50 doesn't mean a run is. If I know the

>person I am playing won't be able to run the table (because balls are

>frozen or he sucks), I will leave a dead in shot hoping they will clear a

>few balls for me. If I am playing either a better spread or a better

>player, I will leave a harder shot.

Yes, the percentages of winning and losing are not the same as the

optional shot percentages. Perhaps this is part of the controversy? On

any given shot, there may be several ways to pocket a ball, to play

position, or to play a safety, and there is a win/loss percentage

associated with each option. The product of all of the most favorable

individual shot options for each ball is the overall probability for the

win (well, the way I worded it this is actually the maximum, but that is a

separate topic). However, if there are more than 2 or 3 balls then this

is largely just theory; there are too many possibilities in most

situations to assess quantitatively the winning percentage in this way.

This is where judgement based on past experience must be used.

$.02 -Ron Shepard