#### Skin

##### Verified Member

- Joined
- Sep 11, 2008

- Messages
- 2,149

**Skin**: If you don't mind, I'd like to ask you the simple question again about the one-pocket pool game to get your math analysis.

__The scenario__:

An even game between two players of the same skill level is 8-8. That is, each player must make 8 balls in his pocket before the other does to win. If a player fouls in any way, the penalty is he must remove a ball from his pocket and place it on the foot spot at bottom of the table where the balls are racked and he no longer gets credit for making that ball.

So, the foul penalty in an even game at 8-8 is each player is penalized one ball per foul.

Now, suppose the game is handicapped to make it an "even" match between two players of different skill levels. The skilled player (S) must make 18 balls and the unskilled player (U) must make 4 balls to win. What do you figure is the fair penalty for each player on a foul, determined before the game begins? Is it still the same as for an 8-8 game (1S:1U) or should it be adjusted to match the new percentages of balls needed to win (4.5S:1U)? Is there a way to be certain of this mathematically that you know of?

**Probability Expert**:

*First of all, I can take away one of the words above (the 8th-to-the-last word in you final question): certainty.*

The problem with probability is it AVERAGES to that level; each event might vary widely from the next.

So, if you are counting on the stated odds, you probably will be wrong.

True, you are best to guess the odds (rather than any other number) because they happen more often than other odds you would hold to (because the bell curve event mean is the most often occurring).

How wrong you are depends on the magnitude of the standard deviation (or standard error of the mean); if it is small, you will be CLOSER to certainty.

To answer your question, we need to ask two sub-questions, very similar to the ones we discussed yesterday (or was it Monday?).

1) Does the overall ball handicap between two opponents incorporate the propensity to scratch?

2) Is the likelihood to scratch the same odds as the skill to pocket balls?

You can venture an answer to these questions if you know the demands of the game, what level each player has “mastered” the individually-identified features of excellent play, as well as which of these features are employed with “scratch” strategy and error.

Even if it is incorporated into the overall handicap, scratch handicap is unlikely to be the same as overall handicap between the two players.

Overall handicap is estimated from data of competitive play between these two players or competitors in-common.

This is somewhat of a moving target because there is a “reactionary” aspect of playing a different player, employing slightly different strategy.

Also, some players improve their play faster than others.

Similarly, scratch handicap data can be collected during match play by recording the circumstances, advantages, and disadvantages of scratch strategy and error.

You cannot answer the question until these data are collected - it is a unique feature of play between these two opponents.

I would guess some players tend to scratch more than others. This is the nature of data collecting. However, this does not get us much closer to the answer to your original question (or the answers to the two sub questions).

So, my main answer is: collect data and we will see what we have.

Record under what circumstances, employing what strategies, and making what mistakes a player scratches.

I’d be glad to sift through your first set of data with you!

The problem with probability is it AVERAGES to that level; each event might vary widely from the next.

So, if you are counting on the stated odds, you probably will be wrong.

True, you are best to guess the odds (rather than any other number) because they happen more often than other odds you would hold to (because the bell curve event mean is the most often occurring).

How wrong you are depends on the magnitude of the standard deviation (or standard error of the mean); if it is small, you will be CLOSER to certainty.

To answer your question, we need to ask two sub-questions, very similar to the ones we discussed yesterday (or was it Monday?).

1) Does the overall ball handicap between two opponents incorporate the propensity to scratch?

2) Is the likelihood to scratch the same odds as the skill to pocket balls?

You can venture an answer to these questions if you know the demands of the game, what level each player has “mastered” the individually-identified features of excellent play, as well as which of these features are employed with “scratch” strategy and error.

Even if it is incorporated into the overall handicap, scratch handicap is unlikely to be the same as overall handicap between the two players.

Overall handicap is estimated from data of competitive play between these two players or competitors in-common.

This is somewhat of a moving target because there is a “reactionary” aspect of playing a different player, employing slightly different strategy.

Also, some players improve their play faster than others.

Similarly, scratch handicap data can be collected during match play by recording the circumstances, advantages, and disadvantages of scratch strategy and error.

You cannot answer the question until these data are collected - it is a unique feature of play between these two opponents.

I would guess some players tend to scratch more than others. This is the nature of data collecting. However, this does not get us much closer to the answer to your original question (or the answers to the two sub questions).

So, my main answer is: collect data and we will see what we have.

Record under what circumstances, employing what strategies, and making what mistakes a player scratches.

I’d be glad to sift through your first set of data with you!