Thought 2: Probability (on chance vs skill)

From Google Dictionary

prob·a·bil·i·ty/ˌpräbəˈbilətē/Noun

1. The extent to which something is probable.

Mathisfun.com describes probability as:

Probability is the chance that something will happen - how likely it is that some event will happen.

Sometimes you can measure a probability with a number: "10% chance of rain", or you can use words such as impossible, unlikely, possible, even chance, likely and certain. 

This is in accurate definition, however, I feel that it is incomplete.  This makes probability seem all chance based.  Probability originally began as a tool to understand games of chance.  Since then many advancements have been made and now probability and statistical sciences are used in almost every industry.  One of the evolutions of probability was its application to sports and sports betting.  Let's use basketball as an example:  In basketball the major number expressed as a percentage is shooting percentage.  An average shooting percentage is around 45% for a team, however, this has much bearing on how well the opposing team is playing.  So instead we shall use free throw shooting percentage.

Comparison:

Free Throw % Vs. Dice Rolling

Dice Rolling:

Assume we're rolling two six-sided dice.  A successful roll of the dice in our game is a 7.  So lets analyze our chance of winning.  There are two six-sided dice, so that means our chance will be our winning combinations divided by 6*6=36.  This is because there are 36 total combinations, so if we divided winning combinations by total combinations we have our chance of winning.

So to win we could roll a (given by dice 1 result, dice 2 result):

1,6

5,2

4,3

3,4

5,2

6,1

So, there are 6 total winning combinations of a possible 36:  6/36 = 1/6 = 16.67%

Now, I can claim over the long run that 16.67% of the time I play this game I will win.  I can bet accordingly on the outcome of the game.  If the odds pay me 6 to 1 (I receive 6 dollars for every 1 I bet) then the game will be a fair equal value game.  In the long run I should walk away with just as much money as I put down.  This is because on average (assuming 1 dollar bets) it will take me 6 bets to make 6 dollars.

This game is easy to see that the probability is all chance based.

Free Throw %:

In the game of basketball, if a player is fouled while shooting or a team has fouled excessively in a period of time, players are alloted free throw attempts.  A free throw is shot from the free throw line 15' directly in front of the basket.  Players all shoot varying percentages from the free throw line so this indicates that their individual probabilities of making the shoot are different.  So now in this game, chance is less involved as skill is.  Lets look further:

Steve Nash who is widely considered one of the best free throw shooters in the NBA shot 91.2% from the free throw line this season.  Dwight Howard, known for his size and aggressive interior play, shot only 59.6% from the free throw line.  So to get rid of the chance argument here, if one claims free throws are based on chance then Steve Nash shotting 30% better with free throws then did Dwight Howard was just a fluke, Steve Nash got lucky Dwight Howard got unlucky.  However, this clearly is not the case as it happens every year.  This means that this game is affected more so on player skill then by chance.

So now we can say:  Steve Nash has a 91.2% chance of making a free throw.  I still don't like it.  It sounds like Steve Nash isn't responsible for his misses.  91.2% is absurdly high, but it should still be phrased like this:  Steve Nash shoots 91.2% of his free throws correctly.  The result of a correct free throw is a make, the result of an incorrect one is a miss.  Steve Nash is responsible for both the makes and the misses it isn't controlled by chance it's controlled by him.  Over the long run, we begin to see a pattern in the 'chance a player will shoot correctly'.  So, over Steve Nash's career he has shot correctly 90.4%, or Steve Nash is 90.4% a perfect free throw shooter.  Now, we can use this to predict if he will make these shots in the future.

Free Throws are of the simplest skill based probability examples because there is no opposition like in most other cases in sports.

Hopefully this clears the air a bit on chance vs skill based probability.  Any feedback or questions please post below.