"A Mathematical Look at Sports" Statistics in Basketball Thanks for listening! Conclusion Statistics in Track & Field Krystal Statistics in Baseball Harrison Statistics in Football Cameron Introduction to Statistics Based on sampling of numbers, the idea of statistics is a gathering and collection in order to present the numerical data as a whole.

Within sports, statisticians calculate all attempts, ranges, and ability to provide statistics for each individual person, or the team in general.

Statistics allow for rankings, and a distribution and understanding for talent. Introduction to Probability The chances of something occurring, the relative frequency.

Based on factual information, or a collection of different information, what the outcome will be.

For sports, the statistics collected, shape the probability, and the chances of it occurring or not occurring. Importance of Statistics in Basketball:

Records a players attempted and made shots

-Three-point shots

-Free Throws

-Inside Shots

-Blocks

-Steals

-Assists

Sets individual players at their standing.

The team based on wins in their standing within the league.

Compare and contrast players of like positions. It helps shape their accuracy, along with improving different aspects of their individual game.

The gathering of all this information by attempted and successful creates their overall statistics.

By dividing the attempted by the made, creates their percentage for a specific shot. For example, the Three-Pointer. The statistics drive the outcome of the probability.

Based on the statistics that a player has, the statisticians or even viewers can slightly predict the outcome.

The probability that is shaped around the statistics gives the player an idea of what to work on, and what shots to take or not to take during the game.

Basically, the chances of the outcome. Probability in Basketball This shows his prior experience based on knowledge of statistics and skill, and why the probability for the outcome to be successful is so high. Importance of Statistics in Baseball:

-Records a player's Batting Average as well as...

Pitcher's Earned Run Average (ERA)

On Base Percentage (OBP)

Base On Balls (Walks)

Slugging Percentage (SLG)

Runs Batted In (RBI) and Runs Scored (R)

Fielding Percentage (FPCT)

and many more!!

Sets individual players at their standing.

The team based on wins in their standing within the league.

Compare and contrast players of like positions. • Usually we just look at Batting Average (BA) and Runs Batted In (RBI) as the only important forms of statistics in baseball.

• Sabermetrics - the recent use of sabermetrics has created statistics drawing from a greater depth of player performance measures and playing field variables. Sabermetrics and comparative statistics attempt to provide an improved measure of a player's performance and contributions to their team from year to year, frequently against a statistical performance average.

• Moneyball - movie starring Brad Pitt and Jonah Hill. Billy Beane (Manager) of the Oakland A's in 2003 used a team analytical, evidence-based, sabermetric approach to assembling a competitive baseball team, despite Oakland's disadvantaged revenue situation. OBP and SLG more important than speed and contact... also cheaper. Ended up making the playoffs. • Ex. of Moneyball Sabermetrics:

- Buster Posey in 2012

- 24 HR, 103 RBIs, .336 BA, .408 OBP

- Joe Mauer in 2012

- 10 HR, 85 RBIs, .319 BA, .415 OBP

- Has the advantage and is cheaper

• There is also now more emphasis on Defense-Independent Pitching Statistics, including Defense-Independent ERA (dERA), in an attempt to evaluate a pitcher's performance regardless of the strength of the defensive players behind him. In football, statistics are used to rank individual players and teams to their success and value in the league.

The various data collected can help compare different players of the same position.

Set a standard for success of teams and the league. Different areas are looked at for the various players by statisticians.

1. For Offensive Linemen:

- Sacks Allowed -3rd Down Conversions

- Sack Yards Allowed

- QB Hits

- Touchdowns

- Interceptions

- Tackles Loss

- Red Zone Successes 2. For quarterbacks, we can analyze all these things and successful/non-successful passes, as well as sacks avoided/sacks.

3. For Defensive Linemen:

-Tackles - Interferences

- Assists - Fumble Recovery

- Sacks - Force Safety

- All of these are helpful in ranking the players, helping shape their accuracy, and establishing salaries and the value of each position. By measuring these different elements to each position, we are able to also figure out the probability that any given player will succeed, such as the likelihood that a particular quarterback will throw a successful pass.

Stats and probability can help the players to better themselves.

These values are also very important for fantasy leagues who use these statistics to determine the best players and make their own most successful teams. Sprinting The sprinting ability of track and field can be measured by the mass of the runner, the distance in time of the race, and the runner’s velocity.

The formula to determine the motion of a runner is: D=P/k [T-(1/k)(1-e^kT)].

The motion of the runner determines how fast the runner can potentially be. Pole Vaulting Event using a flexible pole to aid the athlete to jump over a bar.

Individuals use physics in order to determine their maximum potential height in this event which can be used to predict the results of track meets.

To do this, you must set potential energy formula and the kinetic energy formula equal to each other to solve for x. Using equation to find max height mgx = 1/2 mv2

(18.8)(9.8)(x) = 1/2(18.8)(2.31)^2

(9.8)(x) = 1/2(5.3)

9.8x = 2.7

x = 28 feet What the results tell us? If it were humanly possible to convert all of one's potential energy into kinetic energy, Andrew's maximum height would be 28 feet.

Kinetic energy is lost because of friction and air resistance.

Andrew's realistic maximum height is approximately 16 feet after taking these factors into account. Why are probability & statistics useful? Individuals are able to determine talent and physical ability in sports such as Basketball, Baseball, Football, and Track & Field.

Predictions of game results can be made.

Career goals for athletes can be set based on the math that is used.

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# Probability and Statistics in Sports

Math 131

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