Triplett - Sports Questions 1/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 47 / 48

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving... ()

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Question

Points

1	2	3	4	5	6	7
2/2	18/18	2/2	4/4	10/11	2/2	9/9

Total

47/48 (97.9%)

Instructions

The WebAssign Sports Question Bank features sports-themed math and statistics questions designed to increase student engagement by using real-world data. The question bank covers a wide range of sports from bowling to cricket and features step-by-step tutorials and a glossary of terminology as a resource. This content is suitable for any algebra through precalculus course or introductory statistics course and is available free for WebAssign users.

Questions 1-4 are examples from an algebra course level, question 5 is suitable for precalculus courses, and questions 6-7 are applicable to statistics courses.

Question 1 is an application from football that uses a formula (QBR) to rate a quarterback's performance. The problem is randomized to use data from the most famous quarterbacks and the level of math is suitable for algebra courses.

Question 2 uses a stepped approach that takes students through an activity requiring them to use different methods to compare hitting performance of baseball players. This algebra-based activity shows how different ways of measuring performance could result in different answers to "who is the best baseball player?"

Question 3 gives algebra students an early introduction to predicting the number of wins a hockey team will have from one year to the next, using real world data.

Question 4 gives algebra students an opportunity to learn how to score bowling and to see the benefits of bowling a spare or strike.

Question 5 is a precalculus activity that uses two different methodologies to predict the number of wins a baseball team will have. One approach uses Bill James' Pythagorean Formula and the other uses marginal runs. This questions steps the students through the various methods and asks them to compare their results at the end.

Question 6 is an application from statistics that uses z-scores to highlight height differences between NBA and WNBA players.

Question 7 is an activity that uses wins and goals-scored data of various Premier League soccer teams in England to step the student through modeling how to estimate the number of games a team would have won based on goals scored. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 2/2 points | Previous Answers ATSports1 1.1.002. My Notes

One way to rate a quarterback's (QB's) performance is by using quarterback ratings (QBR).

NFL - National Football League

QBR_NFL =

COMP

ATT

· 100 − 30

/20 +

ATT

· 100

/5 +

9.5 −

INT

ATT

· 100

/4 +

YDS

ATT

− 3

0.06

NCAA - National College Athletic Association

QBR_NCAA =

COMP

ATT

· 100

+ 3.3 ·

ATT

· 100

− 2 ·

INT

ATT

· 100

+ 8.4 ·

YDS

ATT

Let's compute quarterback ratings for some of the most famous quarterbacks to play in the Big Game. (Use the NFL formula. Consider that YDS means passing yards, TD means touchdown passes, COMP means passing completions, INT means interceptions thrown, and ATT means passing attempts. Round your answers to two decimal places.)


	BOWL YEAR	TEAM	YDS	TD	COMP	INT	ATT	Rating
Roger Staubach	1972	DAL	119	2	12	0	19
Ken Stabler	1977	OAK	180	1	12	0	19

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2. 18/18 points | Previous Answers ATSports1 1.2.002.Tut. My Notes

Question Part

Points

Submissions Used

1/1

1/5

3/5

1/5

2/5

1/5

Total

18/18

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Using different measures of baseball hitting performance, who is better? Stan or Melvin?

Part 1 of 9

During a baseball season, Stan had 400 hits (H) in 1250 at-bats (AB). What is Stan's batting average (AVG)?

AVG =

AVG = 0.320

0.320

Part 2 of 9

Now suppose that you know more information about Stan. You know that of his 400 hits, 87% of them are singles (1B), 7% of the hits are doubles (2B), 1% are triples (3B) and the rest are home runs (HR). Calculate the number of singles, doubles, triples and home runs.

singles 348

348

doubles 28

triples 4

home runs 20

Part 3 of 9

Now calculate Stan's slugging percentage (SLG). The formula is given by the following equation.

SLG =

1B + 2 · 2B + 3 · 3B + 4 · HR

Find Stan's slugging percentage. (Round your answer to three decimal places.)

SLG = 0.397

0.397

Part 4 of 9

Now suppose that you knew that Stan has a friend who also has a batting average of 0.320 with 400 hits. If the friend also has 87% of his hits as singles, what is the greatest number of home runs that the friend could have hit?

What is the least number of home runs that the friend could have hit?

Part 5 of 9

One of Stan's teammates is named Melvin. Given that Melvin has 400 hits in 1250 at bats, among which 350 of them are singles, 40 are doubles, 4 are triples and the rest are home runs, calculate Melvin's slugging percentage. (Round your answer to three decimal places.)

SLG = 0.373

0.373

If we were to compare Stan and Melvin by slugging percentage, who is better? (Assume a higher SLG indicates a better player.)

Stan Melvin

Part 6 of 9

Now, On-base Percentage (OBP) is defined by the following equation.

OBP =

H + BB + HBP

AB + BB + HBP + SF

Compute Stan's OBP if he was walked (BB) 24 times, was hit by pitch (HBP) 9 times and had 3 sacrifice flies (SF). (Round your answer to three decimal places.)

OBP = 0.337

0.337

Part 7 of 9

Now we know that if we look only at batting average, then Stan and Melvin are equivalent. Perhaps OBP will give us a better idea of how they compare. Compute Melvin's OBP if he was walked (BB) 33 times, was hit by pitch (HBP) 1 time and had 12 sacrifice flies (SF). (Round your answer to three decimal places.)

OBP = 0.335

0.335

If we were to compare Stan and Melvin by On-base Percentage, who is better? (Assume a higher OBP indicates a better player.)

Stan Melvin

Part 8 of 9

For our last measure, we look at On-base Plus Slugging (OPS). The On-base percentage measures the effectiveness of a batter reaching base. The slugging percentage measures the batter's ability to advance runners. One way of measuring the combined skill of the batter to get on base and advance runners is to add the On-base percentage to the slugging percentage to create On-base Plus Slugging. This is given in the following equation.

OPS = OBP + SLG

Compute OPS for Stan and Melvin. (Round your answers to three decimal places.)

Stan's OPS 0.734

0.734

Melvin's OPS .708

0.708

Part 9 of 9

Many people consider OBP to be more important than SLG. If we weight OBP to be twice as important as SLG, we can compute a sort of modified OPS. Compute the

modified OPS = 2 · OBP + SLG

for Stan and Melvin. (Round your answers to three decimal places.)

Stan's modified OPS 1.071

1.071

Melvin's modified OPS 1.043

1.043

If we were to compare Stan and Melvin using this modified OPS, who is better? (Assume a higher modified OPS indicates a better player.)

Stan Melvin

You have now completed the activity.

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3. 2/2 points | Previous Answers ATSports1 1.4.002. My Notes

The formula we will use for the following exercise is given below.

Predicted Year (N + 1) wins ≈ 4.87 + 0.42 · (Actual Year N Wins) + 0.39 · (Year N Predicted Wins)

Predict the wins and compute the error for Anaheim Ducks, where

error = |Actual wins − Predicted wins|.

(Round your answers to the nearest win.)

Team	Actual 2013–14 wins	Predicted 2013–14 wins	Actual 2014–15 wins
Anaheim Ducks	54	51	51
(Arizona) Phoenix Coyotes	37	38	24
Boston Bruins	54	56	41
Buffalo Sabres	21	23	23
Calgary Flames	35	35	45
Carolina Hurricanes	36	37	30
Chicago Blackhawks	46	49	48
Colorado Avalanche	52	46	39
Columbus Blue Jackets	43	44	42
Dallas Stars	40	42	41

Predicted 2014-15 wins =

wins error =

wins

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4. 4/4 points | Previous Answers ATSports1 1.5.001. My Notes

When a strike is bowled, the bowler is awarded the score of 10 (for knocking down all ten pins), plus he gets to add the total of his next two rolls to that frame. For a spare, the bowler gets the 10, plus the total number of pins knocked down on the next roll only. For a strike or a spare in the tenth frame, the bowler gets no extra score.

X represents a strike and / represents a spare.

Find the missing subscores and the final score of the game.

1		2		3		4		5		6		7		8		9		10
4	/		X	6	/	2	/	2	7	8	1	8	/	0	/		X	X	9	/
20		40		52		64		73		82

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5. 10/11 points | Previous Answers ATSports1 2.2.001.Tut. My Notes

In baseball there are many ways to estimate what a team's winning percentage (w) should be against its opponents, given the total runs it has scored and the total runs it has allowed in a certain number of games. Bill James's Pythagorean Formula for the winning percentage estimator is given below.

wpe = w =

(# runs scored)²

(# runs scored)² + (# runs allowed)²

Part 1 of 3

In 2015, the Texas Rangers won 88 games and lost 74 games. What percentage of their games did they win? (Round your answer to two decimal places.)

54.32

Part 2 of 3

The Texas Rangers scored 751 runs and allowed 733 runs. Compute their wpe. (Round your answer to four decimal places.)

wpe =

(# runs scored)²

(# runs scored)² + (# runs allowed)²

0.5121

How many wins does this wpe predict for a 162 game season? (Round your answer to the nearest win.)

wins

Find the error of this estimation.

Error = |(Actual Wins) - (Estimated Wins)|

wins

Part 3 of 3

Now let's estimate the number of wins of the Texas rangers using marginal runs.

There are 15 teams in the American League. The total number of runs for the AL was 10,651. What is the average number of runs for each team in the league? (Round your answer to one decimal place.)

710.1

runs

Calculate the Offensive Marginal Runs (OMR) for the Texas Rangers. (Round your answer to one decimal place.)

OMR = Team Runs −

(League Average Runs)

OMR =

396

396.0

runs

Calculate their Defensive Marginal Runs (DMR). (Round your answer to one decimal place.)

DMR =

(League Average Runs) − (Team Runs Allowed)

DMR =

332.15

332.1

runs

Calculate their Marginal Runs (MR). (Round your answer to one decimal place.)

MR = OMR + DMR

MR =

728.2

728.1

runs

Calculate their estimated winning percentage. (Round your answer to two decimal places.)

Estimated Winning Percentage =

2(League Average Runs)

51.28

0.51

How many wins does this wpe predict for a 162 game season? (Round your answer to the nearest win.)

83.06

wins

Find the error of this estimation. (Round your answer to the nearest win.)

Error = |(Actual Wins) - (Estimated Wins)|

wins

In this case, both methods give the same estimated number of wins.

You have now completed the activity.

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6. 2/2 points | Previous Answers ATSports1 3.3.003. My Notes

The heights of WNBA players are normally distributed with a mean of 72" and a standard deviation of 2", and that NBA players' heights have a mean of 79" and a standard deviation of 3".

Find the z-score for 76.5" in the WNBA. (Round your answer to two decimal places.)

Find the z-score for 76.5" in the NBA. (Round your answer to two decimal places.)

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7. 9/9 points | Previous Answers ATSports1 3.6.001.Tut. My Notes

The following statistics are gathered about Premier League Soccer Teams in England during a 12-game stretch. (Let W = wins and GF = goals scored for the team.)

Team	W	GF	Team	W	GF
Manchester City	8	26	Watford	4	11
Arsenal	8	22	Stoke City	4	10
Leicester City	7	25	West Bromwich	4	10
Manchester Utd	7	17	Swansea City	3	12
Tottenham	5	20	Norwich City	3	16
West Ham Utd	6	23	Chelsea	3	16
Southampton	5	19	Newcastle Utd	2	13
Crystal Palace	6	14	Bournemouth	2	12
Everton	4	20	Sunderland	1	13
Liverpool	4	13	Aston Villa	1	10

The line of best fit for this scatterplot is

y = 1.7943x + 8.2946,

when x = number of wins and y = number of goals scored.

Use this trend line to estimate the number of goals scored when a team wins 3 games. (Round your answer to two decimal places.)

goal(s)

Using this trend line, if a team scored 9 goals, how many games would you estimate that they would have won? (Round your answer to two decimal places.)

win(s)

Would it be a good idea to estimate the number of wins a team would have won if they had scored 3 goals?

No, the trend line estimates a negative amount of wins if they scored 3 goals. Yes, the trend line estimates that a team would win 2.95 games if they had scored 3 goals.

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Triplett - Sports Questions 1/e (Homework)

Current Score : 47 / 48

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving... ()

Instructions

Assignment Submission

Assignment Scoring

1	2	3	4	5	6	7	8	9	10	11
1/1	1/1	1/1	1/1	1/1	1/1	1/1	1/1	0/1	1/1	1/1
1/5	1/5	1/5	1/5	1/5	1/5	2/5	2/5	5/5	1/5	1/5

1	2	3	4	5	6	7	8	9
1/1	1/1	1/1	1/1	1/1	1/1	1/1	1/1	1/1
1/5	1/5	1/5	1/5	1/5	2/5	2/5	4/5	1/5