Standardized Scores: Who should I draft for my fantasy baseball team?
Obviously, having good players is the most important factor in building a winning fantasy team. Deciding who to draft for your team can be challenging because the variables used to measure the players’ PERFORMANCES are on very different scales. For example, in 2009 Ichiro Suzuki of the Seattle Mariners had a 0.352 batting average while Adam Dunn of the Washington Nationals hit 38 home runs. Both were outstanding PERFORMANCES, but which was better? And what about their PERFORMANCES in other categories? To solve the problem of evaluating PERFORMANCES that are measured on different scales, we need to learn how to standardize these PERFORMANCES so they will be on the same scale.
Go to the website http://www.espn.com/mlb/. Click on the “team” tab to see what teams are part of the league and choose two teams. Then, click on one of the teams and then once that team’s page comes up, click on the “stats” tab. This should bring up all of the players on the team roster.
You are only going to look at the players that have been “up to bat”. You can tell because their “AB” number is not zero.
1) Create a table with two columns, one for BA (batting average) and one for HR (home run) and record all of the data for all players of the two teams who have at least one AB score.
2) Find the mean and standard deviations for both columns of data using the raw data
3) Create two histograms – one for HR and one for BA making sure to have at least 10 intervals. You may have to refresh your memory on how to create a frequency chart, the intervals, etc.
4) Estimate the mean and standard deviation for both histograms. Calculate the percent error of your estimate
5) Please CUSS both histograms using the terminology you have been taught.
The histogram for the BA should appear bimodal with a secondary mode at zero. This was a group of players who did not get a hit. We are now going focus on this data for a moment.
6) Remove from the BA data all zero values, and use your calculator to create a histogram, using the same intervals as your “by hand” version. Ask for help if you do not know how to do this.
7) Assess if this data is approximately normal using a boxplot and NPP. Sketch the box plot and NPP.
You are now going to find who you think are the two best players out of your two teams. They can both be from the same team or not. You are only going to use the HR and BA stats to make your decision.
8) Once you have picked your two best players, normalize their HR and BA scores. Then add the normalized HR and BA scores for the first player and repeat for the second player. Give the player names and total z-scores to your teacher, with your name, to be compared with the scores of your classmates’ players.
Finally, how out of the ordinary are the best home run hitters in the history of baseball? Even though the HR data did not look “Normal” but was skewed left we are still going to calculate z-scores, as we do not know of another method to use at this time.
9) Below you will find the yearly total HR’s of four top baseball players in history. Calculate the yearly average for each player.
10) Using the HR calculations from step 2, find the z-score of the four players. Then, using the standard normal curve (µ=0, σ=1), even though we understand that we shouldn’t because the typical HR distribution is not “normal”, find the probability that a player could get that z-score or higher. Please make conclusions based on your findings.
Baseball Data
Babe Ruth Roger Maris Mark McGwire Barry Bonds
1914-35 1957-68 1986-2001 1986-2007
11 14 3 16
29 28 49 25
54 16 32 24
59 39 33 19
35 61 39 33
41 33 22 25
46 23 42 34
25 26 9 46
47 8 9 37
60 13 39 33
54 9 52 42
46 5 58 40
49 70 37
46 65 34
41 32 49
34 29 73
22 46
6 45
45
5
26
28