More descrip+ve sta+s+cs:

Percen+les, boxplots, and z-scores

Outline for today

Be#erknowaplayerWadeBoggsReview:•  Centraltendencyandmeasuresofvaria

Be>er a player

WadeBoggsAnyques

Descrip+ve sta+s+cs

Whatisasta$s$c?Asta$s$cisanumericalsummary(func

The mean

Mean=x1+x2+x3+…+xn= Σxin n

Samplemean(x̅)vs.popula

The median

Themedianisthevalueinthemiddleofyourdata•  ½ofthevaluesaregreaterthanthemedianand½areless

Themedianisresistanttooutlierswhenthemeanisnot

The standard devia+on

Mean

Mean±stdev

Large vs small standard devia+ons

Samemean,differentstandarddevia

The 95% rule (of thumb)

Ifadistribu

Percen+les

Thepthpercen$leisthevalueofaquan

Percen+les/quan+les

h#ps://emeyers.shinyapps.io/baseball_stat_percen

What is a good sta+s+c for…?

Usethewebsitetodeterminewhat“good”valuesareforthefollowingsta

PuOng sta+s+cs in context

90thpercen

PuOng sta+s+cs in context

90thpercen

Calcula+ng percen+les

Thepthpercen$leisthevalueofaquan

Calcula+ng percen+les

Thepthpercen$leisthevalueofaquan

Calcula+ng percen+les

Thepthpercen$leisthevalueofaquan

Order 1 2 3 4 5 6 7 8 9 10 11Sorted data 23 23 28 29 30 32 35 35 37 38 54Percen+le 0 10 20 30 40 50 60 70 80 90 100

Calcula+ng percen+les

Typicallyweaskforavaluethatisatthepthpercen

Five Number Summary

FiveNumberSummary=(min,Q1,median,Q3,max)Q1=25thpercen

Range and Interquar+le Range

Range=maximum–minimum

Interquar$lerange(IQR)=Q3–Q1

R: IQR(x)

Compute: 5 number summary, range, and IQR fro David Or+z home runs

1.FiveNumberSummary=(min,Q1,median,Q3,max)2.Range=maximum–minimum3.Interquar$lerange(IQR)=Q3–Q1

Alsousethepercen

5 number summary, range, and IQR fro David Or+z home runs

1.FiveNumberSummary:(23,28.5,32,36,54)2.Range:313.Interquar$lerange(IQR)=7.5

The5numbersummaryforHRsforallplayer-seasonwithover500PAis:(0,4,10,20,73)

54 35 23 28 3229 23 30 35 3738

Detec+ng of outliers

Asaruleofthumb,wecalladatavalueanoutlierifitis:

Smallerthan:Q1-1.5*IQR

Largerthan:Q3+1.5*IQRArethereanyoutliersinDavidOr$zhomerunnumbers?

1.FiveNumberSummary:(23,28.5,32,36,54)2.Range:313.Interquar

Boxplots

Aboxplotisagraphicaldisplayofthe5numbersummaryandconsistsof:

1.DrawingaboxfromQ1toQ3

2.Dividingtheboxwithalinedrawnatthemedian

3.Drawalinefromeachquar

Box plot of David Or+z home runs

R: boxplot(x)

Homeruns

Box plot quizHo

meruns

Whatis:•  Q1?•  Q3?•  Themedian?•  Mostextremevaluesthatarenotoutliers•  Outliers

A

B

D

C

E

F

Two current players: who is best?

MiguelCabrera:HRin2014=25

DavidOr

Comparing players with side-by-side box plots

HowwouldyoudescribethedifferencesbetweenthesetwoplayersintermsofHRs?Whoisbe#er?

A B

Let’s compare two more players1985

WadeBoggs:BA=.368 TedWilliams:BA=.406

1941

Careerbestseasons Whoisbe#er?

Who is best here?

IsTedWilliamsbe#erthanWadeBoggs?

TedWilliamshit.406in194123plentyofpeoplehitover.400beforehimbutnoonehassince…

Have the best players go>en worse at hiOng over the past 140 years?

Maxbaf

ngaverage

Year

Comparing players across +me periods

Problem:baseballhaschangedfrom1871tonow

Wecan’tsimplycomparesta

Histograms of baOng average 1941 vs. 1985

Dothebafngaverageslooksimilarintheseyears?

Density of baOng average 1941 vs. 1985

Dothebafngaverageslooksimilarintheseyears?

z-scores

Thez-scorestellshowmanystandarddevia

z-scores for comparing players across eras

Whencomparingplayersacrosseras,wewillusethemean(x̄),andstandarddevia

Comparing Ted and Wade to their peers

In1941:•  Meanbafngaveragewas:.276•  Standarddevia

Comparing Ted and Wade to their peers

Wade’sbafngaveragez-score:3.82Ted’sbafngaveragez-score:3.97

Whoisthebe#erhi#er?

Career z-scored baOng averages

What about Home Runs…

Next class: correla+on!

QandR:BigDataBaseballchapter4