Data Dive - Week 5
Anurag
2024-02-11
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.4.4 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.0
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(dplyr)
library(rmarkdown)
lahman_data = read.csv("/Users/anuragreddy/Desktop/Statistics with R/Lahmans Databse .csv")Table of Contents:
- 3 columns (or values) in the data which are unclear.
- One element or your data that is unclear even after reading the documentation
- Visualization based on the second bullet point.
Question - 1: A list of at least 3 columns (or values) in your data which are unclear until you read the documentation.
List of unclear columns:
- WSWIN vs WCWIN
- Earned Runs Allowed (ER) vs Earned Runs Average (ERA)
- Saves
1) WSWIN vs WCWIN:
Before reading the document I was confused between WCWIN and WSWIN. I thought it was World Cup Winner and World Series Winner.
Eventually there should be only one winner in a season. When I found count of value - “Y” in WCWIN and WSWIN. WCWIN has more than one “Y” values.
Shouldn’t there be only one winner in a season?
lahman_data |>
group_by(yearID)|>
summarise('No.of WCWINS' = sum(WCWin=="Y"),
'No.of WSWINS' = sum(WSWin=='Y'))## # A tibble: 22 × 3
## yearID `No.of WCWINS` `No.of WSWINS`
## <int> <int> <int>
## 1 2000 2 1
## 2 2001 2 1
## 3 2002 2 1
## 4 2003 2 1
## 5 2004 2 1
## 6 2005 2 1
## 7 2006 2 1
## 8 2007 2 1
## 9 2008 2 1
## 10 2009 2 1
## # ℹ 12 more rowsInterpretation: The above table clearly interprets that - WCWin is not the world Cup winner of a season. After reading documentation I found out that it is a Wild Card winner.
2) Earned Runs Allowed (ER) vs Earned Runs Average (ERA)
Earned Runs is a statistic measure to perform pitching.
Eventually, after understanding the meaning of ER. I interpreted that ERA (Earned Runs Average) is an ER divided by Total no.of games (ER/G).
When I computed ERA values using the above formula. The calculated ERA and the ERA given in the data are entirely different. Lets look at them.
k <- lahman_data |>
mutate(ERA_Cal = ER/G) |>
select(yearID, ER,ERA,ERA_Cal)
k |>
mutate(Error = ERA_Cal-ERA)## yearID ER ERA ERA_Cal Error
## 1 2000 805 5.00 4.969136 -0.0308641975
## 2 2000 855 5.37 5.277778 -0.0922222222
## 3 2000 683 4.23 4.216049 -0.0139506173
## 4 2000 751 4.66 4.635802 -0.0241975309
## 5 2000 775 4.84 4.783951 -0.0560493827
## 6 2000 755 4.71 4.660494 -0.0495061728
## 7 2000 876 5.48 5.407407 -0.0725925926
## 8 2000 819 5.14 5.055556 -0.0844444444
## 9 2000 753 4.76 4.677019 -0.0829813665
## 10 2000 730 4.58 4.534161 -0.0458385093
## 11 2000 720 4.49 4.444444 -0.0455555556
## 12 2000 773 4.86 4.801242 -0.0587577640
## 13 2000 876 5.52 5.407407 -0.1125925926
## 14 2000 821 5.14 5.067901 -0.0720987654
## 15 2000 698 4.35 4.308642 -0.0413580247
## 16 2000 648 4.05 4.000000 -0.0500000000
## 17 2000 849 5.25 5.240741 -0.0092592593
## 18 2000 700 4.33 4.294479 -0.0355214724
## 19 2000 835 5.26 5.154321 -0.1056790123
## 20 2000 729 4.59 4.527950 -0.0620496894
## 21 2000 865 5.42 5.339506 -0.0804938272
## 22 2000 659 4.10 4.067901 -0.0320987654
## 23 2000 755 4.63 4.631902 0.0019018405
## 24 2000 812 5.13 5.012346 -0.1176543210
## 25 2000 670 4.16 4.135802 -0.0241975309
## 26 2000 763 4.77 4.709877 -0.0601234568
## 27 2000 795 4.94 4.907407 -0.0325925926
## 28 2000 733 4.52 4.524691 0.0046913580
## 29 2000 675 4.21 4.166667 -0.0433333333
## 30 2000 698 4.38 4.308642 -0.0713580247
## 31 2001 671 4.20 4.141975 -0.0580246914
## 32 2001 744 4.67 4.592593 -0.0774074074
## 33 2001 667 4.15 4.142857 -0.0071428571
## 34 2001 725 4.55 4.475309 -0.0746913580
## 35 2001 746 4.64 4.604938 -0.0350617284
## 36 2001 795 5.01 4.907407 -0.1025925926
## 37 2001 779 4.87 4.808642 -0.0613580247
## 38 2001 722 4.51 4.456790 -0.0532098765
## 39 2001 649 4.02 4.031056 0.0110559006
## 40 2001 583 3.59 3.598765 0.0087654321
## 41 2001 576 3.54 3.555556 0.0155555556
## 42 2001 781 4.94 4.820988 -0.1190123457
## 43 2001 913 5.71 5.635802 -0.0741975309
## 44 2001 696 4.28 4.296296 0.0162962963
## 45 2001 627 3.87 3.870370 0.0003703704
## 46 2001 578 3.59 3.567901 -0.0220987654
## 47 2001 643 4.03 3.969136 -0.0608641975
## 48 2001 765 4.77 4.722222 -0.0477777778
## 49 2001 841 5.29 5.191358 -0.0986419753
## 50 2001 691 4.32 4.265432 -0.0545679012
## 51 2001 707 4.37 4.364198 -0.0058024691
## 52 2001 685 4.25 4.228395 -0.0216049383
## 53 2001 740 4.64 4.567901 -0.0720987654
## 54 2001 745 4.68 4.598765 -0.0812345679
## 55 2001 654 4.07 4.037037 -0.0329629630
## 56 2001 667 4.15 4.117284 -0.0327160494
## 57 2001 794 5.05 4.901235 -0.1487654321
## 58 2001 724 4.52 4.469136 -0.0508641975
## 59 2001 680 4.18 4.197531 0.0175308642
## 60 2001 627 3.93 3.870370 -0.0596296296
## 61 2002 595 3.69 3.672840 -0.0171604938
## 62 2002 719 4.46 4.438272 -0.0217283951
## 63 2002 603 3.75 3.722222 -0.0277777778
## 64 2002 716 4.53 4.419753 -0.1102469136
## 65 2002 777 4.91 4.796296 -0.1137037037
## 66 2002 773 4.92 4.801242 -0.1187577640
## 67 2002 834 5.21 5.148148 -0.0618518519
## 68 2002 662 4.12 4.111801 -0.0081987578
## 69 2002 625 3.87 3.881988 0.0119875776
## 70 2002 593 3.68 3.660494 -0.0195061728
## 71 2002 654 4.07 4.037037 -0.0329629630
## 72 2002 846 5.29 5.254658 -0.0353416149
## 73 2002 824 5.15 5.086420 -0.0635802469
## 74 2002 767 4.80 4.734568 -0.0654320988
## 75 2002 630 3.92 3.888889 -0.0311111111
## 76 2002 511 3.13 3.173913 0.0439130435
## 77 2002 687 4.29 4.240741 -0.0492592593
## 78 2002 690 4.27 4.259259 -0.0107407407
## 79 2002 825 5.20 5.092593 -0.1074074074
## 80 2002 706 4.36 4.358025 -0.0019753086
## 81 2002 642 4.00 3.962963 -0.0370370370
## 82 2002 598 3.69 3.691358 0.0013580247
## 83 2002 752 4.73 4.641975 -0.0880246914
## 84 2002 641 3.97 3.956790 -0.0132098765
## 85 2002 624 3.89 3.875776 -0.0142236025
## 86 2002 671 4.17 4.167702 -0.0022981366
## 87 2002 664 4.23 4.124224 -0.1057763975
## 88 2002 737 4.62 4.549383 -0.0706172840
## 89 2002 566 3.54 3.493827 -0.0461728395
## 90 2002 595 3.70 3.672840 -0.0271604938
## 91 2003 680 4.28 4.197531 -0.0824691358
## 92 2003 767 4.76 4.705521 -0.0544785276
## 93 2003 729 4.48 4.500000 0.0200000000
## 94 2003 663 4.17 4.092593 -0.0774074074
## 95 2003 682 4.21 4.209877 -0.0001234568
## 96 2003 847 5.30 5.228395 -0.0716049383
## 97 2003 808 5.05 4.987654 -0.0623456790
## 98 2003 716 4.41 4.419753 0.0097530864
## 99 2003 653 4.02 4.006135 -0.0138650307
## 100 2003 582 3.63 3.592593 -0.0374074074
## 101 2003 602 3.76 3.716049 -0.0439506173
## 102 2003 787 4.93 4.858025 -0.0719753086
## 103 2003 903 5.67 5.574074 -0.0959259259
## 104 2003 748 4.69 4.617284 -0.0727160494
## 105 2003 621 3.84 3.833333 -0.0066666667
## 106 2003 663 4.10 4.092593 -0.0074074074
## 107 2003 619 3.83 3.820988 -0.0090123457
## 108 2003 818 5.09 5.049383 -0.0406172840
## 109 2003 821 5.20 5.067901 -0.1320987654
## 110 2003 648 4.04 4.000000 -0.0400000000
## 111 2003 622 3.86 3.839506 -0.0204938272
## 112 2003 511 3.16 3.154321 -0.0056790123
## 113 2003 810 5.02 5.000000 -0.0200000000
## 114 2003 640 4.01 3.950617 -0.0593827160
## 115 2003 704 4.48 4.372671 -0.1073291925
## 116 2003 648 4.04 4.000000 -0.0400000000
## 117 2003 744 4.64 4.592593 -0.0474074074
## 118 2003 774 4.87 4.777778 -0.0922222222
## 119 2003 595 3.73 3.695652 -0.0343478261
## 120 2003 748 4.60 4.617284 0.0172839506
## 121 2004 692 4.28 4.271605 -0.0083950617
## 122 2004 760 4.70 4.691358 -0.0086419753
## 123 2004 674 4.18 4.160494 -0.0195061728
## 124 2004 782 4.91 4.827160 -0.0828395062
## 125 2004 784 4.81 4.839506 0.0295061728
## 126 2004 788 4.93 4.864198 -0.0658024691
## 127 2004 813 5.15 5.018519 -0.1314814815
## 128 2004 661 4.03 4.080247 0.0502469136
## 129 2004 752 4.69 4.641975 -0.0480246914
## 130 2004 682 4.17 4.209877 0.0398765432
## 131 2004 772 4.76 4.765432 0.0054320988
## 132 2004 757 4.81 4.701863 -0.1081366460
## 133 2004 724 4.53 4.469136 -0.0608641975
## 134 2004 775 4.91 4.813665 -0.0963354037
## 135 2004 794 4.98 4.901235 -0.0787654321
## 136 2004 603 3.74 3.722222 -0.0177777778
## 137 2004 621 3.81 3.833333 0.0233333333
## 138 2004 832 5.19 5.135802 -0.0541975309
## 139 2004 883 5.54 5.450617 -0.0893827160
## 140 2004 655 4.10 4.043210 -0.0567901235
## 141 2004 650 4.05 4.012346 -0.0376543210
## 142 2004 647 4.01 3.993827 -0.0161728395
## 143 2004 679 4.24 4.217391 -0.0226086957
## 144 2004 696 4.33 4.296296 -0.0337037037
## 145 2004 658 4.09 4.061728 -0.0282716049
## 146 2004 724 4.45 4.469136 0.0191358025
## 147 2004 680 4.29 4.223602 -0.0663975155
## 148 2004 645 4.03 3.981481 -0.0485185185
## 149 2004 695 4.29 4.290123 0.0001234568
## 150 2004 605 3.75 3.734568 -0.0154320988
## 151 2005 724 4.56 4.469136 -0.0908641975
## 152 2005 752 4.74 4.641975 -0.0980246914
## 153 2005 592 3.61 3.654321 0.0443209877
## 154 2005 582 3.61 3.592593 -0.0174074074
## 155 2005 719 4.51 4.438272 -0.0717283951
## 156 2005 862 5.49 5.320988 -0.1690123457
## 157 2005 598 3.68 3.691358 0.0113580247
## 158 2005 604 3.71 3.728395 0.0183950617
## 159 2005 718 4.52 4.432099 -0.0879012346
## 160 2005 594 3.69 3.666667 -0.0233333333
## 161 2005 712 4.49 4.395062 -0.0949382716
## 162 2005 851 5.39 5.253086 -0.1369135802
## 163 2005 794 4.96 4.901235 -0.0587654321
## 164 2005 653 4.06 4.030864 -0.0291358025
## 165 2005 783 4.84 4.833333 -0.0066666667
## 166 2005 639 3.98 3.944444 -0.0355555556
## 167 2005 671 4.19 4.141975 -0.0480246914
## 168 2005 820 5.15 5.030675 -0.1193251534
## 169 2005 808 5.13 4.987654 -0.1423456790
## 170 2005 666 4.16 4.111111 -0.0488888889
## 171 2005 563 3.51 3.453988 -0.0560122699
## 172 2005 695 4.38 4.290123 -0.0898765432
## 173 2005 635 3.97 3.919753 -0.0502469136
## 174 2005 599 3.76 3.697531 -0.0624691358
## 175 2005 672 4.21 4.148148 -0.0618518519
## 176 2005 706 4.42 4.358025 -0.0619753086
## 177 2005 668 4.13 4.123457 -0.0065432099
## 178 2005 695 4.33 4.290123 -0.0398765432
## 179 2005 560 3.49 3.456790 -0.0332098765
## 180 2005 627 3.87 3.870370 0.0003703704
## 181 2006 843 5.35 5.203704 -0.1462962963
## 182 2006 773 4.83 4.771605 -0.0583950617
## 183 2006 743 4.61 4.586420 -0.0235802469
## 184 2006 698 4.41 4.308642 -0.1013580247
## 185 2006 618 3.84 3.814815 -0.0251851852
## 186 2006 896 5.65 5.530864 -0.1191358025
## 187 2006 652 4.04 4.024691 -0.0153086420
## 188 2006 632 3.95 3.901235 -0.0487654321
## 189 2006 708 4.41 4.370370 -0.0396296296
## 190 2006 679 4.21 4.191358 -0.0186419753
## 191 2006 739 4.60 4.561728 -0.0382716049
## 192 2006 782 4.96 4.827160 -0.1328395062
## 193 2006 731 4.60 4.512346 -0.0876543210
## 194 2006 694 4.37 4.283951 -0.0860493827
## 195 2006 727 4.48 4.487654 0.0076543210
## 196 2006 736 4.60 4.543210 -0.0567901235
## 197 2006 758 4.74 4.679012 -0.0609876543
## 198 2006 725 4.51 4.475309 -0.0346913580
## 199 2006 749 4.66 4.623457 -0.0365432099
## 200 2006 696 4.37 4.296296 -0.0737037037
## 201 2006 666 4.08 4.111111 0.0311111111
## 202 2006 686 4.23 4.234568 0.0045679012
## 203 2006 763 4.82 4.709877 -0.1101234568
## 204 2006 673 4.14 4.154321 0.0143209877
## 205 2006 747 4.60 4.611111 0.0111111111
## 206 2006 720 4.52 4.444444 -0.0755555556
## 207 2006 629 3.87 3.882716 0.0127160494
## 208 2006 735 4.63 4.565217 -0.0647826087
## 209 2006 721 4.54 4.478261 -0.0617391304
## 210 2006 803 5.03 4.956790 -0.0732098765
## 211 2007 827 5.17 5.104938 -0.0650617284
## 212 2007 618 3.87 3.814815 -0.0551851852
## 213 2007 763 4.77 4.709877 -0.0601234568
## 214 2007 658 4.05 4.061728 0.0117283951
## 215 2007 735 4.57 4.537037 -0.0329629630
## 216 2007 716 4.48 4.419753 -0.0602469136
## 217 2007 674 4.23 4.160494 -0.0695061728
## 218 2007 663 4.15 4.092593 -0.0574074074
## 219 2007 724 4.49 4.469136 -0.0208641975
## 220 2007 689 4.28 4.253086 -0.0269135802
## 221 2007 754 4.73 4.654321 -0.0756790123
## 222 2007 879 5.53 5.425926 -0.1040740741
## 223 2007 755 4.75 4.660494 -0.0895061728
## 224 2007 644 4.00 3.975309 -0.0246913580
## 225 2007 662 4.13 4.086420 -0.0435802469
## 226 2007 665 4.11 4.104938 -0.0050617284
## 227 2007 650 4.04 4.012346 -0.0276543210
## 228 2007 796 4.94 4.913580 -0.0264197531
## 229 2007 706 4.32 4.331288 0.0112883436
## 230 2007 793 4.94 4.895062 -0.0449382716
## 231 2007 761 4.68 4.697531 0.0175308642
## 232 2007 677 4.20 4.179012 -0.0209876543
## 233 2007 708 4.41 4.370370 -0.0396296296
## 234 2007 687 4.26 4.240741 -0.0192592593
## 235 2007 767 4.73 4.734568 0.0045679012
## 236 2007 793 4.93 4.895062 -0.0349382716
## 237 2007 611 3.70 3.748466 0.0484662577
## 238 2007 677 4.19 4.179012 -0.0109876543
## 239 2007 741 4.65 4.574074 -0.0759259259
## 240 2007 736 4.58 4.543210 -0.0367901235
## 241 2008 810 5.13 5.031056 -0.0989440994
## 242 2008 645 4.01 3.981481 -0.0285185185
## 243 2008 658 4.06 4.036810 -0.0231901840
## 244 2008 711 4.45 4.388889 -0.0611111111
## 245 2008 786 4.90 4.851852 -0.0481481481
## 246 2008 720 4.48 4.444444 -0.0355555556
## 247 2008 644 3.99 3.975309 -0.0146913580
## 248 2008 675 4.16 4.141104 -0.0188957055
## 249 2008 685 4.28 4.228395 -0.0516049383
## 250 2008 640 4.01 3.975155 -0.0348447205
## 251 2008 754 4.73 4.654321 -0.0756790123
## 252 2008 618 3.82 3.814815 -0.0051851852
## 253 2008 860 5.37 5.308642 -0.0613580247
## 254 2008 561 3.49 3.462963 -0.0270370370
## 255 2008 635 3.98 3.919753 -0.0602469136
## 256 2008 714 4.46 4.407407 -0.0525925926
## 257 2008 624 3.87 3.875776 0.0057763975
## 258 2008 729 4.55 4.500000 -0.0500000000
## 259 2008 766 4.77 4.728395 -0.0416049383
## 260 2008 707 4.43 4.391304 -0.0386956522
## 261 2008 691 4.36 4.291925 -0.0680745342
## 262 2008 591 3.68 3.648148 -0.0318518519
## 263 2008 623 3.85 3.845679 -0.0043209877
## 264 2008 662 4.07 4.086420 0.0164197531
## 265 2008 625 3.88 3.858025 -0.0219753086
## 266 2008 822 5.08 5.074074 -0.0059259259
## 267 2008 714 4.41 4.407407 -0.0025925926
## 268 2008 701 4.38 4.327160 -0.0528395062
## 269 2008 677 4.19 4.179012 -0.0109876543
## 270 2008 742 4.66 4.608696 -0.0513043478
## 271 2009 817 5.15 5.043210 -0.1067901235
## 272 2009 695 4.35 4.290123 -0.0598765432
## 273 2009 663 4.14 4.092593 -0.0474074074
## 274 2009 806 5.06 4.975309 -0.0846913580
## 275 2009 690 4.29 4.233129 -0.0568711656
## 276 2009 765 4.83 4.722222 -0.1077777778
## 277 2009 715 4.45 4.413580 -0.0364197531
## 278 2009 726 4.50 4.453988 -0.0460122699
## 279 2009 687 4.26 4.240741 -0.0192592593
## 280 2009 685 4.26 4.228395 -0.0316049383
## 281 2009 625 3.87 3.858025 -0.0119753086
## 282 2009 686 4.33 4.234568 -0.0954320988
## 283 2009 698 4.38 4.308642 -0.0713580247
## 284 2009 720 4.47 4.444444 -0.0255555556
## 285 2009 711 4.42 4.388889 -0.0311111111
## 286 2009 581 3.57 3.586420 0.0164197531
## 287 2009 616 3.84 3.826087 -0.0139130435
## 288 2009 677 4.18 4.179012 -0.0009876543
## 289 2009 675 4.22 4.166667 -0.0533333333
## 290 2009 690 4.29 4.259259 -0.0307407407
## 291 2009 722 4.54 4.456790 -0.0832098765
## 292 2009 558 3.41 3.444444 0.0344444444
## 293 2009 770 4.83 4.753086 -0.0769135802
## 294 2009 705 4.45 4.351852 -0.0981481481
## 295 2009 673 4.16 4.154321 -0.0056790123
## 296 2009 723 4.59 4.490683 -0.0993167702
## 297 2009 704 4.37 4.345679 -0.0243209877
## 298 2009 571 3.55 3.524691 -0.0253086420
## 299 2009 586 3.66 3.617284 -0.0427160494
## 300 2009 791 5.00 4.882716 -0.1172839506
## 301 2010 733 4.59 4.524691 -0.0653086420
## 302 2010 679 4.20 4.191358 -0.0086419753
## 303 2010 658 4.09 4.061728 -0.0282716049
## 304 2010 684 4.30 4.222222 -0.0777777778
## 305 2010 690 4.30 4.259259 -0.0407407407
## 306 2010 794 4.97 4.901235 -0.0687654321
## 307 2010 651 4.04 4.018519 -0.0214814815
## 308 2010 638 3.95 3.938272 -0.0117283951
## 309 2010 651 4.06 4.018519 -0.0414814815
## 310 2010 566 3.56 3.493827 -0.0661728395
## 311 2010 628 3.93 3.876543 -0.0534567901
## 312 2010 611 3.78 3.771605 -0.0083950617
## 313 2010 636 3.93 3.925926 -0.0040740741
## 314 2010 676 4.22 4.172840 -0.0471604938
## 315 2010 765 4.81 4.722222 -0.0877777778
## 316 2010 569 3.56 3.512346 -0.0476543210
## 317 2010 668 4.18 4.123457 -0.0565432099
## 318 2010 648 4.01 4.000000 -0.0100000000
## 319 2010 663 4.14 4.092593 -0.0474074074
## 320 2010 652 4.08 4.024691 -0.0553086420
## 321 2010 654 4.09 4.037037 -0.0529629630
## 322 2010 643 4.01 3.969136 -0.0408641975
## 323 2010 733 4.58 4.524691 -0.0553086420
## 324 2010 597 3.70 3.685185 -0.0148148148
## 325 2010 594 3.67 3.666667 -0.0033333333
## 326 2010 784 5.00 4.839506 -0.1604938272
## 327 2010 549 3.39 3.388889 -0.0011111111
## 328 2010 546 3.36 3.370370 0.0103703704
## 329 2010 577 3.57 3.561728 -0.0082716049
## 330 2010 658 4.13 4.061728 -0.0682716049
## 331 2011 786 4.89 4.851852 -0.0381481481
## 332 2011 680 4.20 4.197531 -0.0024691358
## 333 2011 665 4.10 4.104938 0.0049382716
## 334 2011 683 4.23 4.216049 -0.0139506173
## 335 2011 647 4.04 3.993827 -0.0461728395
## 336 2011 716 4.44 4.419753 -0.0202469136
## 337 2011 581 3.57 3.586420 0.0164197531
## 338 2011 724 4.58 4.469136 -0.1108641975
## 339 2011 605 3.73 3.734568 0.0045679012
## 340 2011 597 3.71 3.685185 -0.0248148148
## 341 2011 621 3.90 3.833333 -0.0666666667
## 342 2011 577 3.58 3.561728 -0.0182716049
## 343 2011 607 3.79 3.746914 -0.0430864198
## 344 2011 700 4.32 4.320988 0.0009876543
## 345 2011 609 3.80 3.759259 -0.0407407407
## 346 2011 572 3.48 3.530864 0.0508641975
## 347 2011 690 4.33 4.259259 -0.0707407407
## 348 2011 678 4.16 4.185185 0.0251851852
## 349 2011 713 4.43 4.401235 -0.0287654321
## 350 2011 640 3.95 3.950617 0.0006172840
## 351 2011 719 4.51 4.438272 -0.0717283951
## 352 2011 563 3.54 3.496894 -0.0431055901
## 353 2011 582 3.63 3.592593 -0.0374074074
## 354 2011 674 4.19 4.160494 -0.0295061728
## 355 2011 495 3.02 3.055556 0.0355555556
## 356 2011 650 4.04 4.012346 -0.0276543210
## 357 2011 551 3.42 3.401235 -0.0187654321
## 358 2011 522 3.20 3.222222 0.0222222222
## 359 2011 608 3.74 3.753086 0.0130864198
## 360 2011 577 3.58 3.583851 0.0038509317
## 361 2012 642 3.90 3.962963 0.0629629630
## 362 2012 754 4.70 4.654321 -0.0456790123
## 363 2012 646 4.02 3.987654 -0.0323456790
## 364 2012 766 4.78 4.728395 -0.0516049383
## 365 2012 596 3.75 3.679012 -0.0709876543
## 366 2012 693 4.30 4.277778 -0.0222222222
## 367 2012 640 4.02 3.950617 -0.0693827160
## 368 2012 762 4.77 4.703704 -0.0662962963
## 369 2012 617 3.84 3.808642 -0.0313580247
## 370 2012 569 3.48 3.512346 0.0323456790
## 371 2012 608 3.76 3.753086 -0.0069135802
## 372 2012 518 3.19 3.197531 0.0075308642
## 373 2012 639 3.99 3.944444 -0.0455555556
## 374 2012 745 4.64 4.598765 -0.0412345679
## 375 2012 626 3.93 3.864198 -0.0658024691
## 376 2012 549 3.42 3.388889 -0.0311111111
## 377 2012 708 4.51 4.370370 -0.1396296296
## 378 2012 540 3.34 3.333333 -0.0066666667
## 379 2012 824 5.22 5.086420 -0.1335802469
## 380 2012 721 4.56 4.450617 -0.1093827160
## 381 2012 538 3.34 3.320988 -0.0190123457
## 382 2012 655 4.09 4.043210 -0.0467901235
## 383 2012 682 4.22 4.209877 -0.0101234568
## 384 2012 651 4.09 4.018519 -0.0714814815
## 385 2012 618 3.83 3.814815 -0.0151851852
## 386 2012 615 3.86 3.796296 -0.0637037037
## 387 2012 640 4.01 3.950617 -0.0593827160
## 388 2012 593 3.68 3.660494 -0.0195061728
## 389 2012 603 3.71 3.722222 0.0122222222
## 390 2012 543 3.33 3.351852 0.0218518519
## 391 2013 678 4.20 4.185185 -0.0148148148
## 392 2013 613 3.79 3.783951 -0.0060493827
## 393 2013 643 3.98 3.969136 -0.0108641975
## 394 2013 611 3.82 3.771605 -0.0483950617
## 395 2013 587 3.61 3.623457 0.0134567901
## 396 2013 766 4.79 4.728395 -0.0616049383
## 397 2013 555 3.45 3.425926 -0.0240740741
## 398 2013 685 4.23 4.228395 -0.0016049383
## 399 2013 733 4.55 4.524691 -0.0253086420
## 400 2013 633 3.94 3.907407 -0.0325925926
## 401 2013 574 3.56 3.543210 -0.0167901235
## 402 2013 702 4.31 4.333333 0.0233333333
## 403 2013 608 3.74 3.730061 -0.0099386503
## 404 2013 589 3.62 3.613497 -0.0065030675
## 405 2013 685 4.25 4.228395 -0.0216049383
## 406 2013 651 3.92 4.018519 0.0985185185
## 407 2013 512 3.18 3.160494 -0.0195061728
## 408 2013 643 4.00 3.969136 -0.0308641975
## 409 2013 554 3.38 3.419753 0.0397530864
## 410 2013 708 4.44 4.370370 -0.0696296296
## 411 2013 524 3.25 3.234568 -0.0154320988
## 412 2013 602 3.71 3.716049 0.0060493827
## 413 2013 615 3.84 3.796296 -0.0437037037
## 414 2013 618 3.77 3.814815 0.0448148148
## 415 2013 689 4.32 4.253086 -0.0669135802
## 416 2013 533 3.26 3.290123 0.0301234568
## 417 2013 643 3.98 3.969136 -0.0108641975
## 418 2013 643 4.00 3.969136 -0.0308641975
## 419 2013 555 3.42 3.425926 0.0059259259
## 420 2013 576 3.59 3.555556 -0.0344444444
## 421 2014 557 3.43 3.438272 0.0082716049
## 422 2014 653 4.01 4.030864 0.0208641975
## 423 2014 687 4.29 4.240741 -0.0492592593
## 424 2014 581 3.56 3.586420 0.0264197531
## 425 2014 648 4.01 4.000000 -0.0100000000
## 426 2014 657 4.11 4.055556 -0.0544444444
## 427 2014 565 3.51 3.487654 -0.0223456790
## 428 2014 590 3.58 3.641975 0.0619753086
## 429 2014 728 4.57 4.493827 -0.0761728395
## 430 2014 605 3.75 3.734568 -0.0154320988
## 431 2014 524 3.22 3.234568 0.0145679012
## 432 2014 512 3.17 3.160494 -0.0095061728
## 433 2014 579 3.56 3.574074 0.0140740741
## 434 2014 711 4.49 4.388889 -0.1011111111
## 435 2014 642 4.00 3.962963 -0.0370370370
## 436 2014 683 4.26 4.216049 -0.0439506173
## 437 2014 547 3.38 3.376543 -0.0034567901
## 438 2014 636 3.91 3.925926 0.0159259259
## 439 2014 576 3.59 3.555556 -0.0344444444
## 440 2014 770 4.84 4.753086 -0.0869135802
## 441 2014 554 3.40 3.419753 0.0197530864
## 442 2014 613 3.78 3.783951 0.0039506173
## 443 2014 594 3.67 3.666667 -0.0033333333
## 444 2014 568 3.49 3.506173 0.0161728395
## 445 2014 619 3.79 3.820988 0.0309876543
## 446 2014 562 3.47 3.469136 -0.0008641975
## 447 2014 523 3.27 3.228395 -0.0416049383
## 448 2014 564 3.50 3.481481 -0.0185185185
## 449 2014 564 3.50 3.481481 -0.0185185185
## 450 2014 495 3.03 3.055556 0.0255555556
## 451 2015 646 4.05 3.987654 -0.0623456790
## 452 2015 694 4.31 4.283951 -0.0260493827
## 453 2015 643 3.98 3.969136 -0.0108641975
## 454 2015 584 3.67 3.627329 -0.0426708075
## 455 2015 746 4.64 4.633540 -0.0064596273
## 456 2015 572 3.57 3.530864 -0.0391358025
## 457 2015 601 3.73 3.709877 -0.0201234568
## 458 2015 630 3.94 3.888889 -0.0511111111
## 459 2015 653 4.07 4.030864 -0.0391358025
## 460 2015 652 4.03 4.024691 -0.0053086420
## 461 2015 664 4.14 4.098765 -0.0412345679
## 462 2015 677 4.16 4.179012 0.0190123457
## 463 2015 604 3.74 3.728395 -0.0116049383
## 464 2015 680 4.24 4.197531 -0.0424691358
## 465 2015 609 3.80 3.759259 -0.0407407407
## 466 2015 659 4.04 4.067901 0.0279012346
## 467 2015 698 4.41 4.308642 -0.1013580247
## 468 2015 546 3.36 3.370370 0.0103703704
## 469 2015 700 4.33 4.320988 -0.0090123457
## 470 2015 799 5.04 4.932099 -0.1079012346
## 471 2015 553 3.44 3.413580 -0.0264197531
## 472 2015 638 4.02 3.938272 -0.0817283951
## 473 2015 682 4.28 4.209877 -0.0701234568
## 474 2015 557 3.43 3.438272 0.0082716049
## 475 2015 749 4.69 4.623457 -0.0665432099
## 476 2015 532 3.21 3.283951 0.0739506173
## 477 2015 655 4.09 4.043210 -0.0467901235
## 478 2015 597 3.72 3.685185 -0.0348148148
## 479 2015 478 2.94 2.950617 0.0106172840
## 480 2015 577 3.62 3.561728 -0.0582716049
## 481 2016 671 4.22 4.141975 -0.0780246914
## 482 2016 640 4.00 3.950617 -0.0493827160
## 483 2016 659 4.10 4.067901 -0.0320987654
## 484 2016 617 3.84 3.832298 -0.0077018634
## 485 2016 672 4.24 4.173913 -0.0660869565
## 486 2016 663 4.06 4.092593 0.0325925926
## 487 2016 674 4.21 4.160494 -0.0495061728
## 488 2016 676 4.28 4.172840 -0.1071604938
## 489 2016 814 5.08 5.024691 -0.0553086420
## 490 2016 660 4.16 4.074074 -0.0859259259
## 491 2016 718 4.51 4.432099 -0.0779012346
## 492 2016 647 4.00 3.993827 -0.0061728395
## 493 2016 665 4.20 4.104938 -0.0950617284
## 494 2016 700 4.37 4.320988 -0.0490123457
## 495 2016 613 3.78 3.783951 0.0039506173
## 496 2016 821 5.09 5.067901 -0.0220987654
## 497 2016 725 4.51 4.503106 -0.0068944099
## 498 2016 511 3.15 3.154321 0.0043209877
## 499 2016 786 4.91 4.851852 -0.0581481481
## 500 2016 779 4.91 4.808642 -0.1013580247
## 501 2016 598 3.70 3.691358 -0.0086419753
## 502 2016 646 4.05 4.012422 -0.0375776398
## 503 2016 650 4.08 4.012346 -0.0676543210
## 504 2016 574 3.57 3.543210 -0.0267901235
## 505 2016 739 4.63 4.561728 -0.0682716049
## 506 2016 679 4.21 4.191358 -0.0186419753
## 507 2016 708 4.43 4.370370 -0.0596296296
## 508 2016 593 3.65 3.660494 0.0104938272
## 509 2016 656 4.08 4.049383 -0.0306172840
## 510 2016 570 3.51 3.518519 0.0085185185
## 511 2017 795 4.97 4.907407 -0.0625925926
## 512 2017 610 3.70 3.765432 0.0654320988
## 513 2017 755 4.78 4.660494 -0.1195061728
## 514 2017 529 3.30 3.265432 -0.0345679012
## 515 2017 846 5.36 5.222222 -0.1377777778
## 516 2017 662 4.12 4.086420 -0.0335802469
## 517 2017 737 4.61 4.549383 -0.0606172840
## 518 2017 672 4.20 4.148148 -0.0518518519
## 519 2017 732 4.59 4.518519 -0.0714814815
## 520 2017 599 3.72 3.697531 -0.0224691358
## 521 2017 743 4.67 4.586420 -0.0835802469
## 522 2017 713 4.46 4.401235 -0.0587654321
## 523 2017 638 3.97 3.938272 -0.0317283951
## 524 2017 742 4.66 4.580247 -0.0797530864
## 525 2017 720 4.42 4.444444 0.0244444444
## 526 2017 586 3.66 3.617284 -0.0427160494
## 527 2017 756 4.72 4.666667 -0.0533333333
## 528 2017 636 3.95 3.925926 -0.0240740741
## 529 2017 821 5.17 5.067901 -0.1020987654
## 530 2017 721 4.51 4.450617 -0.0593827160
## 531 2017 543 3.38 3.351852 -0.0281481481
## 532 2017 772 4.82 4.765432 -0.0545679012
## 533 2017 642 4.00 3.962963 -0.0370370370
## 534 2017 799 5.01 4.932099 -0.0779012346
## 535 2017 729 4.55 4.500000 -0.0500000000
## 536 2017 676 4.22 4.172840 -0.0471604938
## 537 2017 742 4.67 4.580247 -0.0897530864
## 538 2017 726 4.50 4.481481 -0.0185185185
## 539 2017 646 4.01 3.987654 -0.0223456790
## 540 2017 623 3.88 3.845679 -0.0343209877
## 541 2019 897 5.59 5.537037 -0.0529629630
## 542 2019 768 4.70 4.740741 0.0407407407
## 543 2019 769 4.90 4.776398 -0.1236024845
## 544 2019 601 3.76 3.709877 -0.0501234568
## 545 2019 835 5.24 5.186335 -0.0536645963
## 546 2019 595 3.66 3.672840 0.0128395062
## 547 2019 824 5.20 5.086420 -0.1135802469
## 548 2019 820 5.12 5.061728 -0.0582716049
## 549 2019 680 4.18 4.197531 0.0175308642
## 550 2019 691 4.31 4.265432 -0.0445679012
## 551 2019 646 3.97 3.987654 0.0176543210
## 552 2019 798 4.99 4.925926 -0.0640740741
## 553 2019 598 3.65 3.691358 0.0413580247
## 554 2019 808 5.06 4.987654 -0.0723456790
## 555 2019 767 4.79 4.734568 -0.0554320988
## 556 2019 691 4.25 4.265432 0.0154320988
## 557 2019 675 4.19 4.166667 -0.0233333333
## 558 2019 657 4.10 4.055556 -0.0444444444
## 559 2019 668 4.18 4.123457 -0.0565432099
## 560 2019 895 5.56 5.524691 -0.0353086420
## 561 2019 541 3.37 3.339506 -0.0304938272
## 562 2019 760 4.74 4.691358 -0.0486419753
## 563 2019 713 4.40 4.401235 0.0012345679
## 564 2019 688 4.24 4.246914 0.0069135802
## 565 2019 731 4.53 4.512346 -0.0176543210
## 566 2019 829 5.18 5.117284 -0.0627160494
## 567 2019 732 4.60 4.518519 -0.0814814815
## 568 2019 715 4.38 4.413580 0.0335802469
## 569 2019 609 3.80 3.759259 -0.0407407407
## 570 2019 683 4.27 4.216049 -0.0539506173
## 571 2020 260 4.51 4.333333 -0.1766666667
## 572 2020 325 5.58 5.416667 -0.1633333333
## 573 2020 223 3.81 3.716667 -0.0933333333
## 574 2020 196 3.29 3.266667 -0.0233333333
## 575 2020 308 5.63 5.310345 -0.3196551724
## 576 2020 251 4.31 4.183333 -0.1266666667
## 577 2020 247 4.30 4.116667 -0.1833333333
## 578 2020 297 5.09 4.950000 -0.1400000000
## 579 2020 204 3.58 3.400000 -0.1800000000
## 580 2020 242 4.35 4.033333 -0.3166666667
## 581 2020 216 3.77 3.600000 -0.1700000000
## 582 2020 289 5.03 4.816667 -0.2133333333
## 583 2020 209 3.56 3.483333 -0.0766666667
## 584 2020 288 5.02 4.800000 -0.2200000000
## 585 2020 268 4.60 4.466667 -0.1333333333
## 586 2020 279 4.84 4.650000 -0.1900000000
## 587 2020 257 4.41 4.283333 -0.1266666667
## 588 2020 230 3.99 3.833333 -0.1566666667
## 589 2020 215 3.84 3.583333 -0.2566666667
## 590 2020 327 5.59 5.450000 -0.1400000000
## 591 2020 181 3.02 3.016667 -0.0033333333
## 592 2020 272 4.86 4.533333 -0.3266666667
## 593 2020 239 4.16 3.983333 -0.1766666667
## 594 2020 284 4.98 4.733333 -0.2466666667
## 595 2020 284 5.14 4.733333 -0.4066666667
## 596 2020 267 4.68 4.450000 -0.2300000000
## 597 2020 223 3.86 3.716667 -0.1433333333
## 598 2020 267 4.64 4.450000 -0.1900000000
## 599 2020 205 3.90 3.534483 -0.3655172414
## 600 2020 285 5.09 4.750000 -0.3400000000
## 601 2021 910 5.84 5.617284 -0.2227160494
## 602 2021 671 4.26 4.141975 -0.1180246914
## 603 2021 581 3.73 3.586420 -0.1435802469
## 604 2021 679 4.34 4.191358 -0.1486419753
## 605 2021 681 4.32 4.203704 -0.1162962963
## 606 2021 607 3.78 3.746914 -0.0330864198
## 607 2021 731 4.64 4.512346 -0.1276543210
## 608 2021 741 4.69 4.574074 -0.1159259259
## 609 2021 762 4.83 4.703704 -0.1262962963
## 610 2021 596 3.74 3.679012 -0.0609876543
## 611 2021 640 4.02 3.950617 -0.0693827160
## 612 2021 688 4.30 4.246914 -0.0530864198
## 613 2021 593 3.67 3.660494 -0.0095061728
## 614 2021 758 4.79 4.679012 -0.1109876543
## 615 2021 610 3.91 3.765432 -0.1445679012
## 616 2021 804 5.11 4.962963 -0.1470370370
## 617 2021 608 3.88 3.776398 -0.1036024845
## 618 2021 765 4.87 4.722222 -0.1477777778
## 619 2021 702 4.40 4.333333 -0.0666666667
## 620 2021 748 4.82 4.645963 -0.1740372671
## 621 2021 486 3.01 3.000000 -0.0100000000
## 622 2021 622 3.96 3.839506 -0.1204938272
## 623 2021 558 3.50 3.444444 -0.0555555556
## 624 2021 597 3.90 3.685185 -0.2148148148
## 625 2021 692 4.39 4.271605 -0.1183950617
## 626 2021 788 5.08 4.864198 -0.2158024691
## 627 2021 651 4.10 4.018519 -0.0814814815
## 628 2021 524 3.24 3.234568 -0.0054320988
## 629 2021 626 3.98 3.864198 -0.1158024691
## 630 2021 743 4.80 4.586420 -0.2135802469
## 631 2022 632 3.97 3.901235 -0.0687654321
## 632 2022 721 4.53 4.450617 -0.0793827160
## 633 2022 631 3.92 3.895062 -0.0249382716
## 634 2022 560 3.46 3.456790 -0.0032098765
## 635 2022 637 4.04 3.932099 -0.1079012346
## 636 2022 465 2.90 2.870370 -0.0296296296
## 637 2022 740 4.70 4.567901 -0.1320987654
## 638 2022 601 3.77 3.709877 -0.0601234568
## 639 2022 636 3.98 3.925926 -0.0540740741
## 640 2022 532 3.30 3.283951 -0.0160493827
## 641 2022 717 4.52 4.425926 -0.0940740741
## 642 2022 577 3.59 3.561728 -0.0282716049
## 643 2022 544 3.41 3.358025 -0.0519753086
## 644 2022 673 4.22 4.154321 -0.0656790123
## 645 2022 620 3.87 3.827160 -0.0428395062
## 646 2022 676 4.25 4.172840 -0.0771604938
## 647 2022 556 3.46 3.432099 -0.0279012346
## 648 2022 642 4.00 3.962963 -0.0370370370
## 649 2022 768 4.86 4.740741 -0.1192592593
## 650 2022 802 5.06 4.950617 -0.1093827160
## 651 2022 451 2.80 2.783951 -0.0160493827
## 652 2022 617 3.86 3.808642 -0.0513580247
## 653 2022 615 3.83 3.796296 -0.0337037037
## 654 2022 570 3.57 3.518519 -0.0514814815
## 655 2022 630 3.97 3.888889 -0.0811111111
## 656 2022 735 4.66 4.537037 -0.1229629630
## 657 2022 611 3.81 3.771605 -0.0383950617
## 658 2022 613 3.85 3.783951 -0.0660493827
## 659 2022 605 3.79 3.734568 -0.0554320988
## 660 2022 785 5.00 4.845679 -0.1543209877Interpretation: After observing the above table, one can infer that ERA is not equivalent to ER/G, as evidenced by the non-zero error values. Even after reading the documentation I couldn’t resolve this issue.
3) Saves (SV)
Being a cricket fanatic the term saves refers to me as - the number of runs saved by a player.
Eventuvally, I thought it is same in Baseball, but the term saves is viewed differently in this sport.
If you see the descriptive of the Saves statistic. One can definitely tell that saves is not the runs saved.
summary(lahman_data$SV)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 6.00 35.00 40.00 39.53 45.00 66.00Interpretation: The minimum value is 6, and the maximum value is 66. In a season, each team typically plays around 162 games. Even if a team were to save one run every two games, the average value would be 81. However, the observed values are significantly lower. The documentation provides no information about the Saves statistic.
Question - 2: At least one element in data set that is unclear even after reading the documentation
In our earlier discussion, we determined that even after consulting the documentation, the columns ERA and SV remain unclear.
To gain further insight, I conducted independent research by exploring websites such as Baseball Reference, FanGraphs, and other baseball-related platforms. These platforms helped me in understanding these columns in a better way.
ERA - Earned Run Average is not ER/G. It is actually no.of runs a pitcher is responsible per game. In baseball 9 innings is concluded as a game. See the below code to compare the calculated ERA and documented ERA.
ERA = 9 * (ER/No.of Innings Played).
No.of Innings Played = IPOuts / 3
p <- lahman_data |>
mutate(ERA_Cal = round(9 * (ER/(IPouts/3)),2)) |>
select(yearID,ERA,ERA_Cal) |>
mutate(Error = ERA_Cal - ERA)
p## yearID ERA ERA_Cal Error
## 1 2000 5.00 5.00 0.00
## 2 2000 5.37 5.37 0.00
## 3 2000 4.23 4.23 0.00
## 4 2000 4.66 4.66 0.00
## 5 2000 4.84 4.84 0.00
## 6 2000 4.71 4.71 0.00
## 7 2000 5.48 5.48 0.00
## 8 2000 5.14 5.14 0.00
## 9 2000 4.76 4.76 0.00
## 10 2000 4.58 4.58 0.00
## 11 2000 4.49 4.49 0.00
## 12 2000 4.86 4.86 0.00
## 13 2000 5.52 5.52 0.00
## 14 2000 5.14 5.14 0.00
## 15 2000 4.35 4.35 0.00
## 16 2000 4.05 4.05 0.00
## 17 2000 5.25 5.25 0.00
## 18 2000 4.33 4.33 0.00
## 19 2000 5.26 5.26 0.00
## 20 2000 4.59 4.59 0.00
## 21 2000 5.42 5.42 0.00
## 22 2000 4.10 4.10 0.00
## 23 2000 4.63 4.63 0.00
## 24 2000 5.13 5.13 0.00
## 25 2000 4.16 4.16 0.00
## 26 2000 4.77 4.77 0.00
## 27 2000 4.94 4.94 0.00
## 28 2000 4.52 4.52 0.00
## 29 2000 4.21 4.21 0.00
## 30 2000 4.38 4.38 0.00
## 31 2001 4.20 4.20 0.00
## 32 2001 4.67 4.67 0.00
## 33 2001 4.15 4.15 0.00
## 34 2001 4.55 4.55 0.00
## 35 2001 4.64 4.64 0.00
## 36 2001 5.01 5.01 0.00
## 37 2001 4.87 4.87 0.00
## 38 2001 4.51 4.51 0.00
## 39 2001 4.02 4.02 0.00
## 40 2001 3.59 3.59 0.00
## 41 2001 3.54 3.54 0.00
## 42 2001 4.94 4.94 0.00
## 43 2001 5.71 5.71 0.00
## 44 2001 4.28 4.28 0.00
## 45 2001 3.87 3.87 0.00
## 46 2001 3.59 3.59 0.00
## 47 2001 4.03 4.03 0.00
## 48 2001 4.77 4.77 0.00
## 49 2001 5.29 5.29 0.00
## 50 2001 4.32 4.32 0.00
## 51 2001 4.37 4.37 0.00
## 52 2001 4.25 4.25 0.00
## 53 2001 4.64 4.64 0.00
## 54 2001 4.68 4.68 0.00
## 55 2001 4.07 4.07 0.00
## 56 2001 4.15 4.15 0.00
## 57 2001 5.05 5.05 0.00
## 58 2001 4.52 4.52 0.00
## 59 2001 4.18 4.18 0.00
## 60 2001 3.93 3.93 0.00
## 61 2002 3.69 3.69 0.00
## 62 2002 4.46 4.46 0.00
## 63 2002 3.75 3.75 0.00
## 64 2002 4.53 4.53 0.00
## 65 2002 4.91 4.91 0.00
## 66 2002 4.92 4.92 0.00
## 67 2002 5.21 5.21 0.00
## 68 2002 4.12 4.12 0.00
## 69 2002 3.87 3.87 0.00
## 70 2002 3.68 3.68 0.00
## 71 2002 4.07 4.07 0.00
## 72 2002 5.29 5.29 0.00
## 73 2002 5.15 5.15 0.00
## 74 2002 4.80 4.80 0.00
## 75 2002 3.92 3.92 0.00
## 76 2002 3.13 3.13 0.00
## 77 2002 4.29 4.29 0.00
## 78 2002 4.27 4.27 0.00
## 79 2002 5.20 5.20 0.00
## 80 2002 4.36 4.36 0.00
## 81 2002 4.00 4.00 0.00
## 82 2002 3.69 3.69 0.00
## 83 2002 4.73 4.73 0.00
## 84 2002 3.97 3.97 0.00
## 85 2002 3.89 3.89 0.00
## 86 2002 4.17 4.17 0.00
## 87 2002 4.23 4.23 0.00
## 88 2002 4.62 4.62 0.00
## 89 2002 3.54 3.54 0.00
## 90 2002 3.70 3.70 0.00
## 91 2003 4.28 4.28 0.00
## 92 2003 4.76 4.76 0.00
## 93 2003 4.48 4.48 0.00
## 94 2003 4.17 4.17 0.00
## 95 2003 4.21 4.21 0.00
## 96 2003 5.30 5.30 0.00
## 97 2003 5.05 5.05 0.00
## 98 2003 4.41 4.41 0.00
## 99 2003 4.02 4.02 0.00
## 100 2003 3.63 3.63 0.00
## 101 2003 3.76 3.76 0.00
## 102 2003 4.93 4.93 0.00
## 103 2003 5.67 5.67 0.00
## 104 2003 4.69 4.69 0.00
## 105 2003 3.84 3.84 0.00
## 106 2003 4.10 4.10 0.00
## 107 2003 3.83 3.83 0.00
## 108 2003 5.09 5.09 0.00
## 109 2003 5.20 5.20 0.00
## 110 2003 4.04 4.04 0.00
## 111 2003 3.86 3.86 0.00
## 112 2003 3.16 3.16 0.00
## 113 2003 5.02 5.02 0.00
## 114 2003 4.01 4.01 0.00
## 115 2003 4.48 4.48 0.00
## 116 2003 4.04 4.04 0.00
## 117 2003 4.64 4.64 0.00
## 118 2003 4.87 4.87 0.00
## 119 2003 3.73 3.73 0.00
## 120 2003 4.60 4.60 0.00
## 121 2004 4.28 4.28 0.00
## 122 2004 4.70 4.70 0.00
## 123 2004 4.18 4.18 0.00
## 124 2004 4.91 4.91 0.00
## 125 2004 4.81 4.81 0.00
## 126 2004 4.93 4.93 0.00
## 127 2004 5.15 5.15 0.00
## 128 2004 4.03 4.03 0.00
## 129 2004 4.69 4.69 0.00
## 130 2004 4.17 4.17 0.00
## 131 2004 4.76 4.76 0.00
## 132 2004 4.81 4.81 0.00
## 133 2004 4.53 4.53 0.00
## 134 2004 4.91 4.91 0.00
## 135 2004 4.98 4.98 0.00
## 136 2004 3.74 3.74 0.00
## 137 2004 3.81 3.81 0.00
## 138 2004 5.19 5.19 0.00
## 139 2004 5.54 5.54 0.00
## 140 2004 4.10 4.10 0.00
## 141 2004 4.05 4.05 0.00
## 142 2004 4.01 4.01 0.00
## 143 2004 4.24 4.24 0.00
## 144 2004 4.33 4.33 0.00
## 145 2004 4.09 4.09 0.00
## 146 2004 4.45 4.45 0.00
## 147 2004 4.29 4.29 0.00
## 148 2004 4.03 4.03 0.00
## 149 2004 4.29 4.29 0.00
## 150 2004 3.75 3.75 0.00
## 151 2005 4.56 4.56 0.00
## 152 2005 4.74 4.74 0.00
## 153 2005 3.61 3.61 0.00
## 154 2005 3.61 3.61 0.00
## 155 2005 4.51 4.51 0.00
## 156 2005 5.49 5.49 0.00
## 157 2005 3.68 3.68 0.00
## 158 2005 3.71 3.71 0.00
## 159 2005 4.52 4.52 0.00
## 160 2005 3.69 3.69 0.00
## 161 2005 4.49 4.49 0.00
## 162 2005 5.39 5.39 0.00
## 163 2005 4.96 4.96 0.00
## 164 2005 4.06 4.06 0.00
## 165 2005 4.84 4.84 0.00
## 166 2005 3.98 3.98 0.00
## 167 2005 4.19 4.19 0.00
## 168 2005 5.15 5.15 0.00
## 169 2005 5.13 5.13 0.00
## 170 2005 4.16 4.16 0.00
## 171 2005 3.51 3.51 0.00
## 172 2005 4.38 4.38 0.00
## 173 2005 3.97 3.97 0.00
## 174 2005 3.76 3.76 0.00
## 175 2005 4.21 4.21 0.00
## 176 2005 4.42 4.42 0.00
## 177 2005 4.13 4.13 0.00
## 178 2005 4.33 4.33 0.00
## 179 2005 3.49 3.49 0.00
## 180 2005 3.87 3.87 0.00
## 181 2006 5.35 5.35 0.00
## 182 2006 4.83 4.83 0.00
## 183 2006 4.61 4.61 0.00
## 184 2006 4.41 4.41 0.00
## 185 2006 3.84 3.84 0.00
## 186 2006 5.65 5.65 0.00
## 187 2006 4.04 4.04 0.00
## 188 2006 3.95 3.95 0.00
## 189 2006 4.41 4.41 0.00
## 190 2006 4.21 4.21 0.00
## 191 2006 4.60 4.60 0.00
## 192 2006 4.96 4.96 0.00
## 193 2006 4.60 4.60 0.00
## 194 2006 4.37 4.37 0.00
## 195 2006 4.48 4.48 0.00
## 196 2006 4.60 4.60 0.00
## 197 2006 4.74 4.74 0.00
## 198 2006 4.51 4.51 0.00
## 199 2006 4.66 4.66 0.00
## 200 2006 4.37 4.37 0.00
## 201 2006 4.08 4.08 0.00
## 202 2006 4.23 4.23 0.00
## 203 2006 4.82 4.82 0.00
## 204 2006 4.14 4.14 0.00
## 205 2006 4.60 4.60 0.00
## 206 2006 4.52 4.52 0.00
## 207 2006 3.87 3.87 0.00
## 208 2006 4.63 4.63 0.00
## 209 2006 4.54 4.54 0.00
## 210 2006 5.03 5.03 0.00
## 211 2007 5.17 5.17 0.00
## 212 2007 3.87 3.87 0.00
## 213 2007 4.77 4.77 0.00
## 214 2007 4.05 4.05 0.00
## 215 2007 4.57 4.57 0.00
## 216 2007 4.48 4.48 0.00
## 217 2007 4.23 4.23 0.00
## 218 2007 4.15 4.15 0.00
## 219 2007 4.49 4.49 0.00
## 220 2007 4.28 4.28 0.00
## 221 2007 4.73 4.73 0.00
## 222 2007 5.53 5.53 0.00
## 223 2007 4.75 4.75 0.00
## 224 2007 4.00 4.00 0.00
## 225 2007 4.13 4.13 0.00
## 226 2007 4.11 4.11 0.00
## 227 2007 4.04 4.04 0.00
## 228 2007 4.94 4.94 0.00
## 229 2007 4.32 4.32 0.00
## 230 2007 4.94 4.94 0.00
## 231 2007 4.68 4.68 0.00
## 232 2007 4.20 4.20 0.00
## 233 2007 4.41 4.41 0.00
## 234 2007 4.26 4.26 0.00
## 235 2007 4.73 4.73 0.00
## 236 2007 4.93 4.93 0.00
## 237 2007 3.70 3.70 0.00
## 238 2007 4.19 4.19 0.00
## 239 2007 4.65 4.65 0.00
## 240 2007 4.58 4.58 0.00
## 241 2008 5.13 5.13 0.00
## 242 2008 4.01 4.01 0.00
## 243 2008 4.06 4.06 0.00
## 244 2008 4.45 4.45 0.00
## 245 2008 4.90 4.90 0.00
## 246 2008 4.48 4.48 0.00
## 247 2008 3.99 3.99 0.00
## 248 2008 4.16 4.16 0.00
## 249 2008 4.28 4.28 0.00
## 250 2008 4.01 4.01 0.00
## 251 2008 4.73 4.73 0.00
## 252 2008 3.82 3.82 0.00
## 253 2008 5.37 5.37 0.00
## 254 2008 3.49 3.49 0.00
## 255 2008 3.98 3.98 0.00
## 256 2008 4.46 4.46 0.00
## 257 2008 3.87 3.87 0.00
## 258 2008 4.55 4.55 0.00
## 259 2008 4.77 4.77 0.00
## 260 2008 4.43 4.43 0.00
## 261 2008 4.36 4.36 0.00
## 262 2008 3.68 3.68 0.00
## 263 2008 3.85 3.85 0.00
## 264 2008 4.07 4.07 0.00
## 265 2008 3.88 3.88 0.00
## 266 2008 5.08 5.08 0.00
## 267 2008 4.41 4.41 0.00
## 268 2008 4.38 4.38 0.00
## 269 2008 4.19 4.19 0.00
## 270 2008 4.66 4.66 0.00
## 271 2009 5.15 5.15 0.00
## 272 2009 4.35 4.35 0.00
## 273 2009 4.14 4.14 0.00
## 274 2009 5.06 5.06 0.00
## 275 2009 4.29 4.29 0.00
## 276 2009 4.83 4.83 0.00
## 277 2009 4.45 4.45 0.00
## 278 2009 4.50 4.50 0.00
## 279 2009 4.26 4.26 0.00
## 280 2009 4.26 4.26 0.00
## 281 2009 3.87 3.87 0.00
## 282 2009 4.33 4.33 0.00
## 283 2009 4.38 4.38 0.00
## 284 2009 4.47 4.47 0.00
## 285 2009 4.42 4.42 0.00
## 286 2009 3.57 3.57 0.00
## 287 2009 3.84 3.84 0.00
## 288 2009 4.18 4.18 0.00
## 289 2009 4.22 4.22 0.00
## 290 2009 4.29 4.29 0.00
## 291 2009 4.54 4.54 0.00
## 292 2009 3.41 3.41 0.00
## 293 2009 4.83 4.83 0.00
## 294 2009 4.45 4.45 0.00
## 295 2009 4.16 4.16 0.00
## 296 2009 4.59 4.59 0.00
## 297 2009 4.37 4.37 0.00
## 298 2009 3.55 3.55 0.00
## 299 2009 3.66 3.66 0.00
## 300 2009 5.00 5.00 0.00
## 301 2010 4.59 4.59 0.00
## 302 2010 4.20 4.20 0.00
## 303 2010 4.09 4.09 0.00
## 304 2010 4.30 4.30 0.00
## 305 2010 4.30 4.30 0.00
## 306 2010 4.97 4.97 0.00
## 307 2010 4.04 4.04 0.00
## 308 2010 3.95 3.95 0.00
## 309 2010 4.06 4.06 0.00
## 310 2010 3.56 3.56 0.00
## 311 2010 3.93 3.93 0.00
## 312 2010 3.78 3.78 0.00
## 313 2010 3.93 3.93 0.00
## 314 2010 4.22 4.22 0.00
## 315 2010 4.81 4.81 0.00
## 316 2010 3.56 3.56 0.00
## 317 2010 4.18 4.18 0.00
## 318 2010 4.01 4.01 0.00
## 319 2010 4.14 4.14 0.00
## 320 2010 4.08 4.08 0.00
## 321 2010 4.09 4.09 0.00
## 322 2010 4.01 4.01 0.00
## 323 2010 4.58 4.58 0.00
## 324 2010 3.70 3.70 0.00
## 325 2010 3.67 3.67 0.00
## 326 2010 5.00 5.00 0.00
## 327 2010 3.39 3.39 0.00
## 328 2010 3.36 3.36 0.00
## 329 2010 3.57 3.57 0.00
## 330 2010 4.13 4.13 0.00
## 331 2011 4.89 4.89 0.00
## 332 2011 4.20 4.20 0.00
## 333 2011 4.10 4.10 0.00
## 334 2011 4.23 4.23 0.00
## 335 2011 4.04 4.04 0.00
## 336 2011 4.44 4.44 0.00
## 337 2011 3.57 3.57 0.00
## 338 2011 4.58 4.58 0.00
## 339 2011 3.73 3.73 0.00
## 340 2011 3.71 3.71 0.00
## 341 2011 3.90 3.90 0.00
## 342 2011 3.58 3.58 0.00
## 343 2011 3.79 3.79 0.00
## 344 2011 4.32 4.32 0.00
## 345 2011 3.80 3.80 0.00
## 346 2011 3.48 3.48 0.00
## 347 2011 4.33 4.33 0.00
## 348 2011 4.16 4.16 0.00
## 349 2011 4.43 4.43 0.00
## 350 2011 3.95 3.95 0.00
## 351 2011 4.51 4.51 0.00
## 352 2011 3.54 3.54 0.00
## 353 2011 3.63 3.63 0.00
## 354 2011 4.19 4.19 0.00
## 355 2011 3.02 3.02 0.00
## 356 2011 4.04 4.04 0.00
## 357 2011 3.42 3.42 0.00
## 358 2011 3.20 3.20 0.00
## 359 2011 3.74 3.74 0.00
## 360 2011 3.58 3.58 0.00
## 361 2012 3.90 3.90 0.00
## 362 2012 4.70 4.70 0.00
## 363 2012 4.02 4.02 0.00
## 364 2012 4.78 4.78 0.00
## 365 2012 3.75 3.75 0.00
## 366 2012 4.30 4.30 0.00
## 367 2012 4.02 4.02 0.00
## 368 2012 4.77 4.77 0.00
## 369 2012 3.84 3.84 0.00
## 370 2012 3.48 3.48 0.00
## 371 2012 3.76 3.76 0.00
## 372 2012 3.19 3.19 0.00
## 373 2012 3.99 3.99 0.00
## 374 2012 4.64 4.64 0.00
## 375 2012 3.93 3.93 0.00
## 376 2012 3.42 3.42 0.00
## 377 2012 4.51 4.51 0.00
## 378 2012 3.34 3.34 0.00
## 379 2012 5.22 5.22 0.00
## 380 2012 4.56 4.56 0.00
## 381 2012 3.34 3.34 0.00
## 382 2012 4.09 4.09 0.00
## 383 2012 4.22 4.22 0.00
## 384 2012 4.09 4.09 0.00
## 385 2012 3.83 3.83 0.00
## 386 2012 3.86 3.86 0.00
## 387 2012 4.01 4.01 0.00
## 388 2012 3.68 3.68 0.00
## 389 2012 3.71 3.71 0.00
## 390 2012 3.33 3.33 0.00
## 391 2013 4.20 4.20 0.00
## 392 2013 3.79 3.79 0.00
## 393 2013 3.98 3.98 0.00
## 394 2013 3.82 3.82 0.00
## 395 2013 3.61 3.61 0.00
## 396 2013 4.79 4.79 0.00
## 397 2013 3.45 3.45 0.00
## 398 2013 4.23 4.23 0.00
## 399 2013 4.55 4.55 0.00
## 400 2013 3.94 3.94 0.00
## 401 2013 3.56 3.56 0.00
## 402 2013 4.31 4.31 0.00
## 403 2013 3.74 3.74 0.00
## 404 2013 3.62 3.62 0.00
## 405 2013 4.25 4.25 0.00
## 406 2013 3.92 3.92 0.00
## 407 2013 3.18 3.18 0.00
## 408 2013 4.00 4.00 0.00
## 409 2013 3.38 3.38 0.00
## 410 2013 4.44 4.44 0.00
## 411 2013 3.25 3.25 0.00
## 412 2013 3.71 3.71 0.00
## 413 2013 3.84 3.84 0.00
## 414 2013 3.77 3.77 0.00
## 415 2013 4.32 4.32 0.00
## 416 2013 3.26 3.26 0.00
## 417 2013 3.98 3.98 0.00
## 418 2013 4.00 4.00 0.00
## 419 2013 3.42 3.42 0.00
## 420 2013 3.59 3.59 0.00
## 421 2014 3.43 3.43 0.00
## 422 2014 4.01 4.01 0.00
## 423 2014 4.29 4.29 0.00
## 424 2014 3.56 3.56 0.00
## 425 2014 4.01 4.01 0.00
## 426 2014 4.11 4.11 0.00
## 427 2014 3.51 3.51 0.00
## 428 2014 3.58 3.58 0.00
## 429 2014 4.57 4.57 0.00
## 430 2014 3.75 3.75 0.00
## 431 2014 3.22 3.22 0.00
## 432 2014 3.17 3.17 0.00
## 433 2014 3.56 3.56 0.00
## 434 2014 4.49 4.49 0.00
## 435 2014 4.00 4.00 0.00
## 436 2014 4.26 4.26 0.00
## 437 2014 3.38 3.38 0.00
## 438 2014 3.91 3.91 0.00
## 439 2014 3.59 3.59 0.00
## 440 2014 4.84 4.84 0.00
## 441 2014 3.40 3.40 0.00
## 442 2014 3.78 3.78 0.00
## 443 2014 3.67 3.67 0.00
## 444 2014 3.49 3.49 0.00
## 445 2014 3.79 3.79 0.00
## 446 2014 3.47 3.47 0.00
## 447 2014 3.27 3.27 0.00
## 448 2014 3.50 3.50 0.00
## 449 2014 3.50 3.50 0.00
## 450 2014 3.03 3.03 0.00
## 451 2015 4.05 4.05 0.00
## 452 2015 4.31 4.31 0.00
## 453 2015 3.98 3.98 0.00
## 454 2015 3.67 3.67 0.00
## 455 2015 4.64 4.64 0.00
## 456 2015 3.57 3.57 0.00
## 457 2015 3.73 3.73 0.00
## 458 2015 3.94 3.94 0.00
## 459 2015 4.07 4.07 0.00
## 460 2015 4.03 4.03 0.00
## 461 2015 4.14 4.14 0.00
## 462 2015 4.16 4.16 0.00
## 463 2015 3.74 3.74 0.00
## 464 2015 4.24 4.24 0.00
## 465 2015 3.80 3.80 0.00
## 466 2015 4.04 4.04 0.00
## 467 2015 4.41 4.41 0.00
## 468 2015 3.36 3.36 0.00
## 469 2015 4.33 4.33 0.00
## 470 2015 5.04 5.04 0.00
## 471 2015 3.44 3.44 0.00
## 472 2015 4.02 4.02 0.00
## 473 2015 4.28 4.28 0.00
## 474 2015 3.43 3.43 0.00
## 475 2015 4.69 4.69 0.00
## 476 2015 3.21 3.21 0.00
## 477 2015 4.09 4.09 0.00
## 478 2015 3.72 3.72 0.00
## 479 2015 2.94 2.94 0.00
## 480 2015 3.62 3.62 0.00
## 481 2016 4.22 4.22 0.00
## 482 2016 4.00 4.00 0.00
## 483 2016 4.10 4.10 0.00
## 484 2016 3.84 3.84 0.00
## 485 2016 4.24 4.24 0.00
## 486 2016 4.06 4.06 0.00
## 487 2016 4.21 4.21 0.00
## 488 2016 4.28 4.28 0.00
## 489 2016 5.08 5.08 0.00
## 490 2016 4.16 4.16 0.00
## 491 2016 4.51 4.51 0.00
## 492 2016 4.00 4.00 0.00
## 493 2016 4.20 4.20 0.00
## 494 2016 4.37 4.37 0.00
## 495 2016 3.78 3.78 0.00
## 496 2016 5.09 5.09 0.00
## 497 2016 4.51 4.51 0.00
## 498 2016 3.15 3.15 0.00
## 499 2016 4.91 4.91 0.00
## 500 2016 4.91 4.91 0.00
## 501 2016 3.70 3.70 0.00
## 502 2016 4.05 4.05 0.00
## 503 2016 4.08 4.08 0.00
## 504 2016 3.57 3.57 0.00
## 505 2016 4.63 4.63 0.00
## 506 2016 4.21 4.21 0.00
## 507 2016 4.43 4.42 -0.01
## 508 2016 3.65 3.65 0.00
## 509 2016 4.08 4.08 0.00
## 510 2016 3.51 3.51 0.00
## 511 2017 4.97 4.97 0.00
## 512 2017 3.70 3.70 0.00
## 513 2017 4.78 4.78 0.00
## 514 2017 3.30 3.30 0.00
## 515 2017 5.36 5.36 0.00
## 516 2017 4.12 4.12 0.00
## 517 2017 4.61 4.61 0.00
## 518 2017 4.20 4.20 0.00
## 519 2017 4.59 4.59 0.00
## 520 2017 3.72 3.72 0.00
## 521 2017 4.67 4.67 0.00
## 522 2017 4.46 4.46 0.00
## 523 2017 3.97 3.97 0.00
## 524 2017 4.66 4.66 0.00
## 525 2017 4.42 4.42 0.00
## 526 2017 3.66 3.66 0.00
## 527 2017 4.72 4.72 0.00
## 528 2017 3.95 3.95 0.00
## 529 2017 5.17 5.17 0.00
## 530 2017 4.51 4.51 0.00
## 531 2017 3.38 3.38 0.00
## 532 2017 4.82 4.82 0.00
## 533 2017 4.00 4.00 0.00
## 534 2017 5.01 5.01 0.00
## 535 2017 4.55 4.55 0.00
## 536 2017 4.22 4.22 0.00
## 537 2017 4.67 4.67 0.00
## 538 2017 4.50 4.50 0.00
## 539 2017 4.01 4.01 0.00
## 540 2017 3.88 3.88 0.00
## 541 2019 5.59 5.59 0.00
## 542 2019 4.70 4.70 0.00
## 543 2019 4.90 4.90 0.00
## 544 2019 3.76 3.76 0.00
## 545 2019 5.24 5.24 0.00
## 546 2019 3.66 3.66 0.00
## 547 2019 5.20 5.20 0.00
## 548 2019 5.12 5.12 0.00
## 549 2019 4.18 4.18 0.00
## 550 2019 4.31 4.31 0.00
## 551 2019 3.97 3.97 0.00
## 552 2019 4.99 4.99 0.00
## 553 2019 3.65 3.65 0.00
## 554 2019 5.06 5.06 0.00
## 555 2019 4.79 4.79 0.00
## 556 2019 4.25 4.25 0.00
## 557 2019 4.19 4.19 0.00
## 558 2019 4.10 4.10 0.00
## 559 2019 4.18 4.18 0.00
## 560 2019 5.56 5.56 0.00
## 561 2019 3.37 3.37 0.00
## 562 2019 4.74 4.74 0.00
## 563 2019 4.40 4.40 0.00
## 564 2019 4.24 4.24 0.00
## 565 2019 4.53 4.53 0.00
## 566 2019 5.18 5.18 0.00
## 567 2019 4.60 4.60 0.00
## 568 2019 4.38 4.38 0.00
## 569 2019 3.80 3.80 0.00
## 570 2019 4.27 4.27 0.00
## 571 2020 4.51 4.51 0.00
## 572 2020 5.58 5.58 0.00
## 573 2020 3.81 3.81 0.00
## 574 2020 3.29 3.29 0.00
## 575 2020 5.63 5.63 0.00
## 576 2020 4.31 4.31 0.00
## 577 2020 4.30 4.30 0.00
## 578 2020 5.09 5.09 0.00
## 579 2020 3.58 3.58 0.00
## 580 2020 4.35 4.35 0.00
## 581 2020 3.77 3.77 0.00
## 582 2020 5.03 5.03 0.00
## 583 2020 3.56 3.56 0.00
## 584 2020 5.02 5.02 0.00
## 585 2020 4.60 4.60 0.00
## 586 2020 4.84 4.84 0.00
## 587 2020 4.41 4.41 0.00
## 588 2020 3.99 3.99 0.00
## 589 2020 3.84 3.84 0.00
## 590 2020 5.59 5.59 0.00
## 591 2020 3.02 3.02 0.00
## 592 2020 4.86 4.86 0.00
## 593 2020 4.16 4.16 0.00
## 594 2020 4.98 4.98 0.00
## 595 2020 5.14 5.14 0.00
## 596 2020 4.68 4.68 0.00
## 597 2020 3.86 3.86 0.00
## 598 2020 4.64 4.64 0.00
## 599 2020 3.90 3.90 0.00
## 600 2020 5.09 5.09 0.00
## 601 2021 5.84 5.84 0.00
## 602 2021 4.26 4.26 0.00
## 603 2021 3.73 3.73 0.00
## 604 2021 4.34 4.34 0.00
## 605 2021 4.32 4.32 0.00
## 606 2021 3.78 3.78 0.00
## 607 2021 4.64 4.64 0.00
## 608 2021 4.69 4.69 0.00
## 609 2021 4.83 4.83 0.00
## 610 2021 3.74 3.74 0.00
## 611 2021 4.02 4.02 0.00
## 612 2021 4.30 4.30 0.00
## 613 2021 3.67 3.67 0.00
## 614 2021 4.79 4.79 0.00
## 615 2021 3.91 3.91 0.00
## 616 2021 5.11 5.11 0.00
## 617 2021 3.88 3.88 0.00
## 618 2021 4.87 4.87 0.00
## 619 2021 4.40 4.40 0.00
## 620 2021 4.82 4.82 0.00
## 621 2021 3.01 3.01 0.00
## 622 2021 3.96 3.96 0.00
## 623 2021 3.50 3.50 0.00
## 624 2021 3.90 3.90 0.00
## 625 2021 4.39 4.39 0.00
## 626 2021 5.08 5.08 0.00
## 627 2021 4.10 4.10 0.00
## 628 2021 3.24 3.24 0.00
## 629 2021 3.98 3.98 0.00
## 630 2021 4.80 4.80 0.00
## 631 2022 3.97 3.97 0.00
## 632 2022 4.53 4.53 0.00
## 633 2022 3.92 3.92 0.00
## 634 2022 3.46 3.46 0.00
## 635 2022 4.04 4.04 0.00
## 636 2022 2.90 2.90 0.00
## 637 2022 4.70 4.70 0.00
## 638 2022 3.77 3.77 0.00
## 639 2022 3.98 3.98 0.00
## 640 2022 3.30 3.30 0.00
## 641 2022 4.52 4.52 0.00
## 642 2022 3.59 3.59 0.00
## 643 2022 3.41 3.41 0.00
## 644 2022 4.22 4.22 0.00
## 645 2022 3.87 3.87 0.00
## 646 2022 4.25 4.25 0.00
## 647 2022 3.46 3.46 0.00
## 648 2022 4.00 4.00 0.00
## 649 2022 4.86 4.86 0.00
## 650 2022 5.06 5.06 0.00
## 651 2022 2.80 2.80 0.00
## 652 2022 3.86 3.86 0.00
## 653 2022 3.83 3.83 0.00
## 654 2022 3.57 3.57 0.00
## 655 2022 3.97 3.97 0.00
## 656 2022 4.66 4.66 0.00
## 657 2022 3.81 3.81 0.00
## 658 2022 3.85 3.85 0.00
## 659 2022 3.79 3.79 0.00
## 660 2022 5.00 5.00 0.00Interpretation: As you can observe, the error metric between calculated ERA and documented ERA is “ZERO”.
Similarly, to understand the concept of Saves (SV), I have explored websites such as Baseball Reference, FanGraphs, and other baseball-related platforms. This is what I have found out.
IT IS NOT THE RUNS SAVED BY A PLAYER.
It is a statistic awarded to a relief pitcher who effectively concludes a game for the winning team, under predetermined circumstances meant to acknowledge the pitcher for safeguarding a lead. I won’t delve into the specifics of those circumstances.
Now it all make sense about the descriptive statistics of the Saves (SV) metric.
Question - 3: Build a visualization which uses a column of data that is affected by the issue you brought up in bullet #2
In this section, our aim is to visually represent the concept of ERA, as discussed in Section 2.
Lets visualize our initial belief about the ERA - ER/G and plot the calculated ERA and documented ERA.
k |>
ggplot()+
geom_point(aes(x=yearID,y=ERA,color='red'))+
geom_point(aes(x=yearID,y=ERA_Cal,color='blue'))+
scale_color_manual(values = c('red' = 'red', 'blue' = 'blue'),
labels = c('red' = 'ERA', 'blue' = 'ERA_Cal'))+
labs(title = "Variation between ERA and ERA calculated")+
theme_classic()
Interpretation: From the above graph we can interpret that calculated ERA and documented ERA are different.
p |>
ggplot()+
geom_point(aes(x=yearID,y=ERA,color='red'))+
geom_point(aes(x=yearID,y=ERA_Cal,color='blue'))+
scale_color_manual(values = c('red' = 'red', 'blue' = 'blue'),
labels = c('red' = 'ERA', 'blue' = 'ERA_Cal')) +
labs(title = "Variation between ERA and ERA calculated")+
theme_classic()
Interpretation: From the above graph we can interpret that calculated ERA and documented ERA are same.