Ex) Baseball statistics¶

$$ \newcommand{\eg}{{\it e.g.}} \newcommand{\ie}{{\it i.e.}} \newcommand{\argmin}{\operatornamewithlimits{argmin}} \newcommand{\mc}{\mathcal} \newcommand{\mb}{\mathbb} \newcommand{\mf}{\mathbf} \newcommand{\minimize}{{\text{minimize}}} \newcommand{\diag}{{\text{diag}}} \newcommand{\cond}{{\text{cond}}} \newcommand{\rank}{{\text{rank }}} \newcommand{\range}{{\mathcal{R}}} \newcommand{\null}{{\mathcal{N}}} \newcommand{\tr}{{\text{trace}}} \newcommand{\dom}{{\text{dom}}} \newcommand{\dist}{{\text{dist}}} \newcommand{\R}{\mathbf{R}} \newcommand{\SM}{\mathbf{S}} \newcommand{\ball}{\mathcal{B}} \newcommand{\bmat}[1]{\begin{bmatrix}#1\end{bmatrix}} $$

ASE1302: Computer programming, Inha University.

Jong-Han Kim (jonghank@inha.ac.kr)
Jun-Hyon Cho (junhyoncho@inha.edu)

Throughout the baseball history, the management guys of ball-clubs have tried to evaluate baseball players, and they created some statistics such as 'Average (타율)', 'Runs Batted In (RBI, 타점)', 'Earned Run Average (ERA, 평균자책점)' and so on. But these have some limitations in measuring the "real value" of the players, so some complicated mathematical stuffs came in and a new approach called 'SABERMETRICS' was introduced.

We will first download a dataset describing the starting pitchers' statistics from the MLB season 2019. For your information, these can be obtained from fangraphs.com.

In [ ]:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

df = pd.read_csv('https://jonghank.github.io/ase1302/files/FanGraphs_Leaderboard_2019.csv')
df

Out[ ]:

	Name	Team	W	L	ERA	G	GS	CG	ShO	IP	TBF	H	R	ER	HR	BB	IBB	HBP	WP	BK	SO	playerid
0	Hyun-Jin Ryu	Dodgers	14	5	2.32	29	29	1	1	182.2	723	160	53	47	17	24	2	4	0	0	163	14444
1	Jacob deGrom	Mets	11	8	2.43	32	32	0	0	204.0	804	154	59	55	19	44	1	7	2	0	255	10954
2	Gerrit Cole	Astros	20	5	2.50	33	33	0	0	212.1	817	142	66	59	29	48	0	3	4	3	326	13125
3	Justin Verlander	Astros	21	6	2.58	34	34	2	1	223.0	847	137	66	64	36	42	0	6	4	0	300	8700
4	Mike Soroka	Braves	13	4	2.68	29	29	0	0	174.2	701	153	56	52	14	41	1	7	3	0	142	18383
5	Jack Flaherty	Cardinals	11	8	2.75	33	33	0	0	196.1	772	135	62	60	25	55	2	7	6	0	231	17479
6	Sonny Gray	Reds	11	8	2.87	31	31	0	0	175.1	708	122	59	56	17	68	1	7	7	1	205	12768
7	Max Scherzer	Nationals	11	7	2.92	27	27	0	0	172.1	693	144	59	56	18	33	2	7	0	0	243	3137
8	Zack Greinke	- - -	18	5	2.93	33	33	0	0	208.2	810	175	73	68	21	30	2	4	2	1	187	1943
9	Clayton Kershaw	Dodgers	16	5	3.05	28	28	0	0	177.1	703	145	63	60	28	41	0	2	7	1	188	2036
10	Charlie Morton	Rays	16	6	3.05	33	33	0	0	194.2	790	154	71	66	15	57	0	12	5	1	240	4676
11	Marcus Stroman	- - -	10	13	3.22	32	32	0	0	184.1	774	183	77	66	18	58	1	1	7	0	159	13431
12	Patrick Corbin	Nationals	14	7	3.25	33	33	1	1	202.0	835	169	81	73	24	70	2	3	4	0	238	9323
13	Walker Buehler	Dodgers	14	4	3.26	30	30	2	0	182.1	737	153	77	66	20	37	0	7	4	0	215	19374
14	Shane Bieber	Indians	15	8	3.26	33	33	3	2	212.1	851	184	85	77	31	40	1	5	6	1	257	19427
15	Stephen Strasburg	Nationals	18	6	3.32	33	33	0	0	209.0	841	161	79	77	24	56	4	10	8	0	251	10131
16	Dakota Hudson	Cardinals	16	7	3.36	32	32	0	0	174.0	754	160	80	65	22	85	8	9	5	0	136	19206
17	Luis Castillo	Reds	15	8	3.40	32	32	0	0	190.2	781	139	76	72	22	79	0	7	5	3	226	15689
18	Lucas Giolito	White Sox	14	9	3.41	29	29	3	2	176.2	705	131	69	67	24	57	1	4	6	0	228	15474
19	Kyle Hendricks	Cubs	11	10	3.46	30	30	1	1	177.0	730	168	78	68	19	32	1	9	1	0	150	12049
20	Jeff Samardzija	Giants	11	12	3.52	32	32	0	0	181.1	740	152	78	71	28	49	4	6	5	0	140	3254
21	Mike Minor	Rangers	14	10	3.59	32	32	2	1	208.1	863	190	86	83	30	68	1	7	2	0	200	10021
22	Lance Lynn	Rangers	16	11	3.67	33	33	0	0	208.1	875	195	89	85	21	59	0	8	18	0	246	2520
23	Jose Berrios	Twins	14	8	3.68	32	32	1	0	200.1	842	194	94	82	26	51	0	9	8	1	195	14168
24	Eduardo Rodriguez	Red Sox	19	6	3.81	34	34	0	0	203.1	859	195	88	86	24	75	2	7	3	0	213	13164
25	Julio Teheran	Braves	10	11	3.81	33	33	0	0	174.2	754	148	81	74	22	83	3	14	5	1	162	6797
26	Anibal Sanchez	Nationals	11	8	3.85	30	30	0	0	166.0	712	153	77	71	22	58	10	4	1	3	134	3284
27	Aaron Nola	Phillies	12	7	3.87	34	34	0	0	202.1	852	176	91	87	27	80	3	11	3	0	229	16149
28	Sandy Alcantara	Marlins	6	14	3.88	32	32	2	2	197.1	838	179	94	85	23	81	5	8	4	1	151	18684
29	Brett Anderson	Athletics	13	9	3.89	31	31	0	0	176.0	743	181	80	76	20	49	2	4	4	0	90	8223
30	Anthony DeSclafani	Reds	9	9	3.89	31	31	0	0	166.2	696	151	77	72	29	49	5	4	2	1	167	13050
31	Mike Fiers	Athletics	15	4	3.90	33	33	1	1	184.2	754	166	82	80	30	53	0	9	13	1	126	7754
32	Madison Bumgarner	Giants	9	9	3.90	34	34	0	0	207.2	844	191	99	90	30	43	3	10	3	0	203	5524
33	Zack Wheeler	Mets	11	8	3.96	31	31	0	0	195.1	828	196	93	86	22	50	4	2	5	0	195	10310
34	Yu Darvish	Cubs	6	8	3.98	31	31	0	0	178.2	731	140	82	79	33	56	1	11	11	0	229	13074
35	Wade Miley	Astros	14	6	3.98	33	33	0	0	167.1	720	164	83	74	23	61	0	5	4	2	140	8779
36	Marco Gonzales	Mariners	16	13	3.99	34	34	0	0	203.0	866	210	106	90	23	56	1	6	2	1	147	15467
37	Miles Mikolas	Cardinals	9	14	4.16	32	32	1	1	184.0	764	193	90	85	27	32	1	12	5	2	144	9803
38	Joey Lucchesi	Padres	10	10	4.18	30	30	0	0	163.2	686	144	78	76	23	56	0	2	8	0	158	19320
39	Brad Keller	Royals	7	14	4.19	28	28	0	0	165.1	709	154	80	77	15	70	2	9	9	1	122	15734
40	Adam Wainwright	Cardinals	14	10	4.19	31	31	0	0	171.2	745	181	83	80	22	64	7	8	2	0	153	2233
41	Noah Syndergaard	Mets	10	8	4.28	32	32	1	1	197.2	825	194	101	94	24	50	2	6	4	0	202	11762
42	Mike Leake	- - -	12	11	4.29	32	32	2	1	197.0	835	227	114	94	41	27	2	10	2	0	127	10130
43	Robbie Ray	Diamondbacks	12	8	4.34	33	33	0	0	174.1	747	150	91	84	30	84	5	5	7	0	235	11486
44	Tanner Roark	- - -	10	10	4.35	31	31	0	0	165.1	722	180	84	80	28	51	1	13	3	0	158	8753
45	Merrill Kelly	Diamondbacks	13	14	4.42	32	32	0	0	183.1	777	184	95	90	29	57	4	2	4	0	158	11156
46	Jon Lester	Cubs	13	10	4.46	31	31	0	0	171.2	764	205	101	85	26	52	0	5	3	0	165	4930
47	Masahiro Tanaka	Yankees	11	8	4.47	31	31	1	1	179.0	744	181	93	89	28	39	0	2	7	0	147	15764
48	Trevor Bauer	- - -	11	13	4.48	34	34	1	1	213.0	911	184	118	106	34	82	0	19	10	0	253	12703
49	Joe Musgrove	Pirates	11	12	4.49	31	31	0	0	168.1	712	168	98	84	21	39	1	9	2	0	156	12970
50	Matthew Boyd	Tigers	9	12	4.56	32	32	0	0	185.1	788	178	101	94	39	50	1	8	6	4	238	15440
51	Homer Bailey	- - -	13	9	4.57	31	31	0	0	163.1	696	162	84	83	21	53	1	4	4	1	149	8362
52	Ivan Nova	White Sox	11	12	4.72	34	34	2	0	187.0	806	225	107	98	30	47	1	9	7	0	114	1994
53	German Marquez	Rockies	12	5	4.76	28	28	1	1	174.0	721	174	96	92	29	35	0	5	14	1	175	15038
54	Jose Quintana	Cubs	13	9	4.80	31	31	0	0	167.0	725	186	98	89	20	43	0	2	11	0	144	11423
55	Jakob Junis	Royals	9	14	5.24	31	31	0	0	175.1	771	192	108	102	31	58	1	11	4	0	164	13619
56	Reynaldo Lopez	White Sox	10	15	5.38	33	33	1	0	184.0	809	203	119	110	35	65	0	8	5	2	169	16400
57	Rick Porcello	Red Sox	14	12	5.52	32	32	0	0	174.1	768	198	114	107	31	45	2	6	5	2	143	2717

One of the most famous stats in sabermetrics is the 'Fielding Independent Pitching (FIP, 수비무관 평균자책점)'. In a ball game, earned runs are not only decided by the pitching skills, but also decided by a lot of other factors such as the size of the field and the fielding skills of position players. Hence, sabermetricians who deal with sabermetrics pay attention to the position-player-independent factors. For example, the strike-outs or the base-on-balls are independent of the performances of position players, but only a pitcher is involved. So the FIP can be represented by using these independent factors as follows.

$$ FIP = \frac{13HR+3(BB-IBB+HBP)-2SO}{IP} +3.20 $$
Here, IP, BB, IBB, HBP, HR and SO denote Inning Pitched, Base on Balls, Intentional Base on Balls, Hit By Pitch, HomeRuns, and StrikeOuts, respectively.

(Problem 1) Calculate the FIP of the pitchers using the above formula, and append it as a new column on your dataframe. Display the results on a plot.

In [ ]:

# your code here

(Problem 2) The MLB is divided into two leagues; the National League(NL) and the American League(AL). By running below cell, you can get the lists made of the NL and the AL teams.

In [ ]:

AL = ['Yankees', 'Rays', 'Red Sox', 'Blue Jays', 'Orioles', 'Twins', 'Indians', 'White Sox', 'Royals', 'Tigers', \
      'Astros', 'Athletics', 'Rangers', 'Angels', 'Mariners']
NL = ['Braves', 'Nationals', 'Mets', 'Phillies', 'Marlins', 'Cardinals', 'Brewers', 'Cubs', 'Reds', 'Pirates', 'Dodgers', \
      'Diamondbacks', 'Giants', 'Padres', 'Rockies']

For each league, list the top five pitchers with lowest FIPs. You may ignore the players with "- - -" on the "Team" field.

In [ ]:

# your code here

AL top 5 pitchers for FIP: ['Gerrit Cole' 'Charlie Morton' 'Lance Lynn' 'Justin Verlander'
 'Shane Bieber']
NL top 5 pitchers for FIP: ['Max Scherzer' 'Jacob deGrom' 'Walker Buehler' 'Hyun-Jin Ryu'
 'Stephen Strasburg']

(Problem 3) Every year, the Cy Young Award is given to the most outstanding pitcher in each league of MLB. The award was introduced in 1956 by Commissioner Ford Frick and approved by the Baseball Writers Association of America. The award is named in honor of Hall of Fame pitcher Cy Young who died a year earlier in 1955. Based on the given dataset, we would like to anticipate who the recipient will be. To predict winners, we can use the following two predictors.

Tom Tango Cy Young Award predictor:

$$ \text{Cy Young Points (Tom Tango)} = \frac{1}{2}IP-ER + \frac{1}{10}SO + W $$

ESPN Cy Young Award predictot:

$$ \text{Cy Young Points (ESPN)} = \frac{5}{9}IP - ER +\frac{SO}{12}+2.5SV + ShO + 6W-2L $$

By using the above two models, predict the future Cy Young Award recipients from each league.

In [ ]:

# your code here

By Tom Tango`s model, Gerrit Cole in AL and Jacob deGrom in NL will win the Cy Young Award
By ESPN`s model, Justin Verlander in AL and Stephen Strasburg in NL will win the Cy Young Award

The list of the Cy Young Award winners, including the season 2019, can be found here: https://www.baseball-reference.com/bullpen/Cy_Young_Award.

Check if your predictors made reasonable predictions.