A comparative ranking of Cricket players

Most of the existing methods for ranking Cricket players are based on the aggregated statistics of players: total runs/total wickets, batting/bowling average, strike rate/economy rate etc. All of these methods suffer from one big flaw, which is that any player can have inflated statistics by playing against “weaker” teams, and therefore achiever a higher ranking which may not reflect the true standing of the player. We present a new ranking method which automatically takes care of the “strong” and the “weak” opponents, and is therefore more reflective of the true rank of the player in relation to his peers.

The new ranking method is based on the approach that we had presented earlier for ranking teams, in which we consider the outcomes of pairwise interactions between the teams. Instead of teams, we consider the pairwise interactions between batsmen and a bowlers, convert the pairwise interactions into “wins” and “losses” for each player and then use the above mentioned method for ranking the players. The conversion of pairwise interactions into wins and losses is based on the calculations of our RAA statistic (see the detailed article). This is purely a comparison based ranking of Cricket players, in the sense that it based on the relative performance of a player with respect to his peers, and not on the aggregated statistics of the player.

Let us first describe the method used to convert the pairwise interactions between batsmen and bowlers into wins and losses. For our illustration, we will consider one-day matches played in year 2012. A total of 283 players appeared in the one-day format in that year. The overall batting average was 32 (this excludes run-outs), and the overall strike rate of the batsmen was 76 runs per 100 balls. Consider the match-up between MS Dhoni and Lasith Malinga in 2012. The outcomes of this match-up are listed in the table given below.

Outcome	Frequency
Dot ball	16
Single	25
Double	3
Triple	1
Four	7
Six	1
Out	2

Let us now convert this interaction into “wins” and “losses” for Dhoni and Malinga.

There were 16 dot balls, which are considered as “wins” for the bowler. Since the average runs per ball is 0.76, so Malinga gets credited with 16 * 0.76 wins, which is equal to 12.16.
Singles, Doubles, Triples and Fours are all considered as wins for Dhoni, since the runs per ball in each of these outcomes is greater than 0.76. For each of these outcomes, Dhoni gets credited with (r – 0.76) wins, where r is the number of runs scored. This comes out to be a total of 39.88 wins for Dhoni.
Malinga got Dhoni out 2 times out of a total of 55 times he bowled to him. The overall batting average is 32, so the value of the two wickets is 2 * 32 = 64. Malinga is assigned total wins of 64 – 0.76 * 55 = 22.20 for getting Dhoni out 2 times out of 55.

Thus, the interaction between Dhoni and Malinga corresponds to a total of 39.88 wins for Dhoni and 12.16 + 22.20 = 34.36 wins for Malinga, i.e. a 39.88 – 34.36 overall score for the Dhoni-Malinga pair. Similarly, we compute the win and loss scores for each pairwise interactions between batsmen and bowlers. We then construct a Markov Chain model similar to what we did for ranking teams, and compute the steady-state probability of this Markov Chain. The ranks of the players are obtained by sorting the players in the decreasing order of their steady state probabilities. We call the ranks so obtained EVrank, and the corresponding scaled steady state probability EVscore. For 2012, the ranks of the players obtained using this method are shown in the table below.

Evrank	Player	Wins	Losses	Net wins	Evscore
1	V Kohli	1164	614	550	0.193
2	SP Narine	1242	877	365	0.192
3	AB de Villiers	760	271	489	0.177
4	SL Malinga	1444	1625	-181	0.175
5	KC Sangakkara	1277	878	399	0.171
6	AD Mathews	1297	1346	-49	0.163
7	HM Amla	752	322	429	0.163
8	TM Dilshan	1438	1493	-54	0.162
9	KMDN Kulasekara	1353	1810	-457	0.156
10	Saeed Ajmal	1050	885	166	0.155
11	SR Watson	1004	824	180	0.154
12	NLTC Perera	1169	1108	61	0.153
13	ST Finn	861	545	316	0.144
14	Mohammad Hafeez	1130	1356	-226	0.141
15	B Lee	1045	995	50	0.140
16	MJ Clarke	934	645	289	0.138
17	CJ McKay	948	961	-13	0.131
18	DJG Sammy	910	941	-31	0.126
19	MN Samuels	998	1038	-40	0.125
20	RJ Peterson	734	567	167	0.121
21	IR Bell	673	431	242	0.120
22	AN Cook	788	559	229	0.118
23	LD Chandimal	907	777	130	0.115
24	DA Warner	847	733	115	0.110
25	DJ Hussey	909	857	52	0.109
26	G Gambhir	746	467	279	0.107
27	KAJ Roach	620	413	207	0.106
28	MS Dhoni	626	352	274	0.105
29	AD Russell	827	797	30	0.104
30	RS Bopara	655	520	135	0.102
31	Nasir Jamshed	565	291	275	0.101
32	JM Anderson	685	617	68	0.100
33	M Morkel	646	453	192	0.100
34	DT Christian	861	910	-49	0.099
35	IK Pathan	753	634	119	0.099
36	RJ Nicol	834	739	95	0.097
37	MA Starc	672	460	212	0.094
38	WU Tharanga	838	871	-33	0.093
39	HDRL Thirimanne	710	600	110	0.093
40	XJ Doherty	820	950	-129	0.093
41	BJ Watling	420	175	245	0.093
42	DPMD Jayawardene	726	626	100	0.090
43	Mahmudullah	574	404	170	0.089
44	Misbah-ul-Haq	624	475	149	0.087
45	TG Southee	684	633	52	0.086
46	JP Duminy	609	553	57	0.084
47	IJL Trott	539	441	98	0.083
48	Azhar Ali	558	468	90	0.081
49	LL Tsotsobe	545	464	81	0.081
50	EJG Morgan	442	265	177	0.079
51	HMRKB Herath	674	993	-319	0.079
52	MEK Hussey	619	544	75	0.079
53	R Ashwin	648	747	-99	0.079
54	Shahid Afridi	728	1081	-353	0.075
55	Abdur Razzak	574	535	40	0.075
56	GJ Bailey	459	360	98	0.074
57	DJ Bravo	613	738	-125	0.073
58	KS Williamson	572	539	33	0.073
59	BW Hilfenhaus	492	482	10	0.072
60	Umar Gul	642	845	-203	0.072
61	KA Pollard	568	599	-31	0.067
62	SK Raina	582	626	-45	0.067
63	MS Wade	675	814	-139	0.066
64	SCJ Broad	513	502	11	0.066
65	KP Pietersen	356	175	180	0.065
66	BMAJ Mendis	460	364	96	0.064
67	BB McCullum	465	418	47	0.062
68	Shakib Al Hasan	488	377	110	0.062
69	KD Mills	575	669	-94	0.062
70	TT Bresnan	440	377	63	0.062
71	JL Pattinson	486	535	-49	0.061
72	DW Steyn	451	496	-45	0.060
73	MJ Guptill	484	418	66	0.059
74	KTGD Prasad	336	277	59	0.059
75	Junaid Khan	363	231	131	0.058
76	GC Smith	427	402	26	0.057
77	R Rampaul	439	491	-52	0.056
78	Umar Akmal	445	409	36	0.055
79	Aizaz Cheema	396	406	-10	0.054
80	JC Tredwell	263	206	57	0.054
81	Tamim Iqbal	412	346	66	0.053
82	CH Gayle	453	414	39	0.053
83	AM Ellis	487	612	-125	0.053
84	Sohag Gazi	349	243	105	0.052
85	Mashrafe Mortaza	457	516	-59	0.052
86	JW Dernbach	311	306	5	0.049
87	Asad Shafiq	373	355	18	0.048
88	WD Parnell	359	441	-82	0.047
89	GP Swann	341	400	-58	0.047
90	NL McCullum	488	657	-169	0.046
91	MF Maharoof	425	574	-149	0.046
92	F du Plessis	364	396	-32	0.045
93	R Vinay Kumar	441	444	-3	0.045
94	SR Tendulkar	354	330	24	0.045
95	Mushfiqur Rahim	295	250	45	0.044
96	LRPL Taylor	240	142	98	0.043
97	PJ Forrest	381	419	-38	0.043
98	C Kieswetter	263	184	78	0.043
99	SMSM Senanayake	365	489	-124	0.042
100	JDP Oram	453	526	-73	0.042
101	V Sehwag	371	448	-77	0.040
102	SR Patel	321	409	-88	0.040
103	Nasir Hossain	300	280	19	0.037
104	MK Tiwary	239	160	79	0.037
105	PW Borren	222	83	138	0.037
106	Mohammad Nabi	377	424	-47	0.037
107	DR Smith	308	405	-97	0.036
108	DM Bravo	288	321	-33	0.036
109	P Kumar	338	487	-149	0.036
110	Z Khan	362	519	-157	0.035
111	TA Boult	308	355	-47	0.035
112	MG Johnson	274	299	-25	0.035
113	Imran Farhat	263	213	49	0.034
114	TL Best	247	205	41	0.033
115	Samiullah Shenwari	273	325	-52	0.033
116	Karim Sadiq	310	308	1	0.032
117	Sohail Tanvir	296	438	-141	0.032
118	Anamul Haque	210	170	40	0.032
119	AB Dinda	266	329	-63	0.031
120	RG Sharma	310	558	-248	0.030
121	D Elgar	183	218	-35	0.030
122	PR Stirling	300	249	51	0.030
123	Abdur Rehman	212	286	-74	0.030
124	AN Kervezee	147	50	97	0.029
125	JEC Franklin	223	251	-28	0.029
126	JH Kallis	262	212	50	0.029
127	EC Joyce	235	174	61	0.029
128	M de Lange	133	47	86	0.028
129	KM Jarvis	237	262	-25	0.028
130	Dawlat Zadran	261	367	-106	0.026
131	CS MacLeod	157	64	93	0.026
132	Younis Khan	271	366	-95	0.026
133	SW Masakadza	220	196	24	0.025
134	Shafiul Islam	173	182	-8	0.025
135	UT Yadav	237	416	-179	0.025
136	RA Jadeja	283	623	-340	0.024
137	Nazmul Hossain	149	92	57	0.024
138	AR Cusack	206	179	26	0.023
139	SO Ngoche	193	128	65	0.023
140	Shapoor Zadran	209	207	2	0.022
141	TLW Cooper	167	88	78	0.022
142	DT Johnston	191	159	31	0.021
143	GJ Maxwell	185	259	-75	0.021
144	TS Nethula	195	296	-101	0.021
145	RAS Lakmal	169	217	-48	0.021
146	Mominul Haque	167	180	-13	0.020
147	GH Dockrell	210	159	51	0.020
148	BRM Taylor	183	145	38	0.020
149	V Permaul	153	161	-7	0.020
150	E Chigumbura	223	329	-106	0.020
151	AB Barath	119	98	21	0.019
152	CO Obuya	145	86	58	0.019
153	P Utseya	150	144	7	0.019
154	MR Swart	192	172	20	0.018
155	Asghar Stanikzai	145	141	4	0.018
156	Izatullah Dawlatzai	185	117	68	0.018
157	Naeem Islam	138	175	-36	0.017
158	B Kumar	80	44	36	0.017
159	DAJ Bracewell	210	340	-130	0.017
160	JA Morkel	176	269	-92	0.016
161	RM Haq	82	37	44	0.016
162	J Charles	157	223	-67	0.016
163	Shoaib Malik	114	163	-49	0.016
164	RW Price	169	242	-74	0.015
165	RR Patel	136	100	35	0.015
166	Shahadat Hossain	156	268	-112	0.015
167	T Taibu	146	144	2	0.015
168	KJ O'Brien	128	111	17	0.014
169	JO Ngoche	117	71	46	0.014
170	TWM Latham	142	221	-79	0.014
171	RJ Harris	143	242	-100	0.014
172	Sarfraz Ahmed	112	89	23	0.014
173	MD Bates	114	125	-12	0.014
174	Javed Ahmadi	168	236	-67	0.014
175	HA Varaiya	124	116	8	0.013
176	R Gunasekera	96	74	22	0.013
177	T Mishra	95	54	41	0.013
178	Mohammad Sami	98	94	4	0.013
179	C de Grandhomme	55	26	29	0.013
180	Wahab Riaz	131	188	-58	0.012
181	CK Kapugedera	108	162	-54	0.012
182	Jahurul Islam	130	198	-68	0.012
183	Mohammad Shahzad	123	188	-65	0.012
184	DC Thomas	135	202	-67	0.012
185	CR Woakes	62	63	-1	0.012
186	DR Briggs	74	49	24	0.012
187	R McLaren	78	123	-45	0.012
188	Gulbodin Naib	128	218	-89	0.012
189	Hammad Azam	91	125	-33	0.011
190	N Pradeep	101	120	-19	0.011
191	KOA Powell	111	194	-83	0.011
192	D Daesrath	85	74	11	0.011
193	PJ Cummins	84	112	-28	0.011
194	Hamza Hotak	94	99	-6	0.011
195	G Goudie	109	100	9	0.010
196	S Prasanna	92	172	-80	0.010
197	AF Milne	59	51	8	0.009
198	JH Davey	99	105	-6	0.009
199	JF Mooney	110	136	-25	0.009
200	D Soraine	92	110	-18	0.009
201	J Botha	58	48	10	0.009
202	Elias Sunny	102	149	-47	0.009
203	AJ McKay	56	138	-82	0.008
204	Nazimuddin	88	156	-68	0.008
205	T van der Gugten	88	65	23	0.008
206	I Sharma	52	59	-7	0.008
207	CKB Kulasekara	67	122	-55	0.008
208	BAW Mendis	51	70	-19	0.008
209	W Barresi	81	61	20	0.007
210	GD Drummond	49	38	11	0.007
211	NM Lyon	77	149	-72	0.007
212	CS Baugh	64	94	-30	0.007
213	PM Seelaar	88	115	-28	0.007
214	KO Meth	71	106	-35	0.006
215	JM Bairstow	41	42	-1	0.006
216	Mirwais Ashraf	69	156	-87	0.006
217	H Patel	53	77	-24	0.006
218	Junaid Siddiqui	45	59	-14	0.006
219	LMP Simmons	67	203	-135	0.006
220	JL Ontong	26	9	17	0.006
221	AN Petersen	65	98	-34	0.006
222	Nawroz Mangal	79	128	-49	0.006
223	R Sharma	64	119	-55	0.006
224	Zeeshan Siddiqi	70	58	12	0.006
225	AC Evans	39	21	18	0.006
226	VD Philander	43	47	-4	0.006
227	DR Flynn	63	145	-83	0.006
228	GC Wilson	56	105	-49	0.006
229	S Weerakoon	43	57	-14	0.005
230	JOA Gordon	66	65	1	0.005
231	NN Odhiambo	91	152	-61	0.005
232	SPD Smith	40	82	-42	0.005
233	Mohammad Irfan	40	66	-26	0.005
234	H Masakadza	67	102	-35	0.005
235	WB Rankin	68	70	-2	0.005
236	RW Chakabva	63	120	-57	0.005
237	Zakiullah Zaki	29	47	-18	0.005
238	PP Ojha	48	93	-45	0.005
239	NJ O'Brien	41	53	-11	0.004
240	AR White	57	119	-61	0.004
241	DO Obuya	56	86	-30	0.004
242	D Ramdin	44	100	-56	0.004
243	MN Waller	46	84	-37	0.004
244	TJ Murtagh	52	105	-53	0.003
245	SJ Myburgh	45	79	-34	0.003
246	I Udana	30	105	-75	0.003
247	AS Hansra	49	57	-8	0.003
248	DG Brownlie	35	44	-9	0.003
249	Najibullah Zadran	38	78	-39	0.003
250	BV Vitori	46	148	-102	0.003
251	NR Kumar	20	43	-22	0.003
252	CRD Fernando	18	108	-90	0.002
253	TMK Mawoyo	20	11	9	0.002
254	AA Obanda	26	43	-17	0.002
255	RD Berrington	30	66	-36	0.002
256	RG Aga	26	55	-28	0.002
257	DI Allan	32	90	-57	0.002
258	RT Ponting	31	169	-138	0.002
259	MAA Jamil	27	62	-35	0.002
260	PL Mommsen	29	73	-43	0.002
261	JH Stander	22	45	-23	0.002
262	WTS Porterfield	29	128	-99	0.002
263	Shabir Noori	15	34	-18	0.002
264	Abul Hasan	24	76	-52	0.001
265	Mudassar Bukhari	25	111	-86	0.001
266	Adnan Akmal	13	33	-20	0.001
267	Rubel Hossain	15	55	-40	0.001
268	JD Ryder	12	69	-56	0.001
269	Yuvraj Singh	10	72	-62	0.001
270	AM Rahane	11	34	-22	0.001
271	Kamran Akmal	11	67	-56	0.001
272	Rahat Ali	8	39	-31	0.001
273	DR Ramsammy	2	2	0	0.001
274	YK Pathan	6	35	-29	0.001
275	CA Ingram	10	59	-48	0.001
276	Noor Ali Zadran	11	33	-22	0.001
277	S Matsikenyeri	9	94	-85	0.001
278	TN de Grooth	8	34	-26	0.000
279	PA Patel	5	32	-27	0.000
280	KJ Coetzer	5	32	-27	0.000
281	Usman Limbada	2	2	0	0.000
282	RMS Eranga	1	1	0	0.000
283	JC Buttler	0	31	-31	0.000

One big advantage of our ranking is that it takes into account both the batting and the bowling performance of a player, and therefore requires no need for generating batting and bowling ranks separately. This is not the case with the existing ranking methods, where the two are always computed separately. In the coming days, we will upload the ranks of the EVranks of the players for each calendar year since 2002, and for Test, ODIs and T20 Internationals, on the website.