Another method of rating batsmen across formats since 2015

Today I got this in my inbox:

Suggest a different method Harsha Bhogle

In reference to this previous thread.

Now, keep in mind, I personally feel that Root is an excellent cross format batsman, who gets vastly underrated due to his faltering test form. Even with that, he is still an excellent test batsman, up there with the best. What is interesting though is the question of whether there are any reasonable ways of making an 'across format' rating for batsmen.

This problem has two key components:

1. Rating players in the three formats.
2. Combining these ratings.

The OP of the other post made the following statement about point 2:

Do a weighted average, if you wanna, he'll still be in the top 3. P×Test+ Q×Odi+ R×T20is/(P+Q+R). Now test,odi and t20is are absolute runs scored in the respective formats. However choosing the parameters 0< P,Q,R<1 is a subjective choice, depending on what importance you assign to each format. You almost cannot generalise that, so I'd say this combined stats is a pretty good approximation from the mathematical and practical pov. 🤷

Now, I disagree with the method of averaging noted. I would suggest, and will use, a geometric mean, as it does the scaling of the different metrics for us naturally, and doesn't lead to the problem that arithmetic averages have in that sense.

The point about arbitrary choices is also important, but ultimately, if we're during a true 'cross format' rating, to me at least, it must be equally weighted.

I also disagree with their 'well, that has arbitrariness, so we can just do anything 🤷' point of view, but that's a different point.

Anyhow, we can proceed knowing that once we have the three different ratings for the three different formats, we can take a straight geometric mean to get our results. Now the question is how to make those ratings.

Also note, for the sake of comparison we'll be doing 2015 to now, as they did the last 5 years. For me this means the 2015 season to now, so the totals will be slightly different. I only thought about the direct comparability after already doing the analysis, but ultimately it's just about the same thing, and the point is more about the process anyhow. I'll also be using a 20 matches and 20 dismissals cutoff for all three formats; there's got to be a cutoff somewhere.

Now, *tests are easy. It's just the batting average. There's a point to raise about this later, which will be discussed then, but for the moment we'll run with this. The top 15 from this method over that period are below.

Tests

Player	Mat	Inns	Runs	Average
SPD Smith (AUS)	47	81	4923	69.34
AC Voges (AUS)	20	31	1485	61.88
V Kohli (INDIA)	53	86	4693	58.66
KS Williamson (NZ)	41	69	3442	56.43
CA Pujara (INDIA)	50	80	3767	49.57
DA Warner (AUS)	48	87	4111	49.53
RG Sharma (INDIA)	22	35	1479	49.30
LRPL Taylor (NZ)	39	65	2607	47.40
JE Root (ENG)	75	137	6091	47.22
Younis Khan (PAK)	22	41	1772	46.63
Babar Azam (PAK)	29	53	2045	45.44
UT Khawaja (AUS)	35	60	2510	44.82
Azhar Ali (PAK)	42	78	3278	44.30
AN Cook (ENG)	52	97	4049	44.01
S Dhawan (INDIA)	21	35	1492	43.88

For ODIs and T20Is this is a bit more complicated. We need to deal with both average and SR to effectively capture their contribution to batting, particularly in T20Is. A straight geometric mean would be one method for both, but this doesn't capture the actual balance of things. Think about the two ways that an innings can go:

1. Team is all out
2. Innings ends with batsmen still at the crease

In the 2nd case, you always want higher SRs to maximise your score. In the first case, you need higher averages to maximise your score. On this basis, a weighted geometric mean, which can be done averaging two numbers A and B as AⁿB^m where n+m=1, would make sense. This weighted will be between the batting average and SR, where batting average will be done to the power of the fraction of innings that the team is all out, and SR will be done to the fraction of innings that there are still batsmen at the crease.

The period chosen will be the same as the data for the players of course. All will be treated the same, even though different teams will have different fractions involved, and this arguably would impact how they play. For those curious, teams are all out 34.5% of the time in ODIs and 16.0% of the time in T20Is over the same. This means, naturally, that SR will be weighted higher in T20Is, as would be expected.

I'd also note the same logic could, to an extent, be applied to Tests, which see teams all out in 71.6% of innings. The issue here, however, is that it's not always a case of teams wanting to maximise runs in uncompleted innings, ie teams wanting draws, the impact of English, weather, etc, all plays a role. So I've decided against including such, as I can't find a self consistent manner to find the innings that this would be valid for. Just going to declarations could work, but even then there's questions about how innings are composed.

Anyhow, below are the top 15 for ODIs and T20Is for the above method:

ODIs

Player	Mat	Inns	Runs	Ave	SR	Rating
JC Buttler (ENG)	87	70	2563	47.46	124.60	89.30
V Kohli (INDIA)	90	89	5330	73.01	97.96	88.51
AB de Villiers (SA)	41	39	1636	52.77	111.90	86.33
DA Warner (AUS)	61	61	3220	57.50	100.16	82.70
RG Sharma (INDIA)	89	88	4895	62.76	95.61	82.68
JM Bairstow (ENG)	73	67	2892	48.20	107.23	81.37
F du Plessis (SA)	69	65	3164	60.85	92.00	79.77
LRPL Taylor (NZ)	73	69	3440	64.91	86.69	78.45
Imad Wasim (PAK)	53	39	952	41.39	109.68	78.35
JE Root (ENG)	92	87	4120	58.03	90.83	77.81
CH Gayle (WI)	32	30	1259	41.97	106.24	77.10
JJ Roy (ENG)	90	86	3459	41.18	107.09	77.00
BA Stokes (ENG)	71	62	2400	50.00	96.66	76.99
Q de Kock (SA)	77	77	3504	48.00	98.54	76.87
Haris Sohail (PAK)	24	24	1128	56.40	89.59	76.37

T20Is

Player	Mat	Inns	Runs	Ave	SR	Rating
GJ Maxwell (AUS)	37	34	1233	45.67	159.10	130.35
AJ Finch (AUS)	39	39	1233	37.36	158.08	125.56
C Munro (NZ)	51	50	1530	33.26	160.55	124.87
V Kohli (INDIA)	54	50	1822	53.59	142.01	121.55
KL Rahul (INDIA)	42	38	1461	45.66	146.10	121.34
E Lewis (WI)	32	31	934	32.21	155.41	120.88
HG Munsey (SCOT)	38	36	987	29.91	154.22	118.69
MJ Guptill (NZ)	40	39	1263	33.24	150.90	118.52
Q de Kock (SA)	24	24	769	33.43	148.46	117.02
Shoaib Malik (ICC/PAK)	55	50	1362	42.56	140.70	116.25
Najibullah Zadran (AFG)	52	45	872	34.88	145.33	115.72
DA Warner (AUS)	27	27	763	36.33	143.69	115.37
Mohammad Nabi (AFG)	53	49	1079	26.98	151.54	115.05
RG Sharma (INDIA)	66	65	2034	33.34	144.05	114.04
EJG Morgan (ENG)	40	39	1005	32.42	144.40	113.76

Finally, we can do the actual comparison. To be eligible, players must be eligible for all three sports in the first place, though no necessarily in the top 15 for each.

Cross Format

Player	Tests	ODI	T20I	Cross
V Kohli (INDIA)	58.66	88.51	121.55	85.78
DA Warner (AUS)	49.53	82.70	115.37	77.89
RG Sharma (INDIA)	49.30	82.68	114.04	77.46
KS Williamson (NZ)	56.43	68.65	103.71	73.79
LRPL Taylor (NZ)	47.40	78.45	102.42	72.49
JE Root (ENG)	47.22	77.81	103.16	72.37
Babar Azam (PAK)	45.44	73.93	110.52	71.87
Q de Kock (SA)	39.26	76.87	117.02	70.69
S Dhawan (INDIA)	43.88	75.30	102.79	69.77
JC Buttler (ENG)	32.54	89.30	113.64	69.12
KL Rahul (INDIA)	34.74	70.72	121.34	66.80
Mushfiqur Rahim (BDESH)	42.27	72.17	91.71	65.40
C de Grandhomme (NZ)	37.03	68.52	105.85	64.52
Sarfaraz Ahmed (PAK)	33.80	65.30	100.06	60.44
N Dickwella (SL)	32.31	65.68	101.49	59.94
BKG Mendis (SL)	36.98	59.54	96.26	59.62
Mahmudullah (BDESH)	32.87	58.56	104.75	58.64
LD Chandimal (SL)	39.76	57.58	86.56	58.30
Liton Das (BDESH)	26.03	65.85	101.59	55.84
MJ Santner (NZ)	25.55	58.81	87.77	50.90

This is the full list of all eligible players. Anyone not on this list did not reach the minimum requirements to be included. This includes Steve Smith, who has only played 18 T20Is in that time.

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