When I posted this thread yesterday, I suspected the main concern would be to do with sample sizes, leading to some players with short careers appearing high on the lists. The main concern generated through such is sample size, which reducing overall certainty in the results.
Of the results, the most controversial were around the bowlers as they were picked, below is the top 50 for your consideration:
| Rank | Player | Matches | Wickets | Average | WPM | Era | Adjust | Rating |
|---|---|---|---|---|---|---|---|---|
| 1 | SF Barnes (ENG) | 27 | 189 | 16.43 | 7.000 | 26.54 | 18.58 | 0.6139 |
| 2 | Sir RJ Hadlee (NZ) | 86 | 431 | 22.30 | 5.012 | 32.17 | 20.79 | 0.4910 |
| 3 | MD Marshall (WI) | 81 | 376 | 20.95 | 4.642 | 32.25 | 19.49 | 0.4881 |
| 4 | PJ Cummins (AUS) | 30 | 143 | 21.83 | 4.767 | 32.11 | 20.39 | 0.4835 |
| 5 | GD McGrath (AUS) | 124 | 563 | 21.64 | 4.540 | 33.10 | 19.62 | 0.4811 |
| 6 | DW Steyn (SA) | 93 | 439 | 22.95 | 4.720 | 33.56 | 20.52 | 0.4796 |
| 7 | DK Lillee (AUS) | 70 | 355 | 23.92 | 5.071 | 31.86 | 22.53 | 0.4745 |
| 8 | J Garner (WI) | 58 | 259 | 20.98 | 4.466 | 31.54 | 19.95 | 0.4731 |
| 9 | Mohammad Asif (PAK) | 23 | 106 | 24.37 | 4.609 | 35.17 | 20.78 | 0.4709 |
| 10 | AA Donald (SA) | 72 | 330 | 22.25 | 4.583 | 31.92 | 20.92 | 0.4681 |
| 11 | FS Trueman (ENG) | 67 | 307 | 21.58 | 4.582 | 30.91 | 20.95 | 0.4677 |
| 12 | CEL Ambrose (WI) | 98 | 405 | 20.99 | 4.133 | 31.85 | 19.77 | 0.4572 |
| 13 | K Rabada (SA) | 43 | 197 | 22.96 | 4.581 | 31.21 | 22.07 | 0.4556 |
| 14 | AK Davidson (AUS) | 44 | 186 | 20.53 | 4.227 | 30.17 | 20.42 | 0.4550 |
| 15 | RJ Harris (AUS) | 27 | 113 | 23.52 | 4.185 | 33.95 | 20.79 | 0.4487 |
| 16 | CEH Croft (WI) | 27 | 125 | 23.30 | 4.630 | 29.93 | 23.36 | 0.4452 |
| 17 | Waqar Younis (PAK) | 87 | 373 | 23.56 | 4.287 | 32.54 | 21.72 | 0.4443 |
| 18 | AV Bedser (ENG) | 51 | 236 | 24.90 | 4.627 | 31.76 | 23.52 | 0.4436 |
| 19 | Imran Khan (PAK) | 88 | 362 | 22.81 | 4.114 | 32.23 | 21.23 | 0.4401 |
| 20 | SR Clark (AUS) | 24 | 94 | 23.86 | 3.917 | 35.33 | 20.26 | 0.4397 |
| 21 | NAT Adcock (SA) | 26 | 104 | 21.11 | 4.000 | 30.05 | 21.07 | 0.4357 |
| 22 | BA Reid (AUS) | 27 | 113 | 24.64 | 4.185 | 32.93 | 22.45 | 0.4318 |
| 23 | SM Pollock (SA) | 108 | 421 | 23.12 | 3.898 | 33.09 | 20.96 | 0.4313 |
| 24 | MA Holding (WI) | 60 | 249 | 23.69 | 4.150 | 31.68 | 22.43 | 0.4301 |
| 25 | PM Pollock (SA) | 28 | 116 | 24.19 | 4.143 | 32.33 | 22.44 | 0.4296 |
| 26 | Wasim Akram (PAK) | 104 | 414 | 23.62 | 3.981 | 32.20 | 22.00 | 0.4253 |
| 27 | Mohammad Abbas (PAK) | 21 | 80 | 21.70 | 3.810 | 30.04 | 21.67 | 0.4192 |
| 28 | AME Roberts (WI) | 47 | 202 | 25.61 | 4.298 | 31.16 | 24.66 | 0.4175 |
| 29 | MG Johnson (AUS) | 73 | 313 | 28.41 | 4.288 | 34.45 | 24.74 | 0.4163 |
| 30 | CA Walsh (WI) | 132 | 519 | 24.45 | 3.932 | 32.17 | 22.80 | 0.4153 |
| 31 | N Wagner (NZ) | 48 | 206 | 26.60 | 4.292 | 32.06 | 24.90 | 0.4152 |
| 32 | MA Starc (AUS) | 57 | 244 | 26.98 | 4.281 | 32.09 | 25.22 | 0.4120 |
| 33 | JA Snow (ENG) | 49 | 202 | 26.67 | 4.122 | 32.64 | 24.51 | 0.4101 |
| 34 | VD Philander (SA) | 64 | 224 | 22.32 | 3.500 | 32.17 | 20.82 | 0.4100 |
| 35 | Shoaib Akhtar (PAK) | 46 | 178 | 25.70 | 3.870 | 33.24 | 23.19 | 0.4085 |
| 36 | TM Alderman (AUS) | 41 | 170 | 27.15 | 4.146 | 32.57 | 25.01 | 0.4072 |
| 37 | IR Bishop (WI) | 43 | 161 | 24.28 | 3.744 | 32.09 | 22.70 | 0.4062 |
| 38 | RR Lindwall (AUS) | 61 | 228 | 23.03 | 3.738 | 30.36 | 22.75 | 0.4053 |
| 39 | Fazal Mahmood (PAK) | 34 | 139 | 24.71 | 4.088 | 29.71 | 24.95 | 0.4048 |
| 40 | JM Anderson (ENG) | 156 | 600 | 26.80 | 3.846 | 33.62 | 23.91 | 0.4011 |
| 41 | WW Hall (WI) | 48 | 192 | 26.39 | 4.000 | 31.62 | 25.04 | 0.3997 |
| 42 | MHN Walker (AUS) | 34 | 138 | 27.48 | 4.059 | 32.42 | 25.43 | 0.3995 |
| 43 | JL Pattinson (AUS) | 21 | 81 | 26.33 | 3.857 | 32.03 | 24.67 | 0.3955 |
| 44 | JR Hazlewood (AUS) | 51 | 195 | 26.20 | 3.824 | 31.83 | 24.69 | 0.3935 |
| 45 | TA Boult (NZ) | 67 | 267 | 27.66 | 3.985 | 32.09 | 25.86 | 0.3926 |
| 46 | MG Hughes (AUS) | 53 | 212 | 28.38 | 4.000 | 32.80 | 25.96 | 0.3925 |
| 47 | CJ McDermott (AUS) | 71 | 291 | 28.63 | 4.099 | 32.22 | 26.66 | 0.3921 |
| 48 | JN Gillespie (AUS) | 71 | 259 | 26.14 | 3.648 | 33.01 | 23.75 | 0.3919 |
| 49 | DW Fleming (AUS) | 20 | 75 | 25.89 | 3.750 | 31.48 | 24.68 | 0.3898 |
| 50 | RGD Willis (ENG) | 90 | 325 | 25.20 | 3.611 | 31.79 | 23.78 | 0.3897 |
Now, these concerns are valid, but because bowling averages have uncertainty that tends with the square root of wickets taken, these uncertainties get small fairly quickly. That said, as pointed out, comparing someone like McGrath, with 563 wickets, to someone like Cummins with 143 does run that concern.
Now, there are a number of ways to take into account this issue with uncertainty. One such method is to use bayesian inference. To do this, we need a prior distribution, which in this instance is the average distribution of bowlers playing test cricket. We need both a mean and a standard deviation for the two metrics used, these being bowling average and wickets per match. To find this, the same analysis was applied to set of all bowlers with at least 20 tests being one of the first four bowlers to bowl in an innings. This took into account the same era effects as before:
| What | Average | WPM |
|---|---|---|
| Mean | 29.80 | 3.083 |
| Stdev | 7.11 | 1.001 |
To make use of this, we need to make a few assumptions:
- All bowlers in the set have sufficiently large samples that the likelihood function for their averages behaves as a normal distribution.
- The samples for bowlers is large enough that wicket taking behaves as an exponential distribution, hence the standard deviation of the distribution of 'runs per wicket' is approximately the same as the average.
- The standard deviation for wickets per match is approximately 0.60 times the wickets per match value.
2 and 3 can be shown to be approximately true in general from surveys of player data (varies by about 10% player to player), while 1 is generally true just from the sample size used. The impact of breaking these assumptions is basically making the next step order of magnitude fiddlier, but doesn't impact the results to any great extent. The method that'll we'll be using is the standard for determining a posterior distribution's average for two normal distributions, breaking the assumptions makes it messier as we can't use that calculation anymore. The calculation itself is annoying to format on reddit, so I'll just post it as an image here. Here, mu represents the averages of the posterior (denoted such) and prior (denoted with a 0) as well as the average from the likelihood function (x-bar) and their respective standard deviations (sigma and sigma 0).
In any case, armed with this, we can use the players averages and the expected distributions of players to determine an average that we, in effect, have the evidence to claim. That is, the way to think about the numbers produced are to see them not as their actual averages, but rather, a value that we can confidently claim with the evidence given. If you've ever wanted to quantify that thought of "well, if a guy has 500 wickets at 25.00, and another has 100 wickets at 24.00, I'd go with the guy with 500 still", this is basically the formal way of doing that. Here, we'll be using
In any case, below is the new top 50, using those adjusted values. I've included the old rating for comparison sake. As would be expected, it has had a large impact on the likes of Cummins and Asif.
| Rank | Player | Matches | Wickets | B-WPM | B-Adj | Old Rat | B-Rat |
|---|---|---|---|---|---|---|---|
| 1 | SF Barnes (ENG) | 27 | 189 | 5.455 | 18.97 | 0.6139 | 0.5363 |
| 2 | Sir RJ Hadlee (NZ) | 86 | 431 | 4.829 | 20.97 | 0.4910 | 0.4799 |
| 3 | MD Marshall (WI) | 81 | 376 | 4.506 | 19.69 | 0.4881 | 0.4784 |
| 4 | GD McGrath (AUS) | 124 | 563 | 4.458 | 19.75 | 0.4811 | 0.4751 |
| 5 | DW Steyn (SA) | 93 | 439 | 4.591 | 20.69 | 0.4796 | 0.4710 |
| 6 | J Garner (WI) | 58 | 259 | 4.314 | 20.24 | 0.4731 | 0.4616 |
| 7 | DK Lillee (AUS) | 70 | 355 | 4.840 | 22.73 | 0.4745 | 0.4615 |
| 8 | PJ Cummins (AUS) | 30 | 143 | 4.407 | 20.90 | 0.4835 | 0.4591 |
| 9 | AA Donald (SA) | 72 | 330 | 4.441 | 21.14 | 0.4681 | 0.4583 |
| 10 | FS Trueman (ENG) | 67 | 307 | 4.430 | 21.19 | 0.4677 | 0.4573 |
| 11 | CEL Ambrose (WI) | 98 | 405 | 4.071 | 19.96 | 0.4572 | 0.4517 |
| 12 | Mohammad Asif (PAK) | 23 | 106 | 4.229 | 21.46 | 0.4709 | 0.4439 |
| 13 | AK Davidson (AUS) | 44 | 186 | 4.082 | 20.82 | 0.4550 | 0.4428 |
| 14 | K Rabada (SA) | 43 | 197 | 4.358 | 22.43 | 0.4556 | 0.4408 |
| 15 | Waqar Younis (PAK) | 87 | 373 | 4.202 | 21.92 | 0.4443 | 0.4378 |
| 16 | Imran Khan (PAK) | 88 | 362 | 4.047 | 21.44 | 0.4401 | 0.4345 |
| 17 | AV Bedser (ENG) | 51 | 236 | 4.425 | 23.80 | 0.4436 | 0.4312 |
| 18 | RJ Harris (AUS) | 27 | 113 | 3.977 | 21.42 | 0.4487 | 0.4309 |
| 19 | SM Pollock (SA) | 108 | 421 | 3.859 | 21.14 | 0.4313 | 0.4273 |
| 20 | CEH Croft (WI) | 27 | 125 | 4.287 | 23.87 | 0.4452 | 0.4237 |
| 21 | SR Clark (AUS) | 24 | 94 | 3.761 | 21.02 | 0.4397 | 0.4230 |
| 22 | MA Holding (WI) | 60 | 249 | 4.050 | 22.71 | 0.4301 | 0.4223 |
| 23 | Wasim Akram (PAK) | 104 | 414 | 3.934 | 22.18 | 0.4253 | 0.4212 |
| 24 | NAT Adcock (SA) | 26 | 104 | 3.834 | 21.75 | 0.4357 | 0.4199 |
| 25 | BA Reid (AUS) | 27 | 113 | 3.977 | 23.04 | 0.4318 | 0.4154 |
| 26 | PM Pollock (SA) | 28 | 116 | 3.952 | 23.02 | 0.4296 | 0.4143 |
| 27 | CA Walsh (WI) | 132 | 519 | 3.898 | 22.93 | 0.4153 | 0.4123 |
| 28 | MG Johnson (AUS) | 73 | 313 | 4.188 | 24.93 | 0.4163 | 0.4099 |
| 29 | AME Roberts (WI) | 47 | 202 | 4.148 | 24.95 | 0.4175 | 0.4077 |
| 30 | N Wagner (NZ) | 48 | 206 | 4.145 | 25.17 | 0.4152 | 0.4058 |
| 31 | VD Philander (SA) | 64 | 224 | 3.473 | 21.15 | 0.4100 | 0.4052 |
| 32 | MA Starc (AUS) | 57 | 244 | 4.157 | 25.45 | 0.4120 | 0.4042 |
| 33 | Mohammad Abbas (PAK) | 21 | 80 | 3.665 | 22.52 | 0.4192 | 0.4034 |
| 34 | JA Snow (ENG) | 49 | 202 | 4.007 | 24.81 | 0.4101 | 0.4019 |
| 35 | Shoaib Akhtar (PAK) | 46 | 178 | 3.787 | 23.56 | 0.4085 | 0.4009 |
| 36 | RR Lindwall (AUS) | 61 | 228 | 3.688 | 23.06 | 0.4053 | 0.3999 |
| 37 | JM Anderson (ENG) | 156 | 600 | 3.821 | 24.02 | 0.4011 | 0.3989 |
| 38 | IR Bishop (WI) | 43 | 161 | 3.675 | 23.12 | 0.4062 | 0.3987 |
| 39 | TM Alderman (AUS) | 41 | 170 | 4.007 | 25.33 | 0.4072 | 0.3977 |
| 40 | Fazal Mahmood (PAK) | 34 | 139 | 3.937 | 25.34 | 0.4048 | 0.3942 |
| 41 | WW Hall (WI) | 48 | 192 | 3.902 | 25.33 | 0.3997 | 0.3925 |
| 42 | MHN Walker (AUS) | 34 | 138 | 3.914 | 25.80 | 0.3995 | 0.3895 |
| 43 | JN Gillespie (AUS) | 71 | 259 | 3.612 | 24.00 | 0.3919 | 0.3879 |
| 44 | TA Boult (NZ) | 67 | 267 | 3.914 | 26.04 | 0.3926 | 0.3877 |
| 45 | JR Hazlewood (AUS) | 51 | 195 | 3.754 | 24.99 | 0.3935 | 0.3876 |
| 46 | CJ McDermott (AUS) | 71 | 291 | 4.019 | 26.80 | 0.3921 | 0.3872 |
| 47 | RGD Willis (ENG) | 90 | 325 | 3.585 | 23.98 | 0.3897 | 0.3867 |
| 48 | MG Hughes (AUS) | 53 | 212 | 3.910 | 26.19 | 0.3925 | 0.3864 |
| 49 | M Ntini (SA) | 101 | 390 | 3.822 | 25.81 | 0.3878 | 0.3848 |
| 50 | JL Pattinson (AUS) | 21 | 81 | 3.700 | 25.33 | 0.3955 | 0.3822 |
Jimmy moves to the 12th XI!
[link] [comments]
from Cricket https://ift.tt/2EGFJNP
via IFTTT
No comments:
Post a Comment