# Chaitanya's Random Pages

## September 25, 2014

### Players with low test cricket + one day international cricket bowling averages

Filed under: cricket,sport — ckrao @ 8:40 pm

Recently I pointed out players with high sum of test cricket and one day cricket batting averages. This time I shall look at those with a low sum of bowling averages.

Amongst former players Joel Garner heads the list while many big names are here. It’s a shame Shane Bond wasn’t able to play more. This first list shows those with a bowling average sum below 50.

Former players

 Test cricket One day international cricket Player Matches Wickets Average Matches Wickets Average Economy Rate Test Average + ODI Average J Garner 58 259 20.97 98 146 18.84 3.09 39.81 SE Bond 18 87 22.09 82 147 20.88 4.28 42.97 GD McGrath 124 563 21.64 250 381 22.02 3.88 43.66 Sir RJ Hadlee 86 431 22.29 115 158 21.56 3.3 43.85 CEH Croft 27 125 23.30 19 30 20.66 3.47 43.96 AA Donald 72 330 22.25 164 272 21.78 4.29 44.03 DK Lillee 70 355 23.92 63 103 20.82 3.58 44.74 MA Holding 60 249 23.68 102 142 21.36 3.32 45.04 CEL Ambrose 98 405 20.99 176 225 24.12 3.48 45.11 M Muralitharan 133 800 22.72 350 534 23.08 3.93 45.80 Sir AME Roberts 47 202 25.61 56 87 20.35 3.4 45.96 Wasim Akram 104 414 23.62 356 502 23.52 3.89 47.14 Waqar Younis 87 373 23.56 262 416 23.84 4.68 47.40 SM Pollock 108 421 23.11 303 393 24.50 3.67 47.61 MD Marshall 81 376 20.94 136 157 26.96 3.53 47.90 DL Underwood 86 297 25.83 26 32 22.93 3.44 48.76 Imran Khan 88 362 22.81 175 182 26.61 3.89 49.42 RGD Willis 90 325 25.20 64 80 24.60 3.28 49.80 DE Bollinger 12 50 25.92 39 62 23.90 4.57 49.82

Among current players with over 50 wickets in both forms of the game only Dale Steyn would qualify for the above list. The list below contains those current players with bowling averages below 30 in both test and ODI cricket.

Current players

 Test cricket One day international cricket Player Matches Wickets Average Matches Wickets Average Economy Rate Test Average + ODI Average RJ Harris 24 103 22.56 21 44 18.90 4.84 41.46 VD Philander 26 115 21.57 15 17 26.05 4.37 47.62 DW Steyn 75 383 22.56 87 135 25.62 4.82 48.18 Saeed Ajmal 35 178 28.10 111 183 22.18 4.13 50.28 KAJ Roach 28 111 25.98 64 98 26.85 4.90 52.83 MG Johnson 59 264 27.42 140 212 26.11 4.84 53.53 M Morkel 59 204 29.90 80 135 24.28 4.88 54.18 ST Finn 23 90 29.40 42 62 28.41 4.74 57.81 SCJ Broad 74 264 29.90 108 168 28.37 5.22 58.27 JM Anderson 99 380 29.72 184 257 29.10 4.94 58.82

Statistics are current to 25 Sep 2014 and are from ESPN Cricinfo here and here. I located current players using Statsguru via this query.

## September 15, 2014

### A good simple approximation of the complementary error function

Filed under: mathematics — ckrao @ 12:12 pm

I learnt from [1] that the complementary error function $\displaystyle \text{erfc}(x) = \sqrt{\frac{2}{\pi}}\int_x^{\infty}e^{-t^2}\ dt$ can be well approximated as follows for positive $x$:

$\displaystyle \text{erfc}(x) \approx \exp(-c_1x-c_2x^2), x > 0$

where

$\displaystyle c_1=1.09500814703333, \quad c_2=0.75651138383854.$

As mentioned in [2], this approximation is found by applying the non-linear least squares method to estimate the parameters $c_1, c_2$ based on 500 points equally spaced in the interval [0,5].

The graphs below show how well this approximation holds across positive $x$. By symmetry one could use $2-\exp(c_1x-c_2x^2)$ as an approximation of $\text{erfc}(x)$ for negative $x$.

Only two parameters are needed, but each were specified to 14 decimal places in to obtain the accuracy (maximum error just over 0.002) seen here. Such an approximation would be useful for working with functions (e.g. products) of error functions  (see [1] for an example).

#### References

[1] Product of two complementary error functions (erfc) – Mathematics Stack Exchange.

[2] W.-J. Tsay, C.J. Huang, T.-T. Fu, I-L. Ho, Maximum Likelihood Estimation of Censored Stochastic Frontier Models: An Application to the Three-Stage DEA Method, No 09-A003, IEAS Working Paper : academic research from Institute of Economics, Academia Sinica, Taipei, Taiwan. Available at http://econ.ccu.edu.tw/academic/master_paper/090323seminar.pdf.

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