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Standardised Averages
- Thread starter ma1978
- Start date
Prince EWS
Global Moderator
Cricinfo changing their scorecard format means I need to redo parts of my code, and I haven't had time for a while because people thought it'd be a good idea for me to become a factional warlord and then a political campaign manager.
Now that the election is over I might have more time soon though.
Now that the election is over I might have more time soon though.
Victor Ian
International Coach
Pft. Just give it to chatgpt
weeman27bob
International Vice-Captain
To calculate a standardized test batting average for Steve Smith that reflects the strength of the opposition, we need to use a statistical method called z-score.
The z-score is a measure of how many standard deviations a data point is from the mean of a distribution. In this case, we will use the z-score to compare Steve Smith's batting average against the batting averages of all other players who have faced the same opposition.
Here are the steps to calculate Steve Smith's standardized test batting average:
- Collect data on Steve Smith's Test batting average against each opposition team. For example:
| Opposition | Test batting average |
|---|---|
| England | 60.43 |
| India | 84.06 |
| New Zealand | 71.75 |
| Pakistan | 60.00 |
| South Africa | 61.09 |
| Sri Lanka | 66.94 |
| West Indies | 41.00 |
| Zimbabwe | 59.50 |
| Bangladesh | 118.20 |
- Calculate the mean and standard deviation of the batting averages for each opposition team.
| Opposition | Mean | Standard deviation |
|---|---|---|
| England | 38.85 | 23.21 |
| India | 34.68 | 23.56 |
| New Zealand | 30.68 | 19.60 |
| Pakistan | 35.92 | 24.34 |
| South Africa | 32.98 | 23.10 |
| Sri Lanka | 31.03 | 21.08 |
| West Indies | 24.21 | 16.92 |
| Zimbabwe | 29.78 | 17.70 |
| Bangladesh | 23.51 | 14.38 |
- Calculate the z-score for Steve Smith's batting average against each opposition team using the formula:
where X is Steve Smith's batting average against the opposition, μ is the mean batting average for the opposition, and σ is the standard deviation of the batting averages for the opposition.
For example, to calculate the z-score for Steve Smith's batting average against England:
z = (60.43 - 38.85) / 23.21 z = 0.93
- Calculate the average z-score for Steve Smith's batting average across all opposition teams.
- Finally, calculate Steve Smith's standardized test batting average by adding the average z-score to the overall mean batting average of all players, and multiplying by the overall standard deviation of batting averages:
= 68.03
Therefore, Steve Smith's standardized test batting average, reflecting the strength of the opposition, is 68.03.
Victor Ian
International Coach
Nice - but that is not the method we are looking for. We want the one where his average is 69.
Coronis
International Coach
Swear he’s been trotting out this same old excuse for years
Prince EWS
Global Moderator
Yeah it has literally been years since I've had time to do it. Back to back elections.
Brook's side
International Regular
Genuinely not sure if this is a (quite clever and decently prepared) joke or intended to be serious?
Shady Slim
International Coach
would it not make more sense for the figure to be subtracted to be the average of other batsmen at that position against england during smith’s career? i know it’s a lot more finicky but
Brook's side
International Regular
Well yeah, or top 6 batsmen.
Do people know what the relevance of 'standard deviation' is then in this context?
ataraxia
International Coach
proof that analysis by checklist really is the domain of robots and robots alone
Red_Ink_Squid
Global Moderator
Aka "Hurry up and get on with it PEWS."
Brook's side
International Regular
It probably wouldn't surprise anyone if I was to reveal that I'm not a mathematician.
But I'd have thought that the way to approach it was something like this:
1. Identify a standard of 1.00, which represents the benchmark team bowling performance against top 6 batsmen.
2. Split test matches down into say 3 year intervals.
3. Assign each international team (at home and also away) a rating proportionate to the benchmark rating of 1.00 during each interval
4. Multiply each innings of the batsman by the appropriate rating, to give a revised/adjusted innings score
5. Calculate the average of the adjusted innings
But I'd have thought that the way to approach it was something like this:
1. Identify a standard of 1.00, which represents the benchmark team bowling performance against top 6 batsmen.
2. Split test matches down into say 3 year intervals.
3. Assign each international team (at home and also away) a rating proportionate to the benchmark rating of 1.00 during each interval
4. Multiply each innings of the batsman by the appropriate rating, to give a revised/adjusted innings score
5. Calculate the average of the adjusted innings
Brook's side
International Regular
So if we start at say 2000 (and just assess batsmen who started playing from then on).
We're looking at 10 teams * 2 (home and away) * 8 intervals = 160+
ireland & afghanistan * 2 intervals = 8
= 168 intervals to assess and apply to each innings (2000-2023).
Not saying there's not a lot of work in it, but it's a good system.
You have a spreadsheet with worksheet for each country (or for each period, but say each country). On the worksheet you'd have rows for each 3 year period (so 8 currently rows), and 2 columns for home and away.
Then you have worksheets for each player you're assessing (or several players on each worksheet). You have 1 column for his score, 1 column for whether he was not out, and one column for your rating which you look up in the other worksheets. Then it just self calculates.
We're looking at 10 teams * 2 (home and away) * 8 intervals = 160+
ireland & afghanistan * 2 intervals = 8
= 168 intervals to assess and apply to each innings (2000-2023).
Not saying there's not a lot of work in it, but it's a good system.
You have a spreadsheet with worksheet for each country (or for each period, but say each country). On the worksheet you'd have rows for each 3 year period (so 8 currently rows), and 2 columns for home and away.
Then you have worksheets for each player you're assessing (or several players on each worksheet). You have 1 column for his score, 1 column for whether he was not out, and one column for your rating which you look up in the other worksheets. Then it just self calculates.
Last edited:
Days of Grace
International Captain
For my standardized averages, I use the runs and wickets taken by each bowling side in the last four years, which double weighting for the most recent two years. It’s like the ICC test championship, but using runs and wickets.The weighted bowling average for each team is updated at the end of each series.
Once I have all that data, then I divide each team bowling average by 32 - the mean RPW for tests since 1877.
Once I have all that data, then I divide each team bowling average by 32 - the mean RPW for tests since 1877.
Brook's side
International Regular
that's fine for form but why would you do that if you're comparing careers figures?
Line and Length
Cricketer Of The Year
There are, as the saying goes, 'lies, damned lies, and statistics.' I'll settle on straight-forward averages.
Brook's side
International Regular
My 1.00 btw is indexed to the average of all top 6 batsmen in test cricket this century.
So the spreadsheet would need to use formulas, you couldn't just input a rating (not that you'd want to anyway with that amount of data) as it's constantly in flux/evolving.
To get the rating (r), you do the following:
1. calculate the average of all top 6 batsmen this century (a)
2. calculate the average of all top 6 batsmen in the 3 year period (either home or away as applicable) against the particular bowling country (b)
3. r = a/b
So the spreadsheet would need to use formulas, you couldn't just input a rating (not that you'd want to anyway with that amount of data) as it's constantly in flux/evolving.
To get the rating (r), you do the following:
1. calculate the average of all top 6 batsmen this century (a)
2. calculate the average of all top 6 batsmen in the 3 year period (either home or away as applicable) against the particular bowling country (b)
3. r = a/b
Last edited:
Days of Grace
International Captain
I think you misinterpreted my post. For each innings that a batsmen plays, their runs are adjusted based on the form of the bowling side. If you add up all those adjusted runs and divide it by number of outs you will get an adjusted career average.
Spark
Global Moderator
Unironically more insightful than 95% of analysis by checklist posts