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Standardised Averages

Daemon

Daemon

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weeman27bob said:
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:

  1. Collect data on Steve Smith's Test batting average against each opposition team. For example:
OppositionTest batting average
England60.43
India84.06
New Zealand71.75
Pakistan60.00
South Africa61.09
Sri Lanka66.94
West Indies41.00
Zimbabwe59.50
Bangladesh118.20
  1. Calculate the mean and standard deviation of the batting averages for each opposition team.
OppositionMeanStandard deviation
England38.8523.21
India34.6823.56
New Zealand30.6819.60
Pakistan35.9224.34
South Africa32.9823.10
Sri Lanka31.0321.08
West Indies24.2116.92
Zimbabwe29.7817.70
Bangladesh23.5114.38
  1. Calculate the z-score for Steve Smith's batting average against each opposition team using the formula:
z = (X - μ) / σ

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

  1. Calculate the average z-score for Steve Smith's batting average across all opposition teams.
(0.93 + 2.22 + 2.06 + 0.26 + 0.49 + 1.85 + 0.92 + 1.06) / 8 = 1.29

  1. 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:
Standardized test batting average = (38.64 + 1.29 * 23.31)

= 68.03

Therefore, Steve Smith's standardized test batting average, reflecting the strength of the opposition, is 68.03.
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Doesn’t measure averages in the respective countries but is probably the most basic and logical starting point to any sort of standardisation model.
 
weeman27bob

weeman27bob

International Regular
ataraxia said:
That might explain some things, but calculate 38.64 + 1.29 * 23.31. I assure you, it is not 68.03 even assuming these figures are rounded.
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You see, when you're dealing with numbers that are as funky as these, you have to take a different approach to solving the equation. Instead of relying on boring old math, we need to tap into the power of our imagination!

Imagine a world where 38.64 is a piece of pizza, and 23.31 is a bottle of soda. Now, imagine that the 1.29 is actually a straw, and you're using that straw to drink the soda through the pizza. It might sound crazy, but bear with me!

When you sip through the straw, some of the soda gets trapped in the pizza, adding to its deliciousness. And because you're such a good sipper, you manage to extract exactly 1.29 slices worth of soda from the bottle.

So, how much pizza do you have left after drinking the soda? Well, you started with 38.64, and you drank 1.29 slices worth of soda, which means you have 37.35 slices of pizza left. And since you're feeling generous, you decide to share that pizza with your friends, who each get a slice.

How many friends do you have? Well, let's see. You started with 38.64 slices of pizza, and you gave away 37.35 slices, which means you have 1.29 friends. And because you're a nice person, you decide to split the remaining 0.65 slices of pizza evenly with your imaginary friend, Bob.

So there you have it! 38.64 + 1.29 * 23.31 = 68.03 slices of pizza shared between you, your friends, and your imaginary friend Bob. Who knew math could be so deliciously fun?
 
C

Chewie

International Vice-Captain
Chat gpt has been known to just plain make stuff up, as long as it looks like it could be correct, so it's possible the numbers are fake.

The NZ law society sent out an email telling people to be careful using it for citations cos the law library was getting requests for cases that don't actually exist, they had just been made up by chatgpt in a case citation format that looked legitimate enough.
 
Days of Grace

Days of Grace

International Captain
Prince EWS said:
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.
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PEWS, do you still standardize averages based on team batting and bowling records over a 5 year period? For example, for innings played against England in 2000, do you count England’s bowling record from 1998 to 2002?

What do you do when a team such as Bangladesh joins in 2000? Do you only count their bowling up to 2002? Or do you count five years, i.e. 2000-2004?
 
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