A kinda academic but important question for those who have done systematic statistical analysis of cricket stats, beyond pivot tables & visualization. Like regression type analysis.
Do y'all also have problems with the IID assumption? I do.
@hganjoo153 @cricketingview
Do y'all also have problems with the IID assumption? I do.
@hganjoo153 @cricketingview
And this might be a concern not just with cricket, but all sports. IID assumes that all outcomes are "independent" and "identically distributed". When you toss a coin or dice, each result truly is IID.
But sports events are so not at all IID!
But sports events are so not at all IID!
In fact, in sports, there should be mandatory autocorrelation terms and some kind of hierarchical var-covar structure. Markov process is an option, but it ties you too strongly to t-1. But year specific, series specific, venue specific covariances make more "theoretical" sense.
Just thinking out loud as I'm starting my first "formal" research project using cricket data. And model specification is where I spend a lot of my time to pre-empt all possible reviewer 3 objections. What even is the underlying distribution? There has to be one.
Let me try to put this in layperson terms.
For us to make inferences and predictions from data, we need to make defensible assumptions about how the phenomenon of interest plays.
Coin toss 50-50 is one such assumption. Normal distribution is another. And so on.
For us to make inferences and predictions from data, we need to make defensible assumptions about how the phenomenon of interest plays.
Coin toss 50-50 is one such assumption. Normal distribution is another. And so on.
So what "distribution" (if a parametric one even exists) does a batter's score come from? Currently, when we calculate things like standard deviations and probability ranges in cricket stats, we assume IID. Like a batter is a roulette wheel, without memory.
Longitudinal models, Markov process etc take care of this by not assuming independence, but rather, assuming a correlation with the previous outcome. Which makes sense for share prices or commodity prices, which have stickiness between t-1 and t. But sports is different.
If Apple stock price yesterday and the day before were around 175, it's not like tomorrow it'll open at 22 or 3500. So that t-1 method captures a lot of the time variance. But in cricket, and many sports, your "score" fluctuates wildly.
Not all sports.
Not all sports.
If you're modeling a sprinter or runner or swimmer's times, yeah, the t-1 will have a lot of info. But a batter at the top of their game can have scores like 175, 0, 23, 117, 3, 222 and you'll be like, wow, great series. But what's the underlying distribution?
I know some of you might be thinking, what about the Random Walk process? Yeah, could work. But still not quite "elegant", is it?
What is the underlying distribution and/or process for a cricket inning? Cos there are sooooo many endogenous variables!
What is the underlying distribution and/or process for a cricket inning? Cos there are sooooo many endogenous variables!
Anyway, just thinking out loud. It's model specification stage where I spend months asking questions like these to myself all day and then trying to answer them.
The research on this specific broader question is sparse, but interesting and providing. Like this 20 year old JASA that tested this for tennis and found that tennis points are very much NOT iid!
Cricket is a way more complex game than tennis.
Cricket is a way more complex game than tennis.
In fact in terms of the sheer range of values for scores, I don't think any sport comes close to cricket. We have stats that range from the thousands and the hundreds to multi dimensional scores to fractions and such. No other sport uses the decimal system so enthusiastically!
Oh I forgot I live in the same city as this guy. Will just go to his office after the holidays and pick his brains. Cos this is exactly what I'm thinking about as well. The memoryless assumptions, be they IID or Markovian, seem to lack face validity.
https://twitter.com/vishalmisra/status/1401193746180587531?s=20
Imagine the number of interesting statistical tests you can run on each single delivery. Soooo many outcomes!
Out or not: Seems like a binomial distribution but with extremely skewed parameters
Runs scored: Zero inflated Poisson?
And many more. Fun stuff.
Out or not: Seems like a binomial distribution but with extremely skewed parameters
Runs scored: Zero inflated Poisson?
And many more. Fun stuff.
This point is more academic/philosophical but just because some data behave like IID doesn't make the underlying process IID by default. Especially when we can very clearly see that there is no such thing as independence or memorylessness in sport. Quasi-IID at best.
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