Sachin Tendulkar better than Don Bradman, new study shows

[honestbharani]

Any study that normalizes averages needs to have some sort of arbitrary adjustment to the data to adjust for different conditions. Numerous such studies have been done and holes can be picked in all of them.

I was just pointing out that when a statistical study turns up a result that one doesn't like - the first response is to discredit it using various means which is many fans do- regardless of whether that criticism is valid or not..

The point is that without having to "normalize" and "assign weights" or having to do any other sort of completely arbitrary data manipulation, it is obvious that Bradman was just MUCH MUCH better than his contemporaries than Sachin ever was. And given the fact inspite of being more than 100 years old, Cricket as a game has always seen an average of around 50 be the benchmark of test match batting greatness shows that things have evened out inspite of the diferences that have come through the game over the different generations. Bradman averages about 100 and Sachin about 56. End of Story.

 

[zaremba]

Imagine the fanboy frenzy if Bradman were Indian, and playing today. There wouldn't be enough tissues in the world.

Let's face it, someone like Hammond would be a great in any era. Yet Bradman was almost twice as good as him. I don't care how many times people try to belittle or twist the stats, Bradman is obviously head and shoulders above all others.

I can't believe I'm descending into this, it's so ****ing ridiculous.

 

[BoyBrumby]

How many innings did it take for Sir Donald to move from 99 first class hundreds to 100? Guessing it's fewer than however many it's already been for Sachin with his 100 international hundreds.

One jests, obvz. I just don't see how these crackpot calculations sucker so many people in. Bradman is such a massive outlier statistically speaking (this article calculates him as being 4.4 standard deviations above the mean) there's no reasonable way anyone can match up to him.

 

[zaremba]

I've said it before and I'll say it again.

Viv Richard's batting average places him closer to Chris Martin than Don Bradman.

 

[smash84]

CLT has no such requirements, and CLT says or assumes nothing about actual underlying distributions.

A random variable (for example runs scored in an innings) can have any underlying distribution (runs scored in an innings is definitely not a normal distribution, it has a very high right skew). If you take samples of that random variable, and calculate sample mean, this sample mean is itself a new random variable. CLT says that irrespective of the underlying distribution the sample mean will converge to a normal distribution as the sample size goes up.

It is a very, very strong result in statistics, the very basis of all stats actually. You can see it in action in simulations. There is this animation I could find on web that shows it. Underlying distribution is a bimodal distribution (anything but normal). But if you calculate mean of ever larger samples, the distribution of sample mean approaches normal.

EDIT: Some more illustrations

Uniform distribution - Central Limit Theorem
Triangular distribution - Central Limit Theorem (triangle)
1/X distribution - Central Limit Theorem 1/X
Parabolic distribution - Central Limit Theorem (parabola)

haha.....I did think that mean = mode assumption in normal distribution was some really flawed understanding by Jake but its good to see our stats guru come up with the proper explanation.

Ankit WAG and WAC

 

[ankitj]

OK, stats time, what distribution would you use to model batsmen's innings?

What tests would you consider as appropriate to make a call on the significance level of their average after 80 Tests?

I would take a memoryless distribution because it's fair to assume that the probability of a batsman getting out any time is independent of what score he is on. And since runs scored in an innings is a discrete variable (one can consider it continuous though for all practical purposes), Geometric Distribution becomes a natural candidate. The parameter p can, rather neatly, be described as the probability of a batsman losing his wicket before he scores the next run. This probability would be assumed independent of the score he is on, and it will be much higher for Chris Martin than for Tendulkar.

This is how the distribution would look:

On test for significance level, I guess t-test should work as always.

 

[Hit Wicket]

However much you choose to discard Bradman's average by 2 points here for playing minnow, 5 points there for playing in 2 countries he is still going to trump everyone, so huge is the margin between him and everyone else.

And, anyways am I supposed to take any ranking seriously which places Kallis and Dravid as the 3rd and 4th best batsmen ever?

 

[ankitj]

haha.....I did think that mean = mode assumption in normal distribution was some really flawed understanding by Jake but its good to see our stats guru come up with the proper explanation.

Ankit WAG and WAC

Well he said mean = median, not mode. And he is right that that holds for a normal distribution. It's just that CLT holds irrespective of what the underlying distribution is.

 

[smash84]

This thread wasn't actually as bad as a lot of people were making it out to be, even though it was never really going to go anywhere particularly good.

One thing people were discussing that I felt I had to comment on was use of the CLT and normal distribution. I'm afraid that doesn't hold at all, the set of all of a batsman's innings can't be modelled as a normal distribution, because a normal distribution assumes that the population mean and mode are equal, and the distribution is symmetric about the mean.

Well he said mean = median, not mode. And he is right that that holds for a normal distribution. It's just that CLT holds irrespective of what the underlying distribution is.

I take back WAG, WAC

 

[Neil Pickup]

haha.....I did think that mean = mode assumption in normal distribution was some really flawed understanding by Jake but its good to see our stats guru come up with the proper explanation.

Ankit WAG and WAC

What are you suggesting to be the mode of a normal distribution, then?

 

[ankitj]

I must have lot of time, and I get high doing spreadsheet work, so I put my suggestion of using geometric distribution to test. I used Tendulkar's test innings because he has the most number of them. I added score in an unbeaten innings to next completed innings, to get scores between successive dismissals. For the geometric distribution, I derived the parameter p as simply reciprocal of his test average i.e. 1/56 or 1.8% (meaning that probability that Tendulkar gets out without adding another run at any stage is 1.8%). This is how the predicted and actual distribution look like:

Not bad

 

[Neil Pickup]

Can you balance out the category widths on that X axis?

 

[ankitj]

Can you balance out the category widths on that X axis?

Done. Edited original post. Looks even better now!

 

[ankitj]

I take back WAG, WAC

My bad Rest of my post holds true though. For normal dist. mean=median=mode, so no big deal.

 

[dhillon28]

here is a compromise:

Sachin greatest player of the professional era

Bradman greatest player of the amateur era

 

[MW1304]

No.

 

[honestbharani]

here is a compromise:

Sachin greatest player of the professional era

Bradman greatest player of the amateur era

here is the truth:


Bradman - The Greatest Player of all eras.

 

[zaremba]

here is a compromise:

Sachin greatest player of the professional era

Bradman greatest player of the amateur era

Let's keep it real. Forget about "eras". Even if we ignore the likes of Richards and Chappell and Sobers, and we restrict the comparison to Tendulkar's direct contemporaries, Warne, Kallis, Ponting, Lara, McGrath, Murali are all as "great" as him, or as near as dammit.

 

[NasserFan207]

I don't think either of them are the greatest players of their eras, but I rate bowlers/allrounders above batsmen.

 

[zaremba]

Out of interest, who would you say was the greatest player of Bradman's era?