Implication, Probability, Logic : IPL

IPL is the most important thing ever happened since India became independent. No matter what the critics say, it is the annual celebration of India, that reaches to every home of India with a TV, and arguably, brings a huge amount of happiness. Which brings us to the current situation of club loyalty. Here is our group, making it anonymous because IPL team support can be truly fanatic.

This establishes a nice pattern to the thing. That is, IPL truly makes you forget what your origin is, it is way more Indian that it is regional, albeit people are supporting regional teams. That is truly an information, and that is good!

The Curse of A True Supporter

Which brings up betting. If any BCCI officials are looking for it, sorry, our bets are about 5 INR, on which team will win today, and more emotional in support than logical, reasonable betting. But then a very interesting pattern emerged on one of my friends support data. Here is how it his success rate of support looked like :

These were enough to raise eyebrows. Is it really happening? I mean, do we have enough data to correlate that if our friend was supporting X team, it was bound to loose? These data set is a very small sample ( initial) of what we noticed.  Of course we claimed that our friend has a curse, like any astrologer would have, and boldly claimed that the team he supports : will lose out. But, then, is there a real curse here?

The Data Visualisation

Here is the plot, taking cue from Data Science ( read Statisticians ).

We showcase (+1) as the win while our friend supported the winning team, and (-1) is where our friends supported in a lost cause.

Curse : As a Coin Toss

Suppose this data were to be generated by a random coin tossing experiment. That is, if Head, then the team our friend supported, wins. If tails, then the team looses. We can create a random variable mapped to as:

CURSE(H) = +1 // When Toss yields Head 
CURSE(T) = -1 // When it is Tails 

and thus, we can estimate the samples estimated probability. It turns out to be approximately : 0.46. Wow! That is something. That is to say, if these whole sequence would be generated by simple chance factor of a coin toss, then the coin is not that much unbiased! It has an observed (estimated) probability close to 0.5. That is fascinating. Can we actually prove that the coin tossed was that of an unbiased coin? Turns out, we actually can do that! Welcome to statistical hypothesis testing.

Proving Our Friend's Innocence

The friendly neighborhood R can solve this for us. What we seek is known as Testing a Coin is Fair or not! Of course we should be testing that, unless we want to prove that there is ESP. Here is an example how. In concrete R terms, this is what we do:

> binom.test(12,28,0.5)

    Exact binomial test

data:  12 and 28
number of successes = 12, number of trials = 28, p-value = 0.5716
alternative hypothesis: true probability of success is not equal to 0.5
95 percent confidence interval:
 0.2446239 0.6282064
sample estimates:
probability of success 
             0.4285714 

Now, the p-value is 0.5716. As this is not less than the significance level of 0.05, we cannot reject the null hypothesis that the probability of head is indeed 0.5. This means that there is no evidence to prove that the coin is not fair!

Thus, my friend is not cursed, or his luck is not even biased to any extent. Those observations of failure were random flukes, and can safely be attributed to chance!

In fact as we are code guys, here is a much simpler interpretation:

l = list([0:28]) -> { random(true) } // create random boolean of size 28
h = select(l)::{ $.o } // select heads 
s = size(h) // 14 ish.

Our friend is only 2 short of that.

Psychology Generates Bias

However, that finding was NOT really the point of the post. The point of the post is, the never fading psychology of bias. People, in high position sometimes take decisions not based on solid data, but on gut feeling. Newsflash, your gut does not have brain.

The observer bias actually is a very real thing. In any stochastic sequence, there will be a run of so called bad luck, that does not make one cursed, because you have sampled a bit, and was unlucky to be just there. That is a sampling bias!

We tend to forget the situations where we won ( in case of IPL ) or we tend to forget the situations when something miserably failed ( in case of kindle fire phone ). This is the observer bias, we want to forget the miserable stuff, and sometime, the same we want to recall the miserable stuff.

Honestly speaking, what should have been my friends success rate at predicting the winning team that would have proved existence of an extra sensory perception or rather a curse? Let's experiment a bit :

> binom.test(8,28,0.5)

    Exact binomial test

data:  8 and 28
number of successes = 8, number of trials = 28, p-value = 0.0357
alternative hypothesis: true probability of success is not equal to 0.5
95 percent confidence interval:
 0.1322365 0.4866683
sample estimates:
probability of success 
             0.2857143 

If he would have failed 20 out of 28 times, then we had to reject the null hypothesis. Here, the p-value is 0.035, lower than that of the 0.05. Our friend's luck is way clear of being that miserable.

Summary

In every decision making, there are inherent biases. Statistics is a nice tool, it may or may not help you to decide, but it definitely helps you take a stand on what not to be decided upon.

PS. Yes, I know, 28 tosses are very low compared to what it should have been, but still the reasoning and the message remains valid. In any case, one IPL will never have more than 100 matches. 28 is good enough. It really is.