What is a Sport

I hope most of us play one or the other sports or game etc..etc..
Why do we play anyway..
Some to win..Some for fitness..Some for relaxation..
This is at gully level So what about international players...Why do they play..Of course for money and fame..But at least I hope some play to win, to earn respect.

If any one of you have seen last night India Vs West Indies 3rd test 2011. None of the above mentioned reasons could confirm why the hell they played for 5 days.

The day started with Edwards and Chandrapaul showing tremendous commitment to save the gave. A Draw if not a win. The Indians eventhough loosing mukund for the first ball were relatively stable requiring 84 runs in 90 balls with 7 wickets in hand. I was watching it on TV although it was 3:00 AM in the night I was looking forward for a tight finish. I wanted to see players battle it out. I was looking forward for an exciting test match which goes till the last ball of a 5 day game. It could be the test match of the year or this decade with lots of twists and turns and still more twists and turns possible and suddenly you know what teams shake hands and out of the blue match is Draw.

This indian team boats of an over rated test ranking position but did not have the guts to atleast push for a win. How timid can that be for a polulation of over 1 billion. There is a mathematical probability of loosing which is highly unlikely with still 7 wickets in hand. No wonder west indies captain was surprised by the timorous approach of the indian team. This irresolute approach by the indian team does no good. Rankings are mere numbers. Actions speak more than numbers. There is will be no satisfaction to even the fans of the indian team with their indecisiveness.

Now after all this Our new coach and Mr grumpy fletcher is still defending his decision by saying that his team team has already exceeded the expectations by playing without 5 senior players and still managing to win both one day and test series. How stupid is that. Being top team team you always have to go for the kill be aggressive in decision making also . Even a small kid will tell the coach how far the risk is and how near the victory was.

I have been so pissed and gutted after seeing the match with still 90 balls of play possible and indian players without any remorse shamelessly shaking hands that even 2003 work cup loss looked small compared to this.

Players accepting defeat without playing.

An Idea and it's conclusion

Recently after a lot of thought and with nothing much to do I watched a movie called "The Social Network". I was very speculative to watch this movie at first because it had not action and seemed like a drama, but I was wrong. The story, script and dialogues are so intense and fast paced that a hard core action movie can never provide. In the first few minutes our hero Mark discussed about a formula on the window of his room. This formula is used for his site facemash.com.

After watching the movie I wanted to check if this formula is for real or is it created by our director. To my surprise this formula is for real and it is known as Elo Rating system.

More details of it can be found here http://en.wikipedia.org/wiki/Elo_rating#Mathematical_details


If Player A has true strength R_A and Player B has true strength R_B, the exact formula ( the expected score of Player A is

Similarly the expected score for Player B is

The maximum possible adjustment per game (sometimes called the K-value) was set at K = 16 for masters and K = 32 for weaker players.

Supposing Player A was expected to score E_A points but actually scored S_A points. The formula for updating his rating is

My analysis for this is.

Suppose there are four players A, B, C, D, E.
We should assign the initial rating for all the players.

This initial rating should be proportional to the no of players playing the game.

Suppose there are 1000 players and you assign a initial player rating of 1000 then it should be fine. But if there are 100000 players and you assign initial player of 100o then there is high probaility for 2 or more players to get the same rating.

so in our example since there are only 5 players let us assign each player intial rating of 1000 points.

Let us assume Player A played played with the other 4 players and the following happened

A	1st	2nd
B	Lost	Win
C	Lost	Win
D	Win	Lost
E	Lost	Win

consider the 1st case
Ea=
1/1 + 10^(1000 - 1000 / 400) = 1/1 + 10^(0 / 400) = 1/1 + 10^0 = 1/(1 + 1) = 0.5

So the actual points scored Sa = 0 + 0 + 1 + 0 = 1
Expected Score Ea = 0.5 + 0.5 + 0.5 + 0.5 = 2 (Since all the 5 players have the same initial rating 1000)

Now the updated rating of our player A = 1000 + 32 (1 -2 ) = 1000 - 32 = 968 Points.

For case 2 :

Actual points Sa = 1 +1 +0 +1 = 3.

Updated Player A rating would be
1000 + 32 (3 -2 ) = 1000 + 32 = 1032 Points.

This case 2 is independent of case 1.

Consider another scenario where case 2 has occured after case1 and we have not updated the Points of B, C, D and E players.

Then
Ea = 1/1 + 10^(1000 - 968 / 400) = 1/1 + 10^(32 / 400) = 1/1 + 2.089 = 0.32

So the actual points scored Sa = 1 +1 +0 +1 = 3.
Expected Score Ea = 0.32 + 0.32 + 0.32 + 0.32 = 1.28 (Since all the 4 players have the same initial rating 1000)

Now the updated rating of our player A = 968 + 32 (3 -1.28 ) = 968 + 56.95 =~ 1025 Points

So if you have noticed the player A instead of getting 1000 points had got 25 points extra. This is because he has won against more stronger opponents and is been rewared more.

The Start

I have always wanted to write blogs and share some ideas, thoughts, moments, etc..etc…but always kept on postponing it thinking that this is not the right moment or searching for that elusive first post that should be uber cool. But the problem is it never happened and I have become very lazy to even think about writing something meaningful.

So now I have decided enough is enough and just start a blog.