Hi guys,

I came across an interesting article about how to estimate how long a continuing phenomenon will last based on the past. It is called Gott's Principle. This is pure statistical in nature, and does not count factors like ageing etc.

Since Federer has been number 1 for last three years, the Gott's principle says that he will last # 1 for another 3/4 years (9 months) to 3*4 years (12 years) with a with 60 percent confidence. If we try to increase our confidence the length span uncertainity will increase.

So with 60 percent certainity based purely on statistics we can say that Federer will be number 1 till a date between September 2007 and 2018!

For more information, check this out:
http://en.wikipedia.org/wiki/J._Richard_Gott

And also do a google search.

Musing.

Interesting theory Musing!

I'm sure that it is difficult to build such a model to apply successfully to something that is essentially fluid with all sorts of caveats.. But that should never deter anyone from at least trying to develop something. There is a phrase in Latin that applies: 'Ceteric Paribus' all other things being equal!

I enjoy science when it is made accessible and applicable to the real world. There was a TV show in the UK many years ago here called 'Think of a Number' and it was brilliant in explaining complex scientific theory in a way that was accessible to non scientific people..

I'm sure that someone could take this principle and apply it to tennis just as you have.. I think that an explanation of the variables, and the ones excluded such as ageing, maybe injury too would go some way to showing how it would work...

Apart from ageing and injuries, what other factors would be excluded from this..?

At last., some genuine 'statistical analysis' btw! :lol:

;) Well, Gotts theory doesnt take into account the human factor at all. Try applying it to Borg in 1981 who suddenly decided hed had enough.

Agreed Al :) There are likely to be BIG assumptions with this theory, but sometimes the discussion of the theory itself can be enlightening, even if it cannot be fully couched in the real world..

Hey Petalp,

Yeah, true we need more scientists/ statisticians to tell us concepts that can be applicable to our very real day to day lives.

Gotts principle is actually very simple. (I hope I have made it simple, but I doubt it :unsure: )

Suppose a phenomenon has already lasted for Tp amount of time. What this essentially says is that, since we do not know how long the phenomenon will last, we could be anywhere along the life span of the phenomenon. So an easy calculation can be made as to what is the probabilty that we are in the middle X% of its life span.


------------------------------
~~~|-----mid X%----|~~~
|-------total life span------|


Which is simply X%. Then, the worst case scenario when the event will end early will be if we are at the end of the mid X% of the life, then the earliest time when the phenomenon will end is Tp*(1-X/100)/(1+X/100) afterwards. And the best scenario is when we are at the begininig of the middle X% of the life span. Then the latest estimate when the phenomenon will end is Tp*(1+X/100)/(1-X/100). :blush: (I hope I got it right...)

So for Federer, if we do not know anything, and play dumb and say he could be anywhere on of his lifespan as world number one, we get the numbers I wrote before, with 60% confidence we can say his end as world number one will end anywhere between September 2007 and December 2018.

:halo: But if we know more information, about where we actually are regarding the lifespan of the phenomena, then we can make more accurate predictions. Suppose we know accurately that we are EXACTLY in the middle of Federer's reign, we can accurately say (100% confidence) that Federer reign as world number one will last another 3 three years!


So how much do we know about Federer? Which means, based on his fitness, how much do we know that Federer is in his prime - based on Numbers?

My heuristic algorithms in my mind, based on past champions, :rolleyes: based on his form, and other players tell me that it is 70 percent surety that we are in the middle 30 percent of his peak powers! Note because of my bias, it is different than Gotts principle (Gott's would give me 70% for 70%)

Which means Federer will last as number one for another 1.6 to 5.6 years with a confidence of 70 percent!!!!!!!!!!! :ok: :ok:

Musing....

:P So much so for statistical Analysis :D

Wow! I shall re-read this when it is not 1 o'clock in the morning and am not feeling so sleepy!

Thanks for that Musing! :ok:

Good night Petalp...