Wikipedia defines "inflection point" as follows:
a point (x,y) on a function, f(x), at which the first derivative, f'(x), is at an extremum, i.e. a minimum or maximum. (This is not the same as saying that y is at an extremum).
It follows from the definition that the sign of f'(x) on either side of the point (x,y) must be the same. If this is positive, the point is a rising point of inflection; if it is negative, the point is a falling point of inflection.
Consider these statistics:
2003: 72-16 win-loss record 7 titles 1 major
2004: 74 -6 win-loss record 11 titles 3 majors
2005: 81-4 win-loss record 11 titles 2 majors
2006: 92-5 win-loss record 12 titles 3 majors
2007: 65-9 win-loss record 7 titles 3 majors
Suppose these statistics were given to a statistician or a mathematician. And he or she were asked,
"please build a statistical model that defines RF's career.
please define a function f(x) that traces his career over time.
calculate its first derivative f'(x) that indicates the rate at which f(x) changes, to trace the rate at which his career changes.
and then pray tell me - is the year 2007 the point of inflection in his career?"
Note that the point of inflection could be either a rising or a falling point of inflection.
One look at the statistics and it is evident that 2003 seems to be the rising point of inflection.
(I dont have his win-loss record in 2002, but he won only 3 titles and no majors in that year.)
If we look at the majors, then 2007 certainly does not seem to be a cause for concern.
However, if we look at the win-loss record, or at the drop in the number of titles won in a year, it certainly seems to be either a blip or a falling point of inflection. (I trust a mathematician or a statistician to prove me right or wrong on this one.)
2 consecutive defeats in 2 consecutive matches is a rarity for RF - this last happened 4 and a half years ago, sometime in 2002.
2 consecutive defeats to the same guy - this happened versus Nalbandian in the last few days, and versus Canas in March early this year - twice in 2007 - when did this last happen? 2002? 2001?
Losing a match versus a guy (Fernando Gonzalez) against whom he had a 10-0 overall career record.
Do these factors fit somewhere into that model f(x)?
If someone does come up with that model, I am sure RF's opponents will certainly be interested to find a statistical based way of beating him.
Btw, here's something interesting for RF's opponents - a couple of factors that need to be plugged in the fuction f(X) - these factors could determine your chances of winning against RF in 2007:
1. you know Spanish (Nadal, Canas, Nalbandian, Gonzo all speak Spanish - exceptions are Djokovic and Volandri - but rumour has it that they underwent Spanish learning sessions in secret)
2. you have long hair (all of them have long hair, with the same exceptions again)
Well! I have the inputs/factors/statistics ready at my disposal.
Just waiting for Mr Statistician / Mr Mathematician to conjure function f(x) and tell me if 2007 is the point of inflection for Mr Roger Federer.
Till then, hopefully, RF will return to his winning ways at the season ending Shanghai Masters.
As one Mr Muhammad Ali once famously said,
hopefully, he will once again dance like a butterfly and sting like a bee.
