The situation slightly, but not too much complex.
Let us say that a player has p% of first serves in and wins p1% of points when the first serve is in. Let us also say, he wins p2% of second serves.
Then his current win % on serves = p*p1 + (1-p)*p2.
If the rule is eliminated and the player decides use his current first serve as his lone serve, then
his % of points won on serve will be = p*p1
If the rule is eliminated and the player decides uses his current second serve as his lone serve, then
his % of points won on serve will be = p2.
Assuming that these are his only strategies to deal with the change of rule (a wrong assumption at
that as players will tweak their serve to a compromise to deal with the rule change), then their
best strategy would yield max(p*p1, p2) of serve pts won. To decide whether the change of rule
hurts or helps a player we need to figure out as to how p*p1 + (1-p)*p2 compares to
max (p*p1, p2). Needless to say p*p1+(1-p)*p2 is always larger than p*p1. Also, as long as
p1 is greater than p2 (which will be the case for almost all players), again p*p1 + (1-p)*p2
will be larger than p2. So, in principle it will be bad for all players. But, that is no brainer and
we don't really need all these algebra.
The real question is how much a player will suffer due to change of rule. In other words,
while all players would be negatively affected, some players would be affected a lot and
some very less.
So, let me just do a typical example. Let us take a power server who is fairly accurate.
Say he lands 60% of first serves in and wins 90% of them when it lands in. Let us say
he has a poor second serve and wins only 40% of points off the second serve. Then
as .60*.90=.54. and 0.40*.40 = .16. Before the rule change this player will be winning
(.54 + .16 = .70) 70% of points. After the rule change, he is better off using his first
serve as the lone serve and he would win only 54%. That is a 26% reduction.
Let us take a server who does not have very good first serve. Let us say he lands
50% of them in, but wins only 80% of them. But his second serve is quite decent
and wins 60% of them. Then his previous percentage of serve points won would
be - .50*.80 + .50*.60 = .70. Now, after the rule change if he uses his first serve
as the lone serve, he wins 40%. But if he uses his second serve as the lone serve
then he wins 60%. So, he is better off using his second serve as the lone serve.
His performance would go down from 70% to 60%. So, it is 14% reduction.
This rule change will negatively impact all players obviously. However, the
impact on players with a reliable second serve is much less than the impact
on players with a bad second serve, but a good first serve.
Rafa is one of the leaders in percentage of points won off his second serve.
No wonder, he supports this rule change. The impact on his serve points
won will be less, but it will negatively impact to a much larger extent on
people who have good first serve and bad second serve.
Federer is indeed dependent on his serve, that I agree with you on! B-)
