I put together my attempt at doing this analytically as best I can. There are two major downsides: 1) I dont really have data pre-2007 2) I only have useful historical numbers every 100 days for some techincal reasons.
The graphs below are 2007 => 2017ish modeled game (not match) win probabilities for the 4 main court types. Probabilities are for the first player playing the second player in the title. I've overlayed market implied dots of the corresponding colours to the extent I have them. Its just a formula to take in the vig free implied match win probability, and move it to game win probability space. In general, the dot should line up relatively closely to the corresponding line. To the extent it doesn't, I would tend to think the model hadn't caught up to something yet, or there was some injury type information that wasn't in the model. If a dot lies above the corresponding line, its probably fair to assume the model is undervaluing the first player at that time and if it lies below the line its fair to assume the model is overvaluing the first player at that time.
There is a lot going on in the plots and we probably need to synthesize them down into fewer numbers. I've taken a few stabs at trying to come up with reasonable numbers. First, lets be mindful of this plot from
https://tt.tennis-warehouse.com/inde...alists.453446/, which shows how frequently people of various ages have made finals of big tournaments:
Given that, I've taken the modeled data and taken 3 date range samples (3/2008 => 10/2014, 2/2008=>9/2016 and 1/2012=>9/2016, the 100 day rule causes screwy start and end dates).
Arguments for and against:
Federer:
- The data strongly indicates he is the best modeled all around tennis player of the three
- Sampling from 2008=>2014 vs Nadal, wherein > 50% of which occurs after Federer's "standard tennis peak" of 20=>29, he is very slightly worse on average, and better if you sample 2007=>2016
- Federer only slightly worse than Novak if you sample 2008=>2014 and 2007=>2016, again periods that ought to a priori favour Novak materially.
- Put another way: in terms of pure ability, Federer is only slightly worse than Novak on an apples to apples comparison if you disregard everything Federer did before 2007, a period in which he won 9 majors
- However, at least since 2007, under performed in important matches running almost 2 majors below expectation in finals
Novak:
- The two data points that stand out in Novak's favour are the average performance he has in the model against Federer and Nadal in 2012=>2016.
- This is the peak Novak argument, I've played around with the numbers, and the only other 4 year strech I can find like that is Federer over Nak 2007=>2010
- Novak is much much better than Nadal and during a period wherein Nadal "should" still be pretty good given his age
- Nadal enjoyed an earlier prime though, and when you look the four years like 2007=>2010, Novak is getting killed by both in a way that the other two never do, and rewarding Novak for Nadal breaking down and Fed being 33 seems iffy
Nadal:
- There probably isnt a solid argument in this data for Nadal in my opinion
- We tend to value tournament wins as opposed to game wins, and being a court specialist like Nadal tends to push up your tournament win probabilities. This is a contrived example, but imagine a world where you face 3 scrubs then a good player in the final:
- The numbers tend to work out in way that you can shift around your game/match probabilities to put all your eggs in one basket and come out ahead. In the example, the generalist has more expected wins in every round but fewer expected tournaments. I don't have an easy way to prove this, but I'm pretty sure that peak Nadal of like 2008=>2014 has a ~= average to Federer but a good amount better expected majors / year because he kind of hacked tennis at the FO
- This is very compelling to me but could not be to others: Rafa got dicked over hard when they were handing out major courts. At or around half of all professional tennis is played on clay courts, but only 25% of the majors are. 2-3% of all tennis is on grass and 25% of the majors are. There are probably alternate universes where we pick the most important tournaments and he is slightly worse off, but there are probably just as many alternative universes where clay makes up a third or a half of all major tournaments and he is so far and away the best player ever by consensus no one is talking about it.
I vote Federer, and I think its going to be very very hard for Novak to get there.