# Mathematicians out there...old swing power vs. new swing power

#### mxmx

##### Hall of Fame
For talented math and physics people:

I was wondering. Is it mathematically (or with physics) possible to compare the power of players like Borg, Becker, Lendl or even Sampras with that of players of today?

For example. Could one measure the swing speed of the hand of lets say Borg and work out how powerful his shots would have been if he used MODERN rackets? (Assuming he and everyone hits the sweet spot).

Someone like Roscoe Tanner. How would his serve have been with modern rackets?

Let's rather focus on some theoretical "worked out" guestamites/answers and not just guessing without theory please. Comments of people with background in the field will be appreciated.

#### BrokenForehand

##### Rookie
so background means PHD student or High School student?

##### Rookie
The moment of inertia is the integral of mass times radius squared along the racket. Since old rackets were both heavier in the head and longer, I can say that they had to apply more force to give the racket the same acceleration when hitting the ball. The other thing is that you can apply a smaller force over a longer period of time, which they probably did, so you can't say that they were swinging stronger when hitting the ball, since they just used longer takebacks. Another thing is that they had slower racquet speed at the point of contact, so they had to accelerate the racquet for a lesser period of time to have the same end velocity

Empirical reasoning suggests that the athletes had more or less the same power in the hands, at least the variance in both past players and current players populations should exceed the difference of their means, which makes it unreasonable to make general assumptions

#### daggerman

##### Professional
Best way to measure something like this is to give current players a go with old racquets and compare the difference

#### mxmx

##### Hall of Fame
so background means PHD student or High School student?
Anyone who has researched this or something similar. No qualifications needed, just evidence/backing/research for big claims instead of trolling.

#### Im(moral) Winner

##### G.O.A.T.
Hitting is not about muscle. It's simple physics. Calculate the velocity, V, in relation to the trajectory, T, in which G, gravity, of course, remains a constant.

#### ChrisRF

##### Hall of Fame
Best way to measure something like this is to give current players a go with old racquets and compare the difference
I fully agree. I’d say there should be at least one exhibition tournament with wooden racquets. But I don’t think the top guys would do this because they wouldn’t risk wrist injuries or to dirsturb their usual rhythm. Therefore I even doubt Federer would participate, despite his love for tennis history.

#### mxmx

##### Hall of Fame
Exactly, which is why it would be great if some clever folk can work it out in reverse. I've played with wooden rackets, and they're very demanding. Perhaps tennis warehouse should work the science out like they do with some of their tools, except this time with wooden racket. But then again, why would they want to? Not as if they're selling any.

#### blablavla

##### Hall of Fame
so background means PHD student or High School student?
would a school student eye test be sufficient?

#### dominikk1985

##### Legend
I think that is hard to do because apart from racket weight and racket power the swing mechanics with the plastic racket changed. The old swings were more linear and now players turn the body more and use the forearm to whip around the racket which would not work with wood rackets. Also players lift more weights now and the top guys weigh 180-190 rather than 160-170 which adds power too.

So to really compare power you have then learn modern strokes early on, give them a modern racket and let them lift weights for 1 to 2 years which you can't really do.

#### JaoSousa

##### Hall of Fame
For talented math and physics people:

I was wondering. Is it mathematically (or with physics) possible to compare the power of players like Borg, Becker, Lendl or even Sampras with that of players of today?

For example. Could one measure the swing speed of the hand of lets say Borg and work out how powerful his shots would have been if he used MODERN rackets? (Assuming he and everyone hits the sweet spot).

Someone like Roscoe Tanner. How would his serve have been with modern rackets?

Let's rather focus on some theoretical "worked out" guestamites/answers and not just guessing without theory please. Comments of people with background in the field will be appreciated.
It is technically possible, but the results may not be too meaningful, because of all the adjustments we would have to do.

Say you came up with this experiment:

Take a stratified random sample of Borg's serves, backhands, and forehands, and a stratified random sample of let us say Federer's serves, backhands, and forehands.

We have to first determine the variables that would change, which would be primarily the balls, strings, and rackets. Adjusting for the difference in mass or material of the ball would not be terribly difficult as long as we knew how fast Borg's arm was accelerating. Given this, we should be able to, given the random sample, calculate how much faster/slower Borg's serve/forehand/backhand would be with modern tennis balls.

The next two factors are the most difficult: rackets and strings. The type of racket directly affects how fast the player is able to swing. Unfortunately, we have somewhat(not really) of a confounding variable here. Now, let us say we ignored this flaw and kept going. Given the acceleration of Borg's arm, we could set up an experiment with a robot or a person who accelerates the same.

Then we could transform the sampling distribution by adding or multiplying by a scalar. The confounding variable here is the issue though.

I am actually more of a mathematician than a physicist, so if a physicist could confirm this, that would be nice. Also, it would help to have a real statistician here because I might have butchered some of the statistical terms.

Edit: technically the balls and strings would also be confounding variables, that would affect how fast Borg is able to swing.

#### JaoSousa

##### Hall of Fame
I think that is hard to do because apart from racket weight and racket power the swing mechanics with the plastic racket changed. The old swings were more linear and now players turn the body more and use the forearm to whip around the racket which would not work with wood rackets. Also players lift more weights now and the top guys weigh 180-190 rather than 160-170 which adds power too.

So to really compare power you have then learn modern strokes early on, give them a modern racket and let them lift weights for 1 to 2 years which you can't really do.
Yes, exactly. Check my post above. The difference in racket directly affects how fast they are able to swing, hence the confounding variable.

#### mxmx

##### Hall of Fame
Doesn't a heavier but lower powered racket (wood) translate into a person needing to be strong? What about someone of that era who transitioned to aluminium or graphite?

Does anyone know the speed of some of Borg's most powerful strokes? Can one work it out by video footage and compare speed to faster modern ball speeds? Possibly, could one then not deduct power of someone like Federer?

For example: one could measure a sample of similar hand speeds of that of Borg and Federer, and then see which balls travel x amount faster. Would that not give a sample or standard of crude formula to work a estimate out? As if Borg and Federer switched rackets so to speak...

#### mxmx

##### Hall of Fame
A bit sidetracked here:

A second question may then be who has the greatest "contact to sweetspot" of all time? Perhaps we are underestimating how good the wood racket players were. I know their shots are much less powerful, but not as much as most people are making them out to be. Was their control, mental game and placement not superior? In other words, they were better, but in another way and worse in others. Is power not overrated?

It's like a counterpuncher beating a power player. Why is that always seen as inferior? I know attack will always fundamentally prevail over defence...but surely the players of the past had something going for them. I am not convinced that the field of today are superior or more talented just because they have more power etc.

Something of the greatness of past players are getting lost in history.

#### mxmx

##### Hall of Fame

Good article. Thanks

Interested in the micro chip tech in Agassi's racket that causes electrical current to make the racket rigid at contact. Is it just marketing or actually possibe? Sounds like Batman's cape.

On topic, all I can say from personal experience, migrating from wood > alluminium > graphite > modern composites, all increased my power each time. Of course my technique increased through the years though.

I cannot imagine Borg not not having way more power than with his wooden donnay. Is it then not safe to add a percentage of speed to his shots if a racket of today is X % more powerful? One could then compare ball speeds of his shots vs modern players.

#### Jaitock1991

##### Hall of Fame
Good article. Thanks

Interested in the micro chip tech in Agassi's racket that causes electrical current to make the racket rigid at contact. Is it just marketing or actually possibe? Sounds like Batman's cape.

On topic, all I can say from personal experience, migrating from wood > alluminium > graphite > modern composites, all increased my power each time. Of course my technique increased through the years though.

I cannot imagine Borg not not having way more power than with his wooden donnay. Is it then not safe to add a percentage of speed to his shots if a racket of today is X % more powerful? One could then compare ball speeds of his shots vs modern players.
Guess this could work to a certain extent. But wouldn't their technique be fundamentally different? After all, the reason players today are able to take such huge cuts at the ball is because of the amount of spin that modern strings generate. This spin allows the ball to dip down and stay inside despite traveling at very high velocity. To the players of the past, this was not even an option, as there was no way that the strings(and the heavier balls) would ever allow them to produce that much spin without sacrificing horizontal racquet head speed and in turn ball speed. Basically if they'd swing as hard on their forehands as today's players do the ball would be going out every single time.

No?

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#### mxmx

##### Hall of Fame
Guess this could work to a certain extent. But wouldn't their technique be fundamentally different? After all, the reason players today are able to take such huge cuts at the ball is because of the amount of spin that modern strings generate. This spin allows the ball to dip down and stay inside despite traveling at very high velocity. To the players of the past, this was not even an option, as there was no way that the strings(and the heavier balls) would ever allow them to produce that much spin without sacrificing horizontal racquet head speed and in turn ball speed. Basically if they'd swing as hard on their forehands as today's players do the ball would be going out every single time.

No?
Technique doesn't bother me as much. The balls and string issue makes it more complicated yes.

Perhaps pre-poly comparisons? I need more clarity and comparisons on the ball differences though...

#### Sysyphus

##### Talk Tennis Guru
Players today swing a bit harder than the scrawny McEnroes and Wilanders of yesteryear, but not quite as powerfully as the handsome bearded female Eastern European sledgehammer throwers of the 1980s