Game Theory: How to BREAK Mario! (Mario Tennis Aces)
*heartbeat* + *cheering* *gasp* *blood curdling* Peach: Oh noooo! Hello Internet, Welcome to GAME THEORY! Spending more time analyzing fictional athletics than actually going outside. I know I recently said that Mario is classified as overweight according to the BMI scale. But one thing BMI doesn’t do a good job at factoring in is muscle mass, which is heavier than fat. And when you take a look at Mario, sure, he may appear like an adorable chubby plumber, but he in fact may be the most athletic character to ever appear in video gamedom. I mean, he’s appeared in 25 sports spin-off titles. Competed in every single Olympic event. Both Summer and Winter. And mastered everything from golf and soccer to non-traditional activities like having Waluigi slowly grind up on him. (Hip hop music) OH YEAH! Oh, Waluigi, you causal lover. You might not make the Smash Bros cut, but you will always have a place on Mario’s dance card. You will be the challenger approaching from the rear every time. Mario’s latest adventure is MARIO TENNIS ACES on the Nintendo Switch. Which loyal theorist may remember from that,other video I made back in April. [slide whistle] Hey! You put those suggestive sound effects away, mister! [sad slide whistle] (Note:LOL!) But at this point, I’m done rummaging my rulers through the Mushroom Kingdom’s sport shorts. Instead, today I want to take a closer look at this game’s coolest addition: zone shots. You see, during matches, players can fill up an energy gauge by rallying the ball. Then, with enough energy, you’re able to hit a zone shot, a fast-moving spike that’s near-impossible to return. NEAR impossible. You see, that’s where there’s this brilliant little bit of strategy involved. You have the choice to either hit your zone shot into the corner of the court, where your opponent will have no chance at returning it, or shooting it directly at them. If you go this route, sure, they have the possibility in returning to hit, but if they miss, their racket may just snap in half, forcing them to forfeit the match entirely. Apparently with Mario hoarding all the gold coins, no one can afford more than one racket in this universe. ANYWAY, this all got me thinking. Is it actually possible to launch a tennis ball so hard that it can break an opponent’s tennis racket? AND if it can break a tennis racket, what other horrific things could that ball do? I know we’ve talked about how deadly some things in the Mario games can get, but could its deadliest weapon actually be a simple tennis ball? Let’s pull out our T1-83s and find out. As with all games, we’ll need to determine a sense of scale, first and foremost. But, luckily for us, gaming’s most reliable ruler, Mario Jumpman Mario is here for us to use. At 155 cm, Mario allows us to convert in-game measurements to real life units. And, uh, shockingly, the courts in Mario Tennis Aces are surprisingly realistic. I found the in-game courts to only be a few centimeters apart from the dimensions of regulation-sized tennis courts, which are usually 78 feet long (23.77 m), and for single’s matches, 27 feet wide or 8.23 m. I mean, the French Tennis Federation has already dis-allowed skin-tight body suits, so I would expect flying clown cars to also be deemed illegal in the game. But heck, at least the court sizes are in accordance with the rule books. Also, the game does us a favor by providing speed of serves in miles per hour, which is similar to what’s done in real-life televised tennis matches. However, a seasoned theorist like myself knows to take these in-game speedometers with a grain of salt. So how does the radar gun in Mario Tennis Aces stack up? Using frame rates and more pixel measurements than I could shake a racket at, I found that the actual speed of any given server was around 10% slower than the speed that was boasted on the radar gun. And while that may seem like Team Nintendo is simply juicing the numbers in their characters’ favor to make things more fast-paced and exciting, the same thing actually happens in real-life tennis matches. The average speed of serves is always less than the speeds listed on television. And for once, it’s not because we’re intentionally being lied to. Instead, the radar reading is always taken right after the ball is hit. At that precise moment, the ball is traveling at its single fastest before it steadily starts slowing down due to air resistance and spin. So unbelievably, Nintendo is actually two-for-two when it comes to accuracy in this game. And we might as well make it three-for-three because I also checked gravity based on the speed of the falling tennis ball during serves, and that checked out too. 9.7 m/s squared which is pretty darn close to the real-life 9.8. Overall, this might be the single most realistic Mario game ever, provided you’re willing to overlook the giant sanction ball of metal, that’s allowed to play tennis. Taking a closer look at how the tennis rackets break in the game, even before doing any calculations, one big concern stands out to me. If you zoom in during a sucessful zone shot, you can clearly see that the racket is breaking at the handle. The thick part where the player is holding the thing. This is an enormous red flag, because in real life when rackets break, they almost always occur at the strings, frame or neck. Physically speaking, this makes the most sense because they are the weakest part of the racket. and thus are the first to break when any sort of force is applied. Either by the ball or when the player decides they need to rage quit And oddly enough, in the image that eventually went viral for other reasons. Nintendo shows Luigi’s racket breaking at the correct point, the strings and neck. But apparently it was just too hard to implement into the actual gameplay, and so we’re stuck with what’s depicted in the game, which I guarantee is gonna yield us some absurd numbers. Now, you might remember from the blue shell episode that impulse is one method of determining the force transferred by a projectile. That’s the measurement here that help us determine whether a ball can break the racket. Impulse is equal to force times time. It’s also defined as the change in momentum, which, for a ball travelling in one direction and then being hit in another direction is gonna be pretty darn easy to find. Momentum is equal to speed times mass. So we need to find mass of the ball, speed headed into the racket, speed headed the opposite way, away from the racket and the amount of time the ball is actually in contact with the strings, giving us a total of four unknown variables that are all pretty easy to find. We first have to assume that the ball has a regulation mass of a tennis ball at 58.5 grams. But, considering how realistic the measurements already are in this game, and the fact that the ball behaves similarly to a real ball on three different style of court. This isn’t that hard of an assumption. The speed of the ball can be calculated using frame rates and pixel measurements. Just like we’ve been doing all episode. And we get that it’s travelling 96 miles per hour before impact (43 meters per second). And 28 miles per hour (12.7 meters per second) in the other direction after being hit. So, with all those numbers in place, we are able to calculate the change in momentum. Final momentum minus original momentum. Because mass always has to be in kilograms for this, we shift the decimal point over a few places, which is always like, the most obnoxious part of these sorts of physics equations, keeping your units together. I just gotta say that to express what I’m sure is the feeling of countless students taking high-school physics. I would say more points and half-points are lost on tests that way than ANY other way. And speaking of those really miner things that are always super obnoxious to keep track of, this is the thing I always have to remind myself when it comes to momentum. The ball is headed in opposite directions before and after the impact. Which means that one velocity has to be positive, and the other one has to be negative. I mean, think about it this way: If they were both positive, that would just tell us that the momentum had slowed down, but it was still in the same direction, which obviously isn’t the case. The total velocity change was the speed going into the racket plus the addition of 12.7 meters per second added to it, going in the opposite way. So in total the whole thing changed speed by 55.7 meters per second. Does that all make sense? Welcome back to school, everybody! Tell your math teacher about this episode, maybe you’ll get to watch it in class… Anyway, doing the math gives us 3.26 Newton seconds, which is stupid and means absolutely nothing to any normal human being. So let’s put it into terms that actually make sense. To do that, though, we’re gonna need to know the impact time, which is as simple as counting the frames that the ball is in contact with the racket. Its only 3 frames, and at 60 frames per second, that translates to .05 seconds, which again, shockingly, is about how long a typical tennis ball in real life will be in contact with the racket’s strings. Mario Tennis Aces, ladies and gentlemen, I’m giving it the award now: Nintendo’s most realistic game. Boom! There’s the sticker. Slap that one on your box art. Interestingly enough, this .05 number tells us that Mario and the crew are pretty much professional-level tennis players. You see, players can control the impact time between the ball and the racket by adjusting the stiffness of their string bed. Beginners might not be able to hit the ball with a whole lot of strength, so they will typically use a racket with a soft and low-tension net, to increase dwell time: the length of time that the ball is staying in contact with the string. This in turn enables us to fish in impulse to bounce back the ball at a high speed, but it comes with a price: a loss of control. In contrast, professional players are already striking the ball at full strength, so they tend to prefer a racket with a tight net to shorten their overall impact time, closer to the types that we see present in Mario Tennis Aces. For them it’s all about spin and trick shots In fact many will actually keep 2 or more rackets on hand with different string bed tensions so they can actually change strategy mid game ANYWAY with all that information we can determine THANK FOR WATCHING!!!!!!!!!!!!!!!!!!!!!!!!!!!!