Mario meets Pareto
Mayerowitz.io<br>Mario meets Pareto
Step on the Front Line and Beat your Friends<br>Written by Antoine Mayerowitz
In Mario Kart 8, choosing your driver, kart's body, tires, and glider isn't just<br>about style — it's as crucial as your racing skills to win a race. Ever<br>wondered how to truly find the best ones?
For each of those four elements, you have tens of options. For each option,<br>there are distinct statistics (speed, acceleration, ...) affecting your<br>performance.
This adds up to an unbelievable amount of builds to choose from.
Hopefully, many choices are just stylistic — they have identical<br>statistics — but even after ignoring those duplicates, it remains a tough<br>job to navigate the thousands of options.
Is there any chance to find the best build or is it<br>just luck? Should you favor speed to be the fastest, or<br>acceleration<br>to quickly recover after taking a hit? Let me show you a solution proposed over a<br>century ago by economist Vilfredo Pareto.
Finding the fastest driver is as simple as ranking them by their speed<br>statistic. Here you might think that<br>Bowser or<br>Wario are a no-brainer.
But you can't just rely on<br>speed<br>to find the optimal build. You have to consider<br>one as well. Now, finding the best<br>driverbodytireglider<br>is not trivial anymore — you have to make trade-offs between
speedaccelerationhandlingweightoffroadmini turbo<br>and<br>speedaccelerationhandlingweightoffroadmini turbo<br>Reset
Look closely though! You'll find out that some options are always dominated. Let's focus on this poor<br>Koopa for instance.
Cat Peach has more speed for the same acceleration, and<br>Toadette has more acceleration for the same speed. Between you and me, if you<br>want to win, never allow<br>Koopa to sit in your kart!
You can identify all efficient drivers that, unlike Koopa, are never dominated<br>on both speed and acceleration. Together, they form what is called<br>the Pareto front (or frontier).
Mind you: not all elements of the frontier are equally good. You probably won't<br>pick a driver sitting on the edge of the frontier because you want some balance<br>between speed and acceleration. The Pareto efficiency is an<br>objective criteria to filter out suboptimal choices, but you still need to make up<br>your final decision.
Given your play style and skills, you may put more<br>weight on one statistic over<br>the other. Those preferences will reveal the component on the frontier that<br>suits you the best.<br>speedaccelerationhandlingweightoffroadmini turbo<br>speedaccelerationhandlingweightoffroadmini turbo
Best<br>driverbodytireglider<br>: {}
In practice, you not only choose a driver, but a full set of body, wheels, and glider.<br>In the next section, I'll display every build as a distinct point. It will however make<br>the number of choices explode. But Pareto's with us!
We've had a bit of fun here, but don't you see the pattern? We're often faced with<br>similar trade-offs. You want a meal that's both cheap and delicious? A job that's both well-paid, easy, and fulfilling?<br>A portfolio with low risks and high returns? A flexible and strong material that's also easy to produce?<br>A fair taxation that remains efficient<br>A high quality LLM that is also fast and cost-efficient. In all these cases, you're facing a multi-objective optimization problem, and you<br>have to make trade-offs.<br>Of course, if you already know the exact weights you want to assign to each dimension<br>(i.e., you know your utility function), you reduce the problem to a single objective<br>optimization. This is because you can combine the dimensions with the weights into a<br>single quantity to optimize (often called utility, cost, or fitness). In that case, you<br>don't need Pareto at all.<br>But you're often faced with situations where your utility function is unknown or<br>uncertain. In those situations, the Pareto front helps you eliminate objectively all the<br>sub-optimal options. It won't reveal the one best option right from the outset, but you<br>may now experiment with these efficient options and select the one that fits you the<br>best.
Acknowledgments<br>I've made some simplifying assumptions in this article to keep it readable for a large<br>audience. In truth, the statistics that I presented are translated into derived in-game<br>stats that are not always linear with the base statistics. Additionally, there are 4<br>speed stats and 4 handling stats for all gears (except for the driver), but I decided to<br>simply average those. I've also completely hidden the functional form of the utility<br>function, which can play a great role. To get access to more details behind this article<br>or if you just like my work and want to see more in the future, please consider<br>donating some coins.<br>Credits<br>Super Mario Wiki<br>Mario Kart 8 Deluxe in-game statistics<br>Henry H.<br>Mario Kart and the Pareto Frontier, 2015