 My final vehicle tier list. My character tier list is slightly further down the page.
Introduction Luckily, I have a few tools to improve the existing lists on Mario Kart tiers. In this case, I am opting for the straightforward data analysis approach of a Liner Regression Model. What is Linear Regression? It is the first model you learn for analyzing data. By taking a cluster of random observations, and a series of traits that each observation has, it attempts to predict the observation’s output based on its traits. For example: the output, or dependent variable may be a student’s final grade. The traits, or independent variables denote things such as study time, previous grades, and participation. Running a Linear Regression attempts to predict each student’s final grade based on a multiplier attached to each variable (study time, previous grades, participation), minimizing the difference, or residual, between the predicted observations and real observations. Method As I am attempting to find a list of the best characters and best karts based on stats, I need a group of reasonably consistent stats to work off. Time Trial Data is what I settled on. All staff ghosts need to be reasonably challenging to beat but are at around the same skill level. Meanwhile, to find the optimal time on a course, I selected world record times for each Time Trial.
After pulling Staff Ghost times from each track, as well as World Record Times (glitchless) from each track, I took the stats for each vehicle and character that the times were made with. This was the most time consuming step but was mostly just a matter of linking Karts to a few tables showing their stats, then adding the character stats. VLOOKUP is your friend here. Initial regressions failed, as certain tracks are very different than others. This includes tracks like Sherbertland or Shy Guy Beach, where off roading is disproportionately powerful. With all the tracks together, I was getting the Offroader as a #1 overall vehicle, which doesn’t seem right. I removed every World Record Time that wasn’t made with Funky Kong and the Flame Runner to address this problem.  Results My regression model now measured the time difference between the staff ghost and the world record, based on Speed, Weight, Acceleration, Handling, Drift, Off Roading, and Mini Turbo. And using the staff ghosts as a skill level that we’re following; I found some interesting results. Speed is obviously the most important aspect of a Kart or Character. But Handling was the second most important, followed by Mini Turbo. Acceleration was a very neutral stat, off roading was the third least important, weight was the second, but drifting is weirdly the worst stat for staff ghosts. If a staff ghost must drift, they will have much worse times in comparison to Funky Kong and the Flame Runner. Speed*61.7742 - Weight*17.9345 - Acceleration*5.301 + Handling*23.08 - Drift*25.2 - Off Road*9.1 + Mini Turbo*19.84 + 3950.93 There are a few issues with this model. The R^2 is pretty low on this equation (around 0.359, which is usually negligible), with an adjusted R^2 of 0.0142. The worst part is that the P values for each variable are very high and therefore insignificant. In the future, I should find better data sources to work off of, but this should still function a little better than the crude existing equations. The Final Ranking system is as follows:
Obviously this is not showing us the best karts or characters in general. In general, the best Kart should be the Flame Runner. The best Character should be Funky Kong. But as our data follows the Staff Ghosts, we are measuring the best vehicle for the staff ghosts, and the staff ghost skill level. Most Mario Kart players in general are around this level, but a lot of people playing now are probably much better than the staff ghosts. That being said, we can always remove things such as handling from the equation or run a different regression if more data is made available. The Tier ListBy now you've already scrolled past my two final tier lists, but here they are again. There is not too much science behind how I placed the vehicles or characters here, but I did penalize Karts and outside drifting bikes before assembling the vehicle tier list. Beyond that, these are my final results, for the best characters and karts for the average Mario Kart Wii player.
In Conclusion Why am I exploring this on House Fish Balloon’s blog? Because Mario Kart is a video game and uses a lot of different characters with different skills and different balancing decisions. When we work on our own games at House Fish Balloon, we use similar approaches in solving game design problems. Trickdraw (Kickstarting until the end of July) is the most recent card game that we tested this with, but we have been using game testing algorithms for a few of our upcoming new games, as well. 
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