College Football

I’ve been in college football spirit lately so I’m going to break away from as the theory-based writing and focus on more real things in this post.

Week 7 of NCAA football has just passed and while many are sad because they have to wait a whole week until the next saturday to watch some football, I am happy because it’s a whole week to interpret the data and most specifically the rankings. The main reason I prefer college football over the NFL is the weekly rankings. On Sunday, following all the games, the multiple rankings systems get updated. The two main rankings systems are AP Poll (made up of 65 sportswriters and broadcasters) and the Coaches Poll (made up of 62 NCAA football coaches). Polls would single-handedly decide the NCAA football champions for over a century, whatever team was ranked #1 at the end of the season would be declared the national champion. In 1998, this tradition ended and it was decided that the #1 and #2 ranked teams would play in a designated bowl game, with the champion becoming the undisputed national champion. While the polls still played a big role in deciding the eventual national champion, it was less of an influence because two teams got a chance to decide it for themselves, and it theoretically should increase the margin of error that the polls will inevitably make. This is the only system I’ve known of my whole life so I was astounded that people would be fine with a poll choosing a “champion” with no championship but apparently it’s pretty normal to my dad. This system changed yet again in 2014 when the College Football Playoff format was formed. The top four teams in terms of the official CFP rankings, a committee of about a dozen people to decide what teams are best, play in a two round playoff format to decide the national championship. You may see a pattern here and it does raise the question of the how far the expansion will go. Many think it will expand to eight for even sixteen. I think there is an argument for eight teams, the theory behind that is any team that has a reasonable chance at winning it all should be in running. If you look at the #16 team they honestly don’t have a high chance of beating the number 1 team, but I think it’s quite unfair to leave the #5 team out of the running because difference between the top 5 teams can be very small.

These systems would all be perfect if polls are perfect. But sadly they are not due to subjectivity and inability to factor in all data. Theoretically you are able to solve this using computer rankings, which are often used, but it’s nearly impossible to make an algorithm that correctly balances all factors. College football in essence is based on a team’s win-loss record. If they go undefeated (doesn’t happen all the time, 3 of the last 5 years though), they should qualify for the national championship. So basing off of W-L record seems like the most correct method but it is not, due to differences in strength of schedule, meaning the average level of your opponents across the season. An example of strength of schedule having a large impact is Ole Miss, who has a win percentage of 50% right now (3-3), yet somehow in the top 25 (#23 on AP) and above an 80% win percentage team Navy (4-1). Also Louisville who is at #7 (AP) while having a loss, yet is above at least 5 undefeated teams. Personally I really like benefiting teams that have a hard schedule because it gives an incentive for teams not just to schedule a season full of pushover teams. Ole Miss might be a bit of a stretch though, they’re a perfect example of people spamming “quality loss” as a reason to be good, yet Ole Miss doesn’t even have a quality win yet. Luckily as the season goes on the rankings will get more accurate as data collects and gets further from pre-season bias. I’m trying to make my own computer ranking algorithm (once I can figure out how to effectively import all the data) and it’ll be super interesting to see how the rankings compare when stressing certain factors versus others.

I didn't really paint a picture of what's going on right now in college football but all you need to know is that Alabama is super super overpowered, while the B1G has the highest consistency as a conference at the very top.

This post strayed from what I was really planning on talking about and kind of lacked a clear focus, may make another college football post later in the season if more thoughts occur. Thanks for reading if you did.

Solved Games and Luck

You may hear, or not, someone talking about a form of competition, primarily games, being “solved”. Examples are Tic-Tac-Toe, Connect 4, and Checkers. What does being “solved” mean. There are different kinds of solved games. Some like Tic-Tac-Toe, are easy to show an algorithm, or what response to every single move, a player should make to perform perfect play which will always force a win or draw (draw in the case of Tic-Tac-Toe). For easily solvable games like Tic-Tac-Toe, it makes game play very boring as anyone out of elementary school can pretty easily see the perfect drawing strategy. Connect 4, is also mathematically solved as a win for whoever goes first, but I’m not sure if many people know the whole algorithm in their head. However even without knowing the exact algorithm, many people will win every single time they go first, just with a general strategy and reacting on the whim to how their opponent plays. So even with people not knowing the algorithm, the game may still be unenjoyable due to inherently low skill cap of the game. Not many people know this but the game checkers is actually solved, it took something like 15+ years with 200 computers, so there’s no way no one out there actually knows perfect play and therefore the fact that it’s solved is not relevant to many.

What about games with luck? A game with luck can not be “solved” in a sense that a certain player can force a win or draw with perfect play. This is because even with perfect play, luck is outside of anyone’s control and cannot ensure anything. However, there is still the concept of “optimal play”. Games like Solitaire or King’s Corner are examples of easily found optimal play but luck involved. So solitaire has pretty easily discoverable best strategy, yet there is no way to guarantee a win due to randomness of starting position (there’s actually only one game that is un-winnable of the millions in Windows version of Solitaire now that I fact-checked it, not sure how it applies to real life solitaire though. Hope you still got the point though). This concept of losing despite perfect play may frustrate many and put people off from certain games. People will even insult a game for “having too much luck”. I believe this is a big indicator of what certain people want in a game: competition or fun. If someone is hyper-competitive (me), then they want to minimize the amount of luck so skill accordingly is increased. On the flip-side, many people just play games to have fun, and luck is a big factor of that. This is the reason gambling is such a profitable business (maybe I’ll touch on that and how it dances on the border of “competition” in another post). You see examples of this in video games where “party games” are very luck-oriented but when people turn the games competitive, such as Super Smash Bros. Melee for the Nintendo GameCube, they try to eliminate all types of luck throughout the game to maximize skill and competition.

The question of whether a game is solved or ever can be may seem trivial to you but many people are excited by this question for the games they love. A prime example is chess. As of right now computers, even on phones, can consistently beat the world’s greatest chess players. While we can make computers that are unbelievably talented at chess, humans are nowhere near close to mathematically solving the game and it’s a debate as to whether it will ever happen or not. I’ve heard that many chess grand masters believe the game will never be solved, but I think it’s just because they have so much pride in their own intellect they think no computer could fully handle it (/s). No one knows whether the solution would mean white (first player) wins every time, draw every time (most probable), or even black wins every time (that’d be crazy).

We only hear of "games" being solved, usually card or board games, but what about video games or sports* (*what is a sport anyway?)? The concept of "perfect play" and solutions being brought out of the theoretical algorithm-based mathematical world and into the physical world brings up way too many questions that I really don't want to answer. However that doesn't stop anyone from trying to achieve that perfect play and optimization.

Who knows though, maybe there will be a team of fast reacting and all physically capable robots that the Super Bowl winner will have to play against at the end of the season every year. Probably not but that'd be entertaining.