Gripes with Sports Fans: The Transitive Property of Sports

     In math, there is something called the transitive property.  Essentially, it means that if a and b have a relationship, and b and c share that relationship, than so will a and c.  It sounds complicated, but it’s really not.  For example, if 3 is greater than 2, and 2 is greater than 1, than by the transitive property, 3 must be greater than 1.  Or, if 1/2 equals .5, and .5 equals 50%, than 1/2 equals 50%.  Some people think this transfers over to sports.  However, it doesn’t, and not much makes me angrier than hearing someone try to pass it off as fact.

     If you’re a sports fan that likes talking and debating about sports with other people, chances are you’ve heard this before: “My team beat this team, and that team beat your team, so my team’s better than yours.”  Transitive property in full effect.  There are two reasons why I believe some people do this.  The first would be that the person is narrow-minded or simply negligent.  I mean, who could really believe in such a flimsy argument?  Right?  Unfortunately, those people do exist.  The second, and more common reason, which I hate even more, is that people use the transitive property simply to be annoying.  That’s it.  People just want to needle by given an undeniable fact that their team did indeed beat someone who beat your team, and then try to agitate you by assigning some meaning to it.  They’re fully aware that it makes little actual sense, but who cares?  It’s an easy way to needle, and needling can be really fun for the needler.
     Regardless of why the transitive property is used, I’ve made it my mission to debunk the myth, if you can even call it that, and crush the notion that the transitive property is an appropriate argument as thoroughly as possible, because there is so much more to determining how good teams are than simply how they played against another team.
     Now, if you aren’t a sports person, than you might be thinking something like this: “I’m not really sure what Connor’s talking about here.  It makes sense that Team A is better than Team C if Team A beat Team B which beat Team C.  Right?”  Well, the main problem with this argument is that as long as the two teams being compared each have wins and losses (obviously the idea can’t work with winless and undefeated teams), it’s basically possible to say that anybody is better than anybody through use of the transitive property.
     Don’t believe me?  Let me introduce you to the NFL Circle of Parity, or what I like to call the Any Given Sunday Circle.  Basically, the idea is that over the course of the NFL season, enough games are played so that a circle can be made of a team who beat a team who beat a team, etc. that includes every team in the league.  It’s proof that if you try hard enough, any team can be viewed as being better than any other team through use of the transitive property, because in the NFL, anyone can beat anyone on any given sunday.  If you want a visual representation of this, here’s a link to last season’s circle:  Keep in mind when you’re looking at the graphic that what is shown is not necessarily the quickest way to connect every team in the league, but simply a way that plays allows for the best and worst teams to fit in.  There were only two teams that lost to the Buccaneers, so it kind of forces teams to be in certain positions.  Most of the time, that route connecting two teams is very short.  For instance, while the circle shows the Dolphins beating the Patriots, the Patriots also beat the Dolphins, so instead of 31 links between the Patriots beating the Dolphins, only one is really necessary.  If you’re interested, a similar circle has been made for every season since 2010, and I’d imagine one can be made for every season in the 16-game era besides 2007, where the Patriots went 16-0, and 2008, where the Lions went 0-16.
     Why is this possible?  Just think about it.  Take an 8-8 team.  If you want to say they’re better than another team, it’s pretty simple.  First off, they’ve beaten eight teams.  Technically it could be fewer if they won two against a division opponent, but let’s call it eight.  If the team you want them to be better than isn’t one of those eight, than you can move onto any team those eight have beaten.  This should get to the desired team the vast majority of the time, because if these teams have an average 8-8 record, than it means they’ve beat a combined 64 teams.  That means on average every team should be beaten twice on average by the eight in question, and only 23 other teams remain, since it’s a 32-team league and your team and the eight they beat don’t count.  If you still haven’t gotten there, than go to the teams these 64 have beaten.  That should be about 512 wins, and the numbers just keep getting higher.  I don’t even think it’s possible to not be able to use the transitive property if the teams in question aren’t undefeated or winless.  It gets slightly more difficult if a team has fewer wins, but still very much possible.
     It’s not just football either.  I would say this is easily possible with every major team sport.  For college sports fans, there is a website appropriately called, where you can compare any two college football, men’s basketball, or women’s basketball teams and see the shortest path connecting the two via the transitive property.  Then for extra fun you can “flip it”, and show how the inferior team is actually better using its own chain of matchups.  Using the website, ere’s proof that arguably the worst FBS football team, 1-11 Georgia State, is actually better than the National Champions, Ohio State:
     Okay, so it’s pretty clear that the transitive property works for just about anyone, and that the larger the season and more wins a team has, the easier it is to use the transitive property.  But why exactly do some teams beat strong opponents and lose to weak ones?  There’s tons of reasons.
     Remember the card game war?  If you don’t, here’s the basic premise.  A standard deck of cards is divided evenly amongst the game’s players.  Then each player flips over the top card in their deck, and the player who flips over the highest card takes everyone’s cards and places them at the bottom of their deck.  This keeps happening until someone gains all 52 cards.  It’s that simple.  In this game, a king will always beat a queen, and a nine always trumps a four.  We can think of sports teams like cards in the deck.  In the NBA, we could call the Warriors an ace, the highest card, and the Lakers a three.  However, the difference is that the ace doesn’t always beat the three.  Sure, the ace is a heavy favorite, and more likely to win against the three than a jack, for instance, but it isn’t a predetermined outcome.
     This shouldn’t come as a surprise, but sports teams don’t perform on the same level in every game they play.  Sometimes a basketball team gets really hot, and seemingly can’t miss a three-pointer, while in other games they’re cold as ice, and can’t buy a bucket.  It happens to everyone.  The best shooter on the planet, Stephen Curry, had one of his worst shooting performances in game 2 of the NBA Finals recently, but then played incredible games later on in the series.  One game really can’t say anything about how good or bad a team is.  A larger sample size is needed.
     For instance, what if a team’s star player is injured for a game.  Surely that has a large impact on the performance of the team.  If someone who is not knowledgeable about sports saw a great team without their best player, they could easily think the team is bad.  Additionally, some teams simply match up well against others.  A poor team whose biggest strength happens to be a great team’s weakness has a much better chance of pulling an upset than if they didn’t have any discernible advantage.
     Home field advantage often plays a large role in who wins games as well.  The home court, fans, and possibly even referee bias can provide a significant advantage, making home teams win 58% of NFL games since 1990, for example.  Some teams, such as the Seattle Seahawks, are almost unbeatable on their own turf.  For the NFL, Vegas typically gives three spread points to whoever is home, meaning that if a team would be a three-point favorite in a matchup at a neutral site, the game is a virtual coin flip if they’re on the road.
     Speaking of on the road, sometimes in the NBA and NHL, teams will play games on back-to-back days, and then three games in four days or four in five.  By the end of these stretches, fatigue is significant and visible on the court.
     Sometimes, even luck plays a role in who wins a game.  Referees will sometimes unknowingly make an incorrect call, and sometimes these end up being large, game-changing events.  In soccer, penalty kicks are largely luck as well.  Sure, some players are more accurate and can drill the ball into a corner better than others, but the goalie diving the right direction?  It’s just a guess.
     The big idea I’m trying to get across is that the winner of a game doesn’t necessarily have to be the best team.  It is, however, the team that performed the best on that given day.  When the Giants upset the 18-0 Patriots in Super Bowl XLII, it wasn’t because they were the better team.  The Patriots, overall, were far superior to any NFL team that year.  Record-wise, there were five teams in the NFC alone better than the Giants.  It’s because it all came together at the right time, and they had a magical performance when it mattered most.
     There’s a reason the NBA, MLB, and NHL play seven-game playoff series.  It’s because they want the best teams to advance, and to prove they are the best teams.  Anyone can win one game, but it takes a lot more to take down four of seven.  Teams that have one or two-game flukes aren’t rewarded by advancing.  Instead, they have an advantage, but still have to prove that over the course of a long series, home and away, they can overcome pressure and fatigue to rise as the rightful victor.
     So stop utilizing the transitive property to explain how your team is really better than your buddy’s.  It’s just plain annoying, and about as weak an argument as there is.  Even if your team beats your friend’s it doesn’t necessarily make them better, especially if we’re talking about baseball, where even the worst teams still win about one game out of every three.  If you bring up how your team beat team X by 24 and your friend’s team only beat them by 10, that’s even worse.  A win is a win.  But just one doesn’t make you better than anybody else.

Readers Comments (2)

  1. Thanks! Yea, it's a decent thought in principle but it doesn't take much thought to see how wrong it really is…

  2. Hey! I don't know if you remember me but your dad sent this to me. It's awesome! I totally agree – the transitive property is useless. Especially in college football where I see it the most! Keep up the good work, I'll be an every day follower now!


Leave a comment

Your email address will not be published.