Mathazine Issue 1
A note from the creators:
WHAT IS MATHAZINE? MATHAZINE was started by a bunch of students who discovered their love of mathematics in unexpected places. Not in thick textbooks, or endless pages of notes. Not only in quadratic equations, formulas, or even in Anjali ma’ams classes. We found maths in the real world. We found it in music, in rhythm and beats. We found it in plants, leaves, flowers, and the patterns hidden in nature. We found it in sports, where probability, angles, movement, strategy, and data can change the way we understand a game. We found it in art, architecture, games, stars, cities, and even the way people make decisions. The strange thing is that most of us only discovered this side of maths when we were older. Now,we want to pass this feeling on to you, before it’s too late. You do not need to think of yourself as a “maths person” to enjoy MATHAZINE. You only need curiosity. And a little bit of patience to solve our games (they can get tricky!) So sit back, relax, and turn the page. And maybe keep a pencil handy. – Aditya, Mrinalini and Varshini
HAPPY READING!
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If you built your dream World Cup team with just people born between January 20 and February 18, you’d have an unbeatable team on your hands. No matter what team you support, there’s bound to be an Aquarius on it. Of course, there’s Portugal’s Cristiano Ronaldo, but there’s also Brazil’s Neymar Jr -- and they were born on February 5th. And there’s more - from the midfield mastery of Xavi on Jan 25th to Luis Suárez on Jan 24th, football success seems to be written in the stars for those born in this blessed window. It turns out, though, that it’s not simple astrology - it’s science!
The relative age effect
It all comes down to recruiting. Most elite youth academies across Europe and South America use a January 1st cutoff for age groups. This creates a phenomenon known as the Relative Age Effect (RAE). A kid born in late January or February (an Aquarius) is about a full year older, stronger, and smarter than a teammate born in November or December. In the cut-throat world of scouting, ten extra months can mean more playing and coaching time, giving them a leg up. By the time they reach the professional level, the "head start" can turn into a career at the top of the FIFA rankings.
It’s in the numbers In our analysis of the Top 20 FIFA National Teams, Aquarius players consistently ranked in the top tier of birth distributions. In squads like Croatia and Germany, they make up a staggering percentage of the roster. This follows the trend we discussed earlier, especially as 63% of Croatian U-15 players are born in the first half of the year.
Cancer 1
Libra 1
Scorpio 1 Aquarius 6
Gemini 1 Capricorn 1
Taurus 2
Aquariuses are everywhere.
croatia’s team Virgo 5
Aries 3
Pisces 5
Why are all your favorite football players Aquariuses? Aquariuses ?
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we had a Date
with destiny -Louis de la Fuente Is de la Fuente right? Was Spain destined to win even before the world cup started? What if there was a statistical model that can predict the probability of each team winning based on their previous matches?
Scenario 1: England beats Sweden. The algorithm says, ‘this was expected, not impressive, Spain’, and Spain gets a few extra points from San Marino.
YES ! The Elo model
Scenario 2: Sweden beats England. The prediction was wrong! Saudi Arabia steals a huge amount of points from England.
1. Every team starts with 1500 baseline points. 2. The algorithm compares points before the match to generate a win probability percentage. 3. Elo is a zero-sum game: The winner steals Elo points from the loser. 4. More matches are played - Stronger teams’ Elo ratings increase and vice versa
David vs Goliath
The amount the Elo ratings increase depends on expectations. Goliath was a warrior giant who fought a small boy, David. Completely unexpectedly, David beat Goliath by using Goliath’s sword to cut off his head. So what if something out of the ordinary happens?What if Sweden (David) beats England(Goliath)?
What if...
The next question is: What if Sweden beat England only by a lucky deflected 1-0 win which they scored in the last 30 seconds? Would it still be fair for them to steal half of England's points? To capture team strength instead of luck, the formula is adjusted using variables like expected goals for a team, home-field advantage, and the margin of victory. For example, if France plays on their home turf, the model already expects a stronger performance, and so if they win, it won’t be as impressive: they won’t gain as many Elo points.. When you apply these to Spain’s previous tournament data, the Elo proves that while Spain might have had one or two lucky wins, winning the world cup was mathematically destined by probability. So, really, Spain did have a date with destiny.
Increase in score
Because the result of a match is random, it would not make sense to predict a single result(a single match) but, rather, the probability distribution across a set of results. This is because there is a high margin of error for predicting the outcome of just one match as there could be many anomalies. For example, flipping a coin once might give you heads but it wouldn’t be right to infer that every time you flip the coin you will get heads. If Argentina played against Brazil once, Brazil may win. But if they played a 1000 times against Brazil, Argentina would win a high percentage of the time and it would be easy to see they are the stronger team. So how does ELO work? It is essentially a rating algorithm used to rank teams based on their previous performances.
Point difference
THE
ROAD TO THE FINAL
Map by The Wall Street Journal
The logistical nightmare Imagine you’re planning the greatest summer road trip! Your plan is to visit every single city on your bucket list, but you need to do that without wasting time driving back and forth across the map. Sounds simple right? Now imagine doing that for 48 football teams, across 16 cities in the USA, Canada and Mexico. Throw in different timezones, schedules for teams to rest, broadcast demands and packed airports, and you’ve got one of the biggest logistical puzzles in sport! Welcome to one of FIFA’s biggest mathematical challenges.
So how does FIFA solve this insane mess? They do it by leveraging a concept called graph theory and optimization. Imagine every stadium on the map as a dot, called a node, and every possible flight between the two stadiums as a single line, called an edge. Together, nodes and edges can be used to create a giant network that computers can analyze. By using optimization algorithms, FIFA can effectively search through millions of possible schedules to find ones that minimise travel, reduce jet lag, keep rest days fair for all teams and maximise TV audiences across the globe.
The Math Behind the Map
Behind Every Match
This mathematical challenge is basically a famous math puzzle called the Travelling Salesman Problem (TSP). The key idea revolves around one fundamental question: what’s the shortest route that visits every destination without wasting time backtracking? While finding the optimal path between 3 or 4 cities sounds like a piece of cake, once you consider doing the same for 16 different stadiums spread across the North American continent, the number of possible routes skyrockets! Therefore, making a perfect schedule becomes extremely arduous and vital.
Without mathematics, the World Cup would be one giant travel nightmare. The math behind the scheduling is what makes the tournament fairer, saves millions of dollars in travel costs, minimises unnecessary carbon emissions and helps players perform better. So the next time you watch your favourite team play, remember: behind every match is a clever piece of mathematics making this exciting tournament possible!
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