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How football betting odds work using Poisson distribution

How football betting odds work using Poisson distribution

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Arpit Mishra
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December 9, 2016
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3 min read
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Key Takeaways:

  • Football betting odds represent the probability of various outcomes in a match, with lower odds indicating higher likelihood, and higher odds indicating more unlikely events.
  • The Poisson distribution is used in football betting to predict the probability of a team scoring a specific number of goals, based on their past performance.
  • By calculating the average attack and defense strength of teams, Poisson distribution helps in determining the likelihood of different scores, which can be converted into betting odds.
  • In a real-world example, Poisson distribution can predict match outcomes, like the probability of a 1-1 draw or 2-2 draw, based on past statistics of teams like Manchester United and Manchester City.
  • While Poisson distribution provides a mathematical way to predict outcomes, it doesn’t account for external factors like player changes or injuries, which can affect the actual match result.
Toward the end of the 19th century, Russia-born Polish economist, Ladislaus Bortkiewicz came up with a strategy to predict the incidence of deaths among Prussian soldiers from horse kicks.

And he did this how? He applied the Poisson distribution. It ended becoming a famous example by the way.

Fast forward a bit...

Poisson distribution can be used in many scenarios—importantly and interestingly in betting.

Sports betting is a global phenomenon, and it is estimated that this industry is worth between $700bn and $1tn globally.

And football betting is most popular among all sports.

But how does football betting odds work? how are football betting odds calculated?

It's difficult to believe that a simple mathematical equation - Poisson distribution is used to calculate the odds for a football match.

Betting on a team winning or losing is done based on the calculation explaining the sports betting across a globe.

What is 'Football betting odds' and how they define bets?

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If you've ever tried placing a few pounds on your favorite team, you would have noticed these confusing numbers in front of you.

These numbers are called 'odds' and they define the probabilities of each possible outcome in an event.

The higher the value of these numbers, the less probable that particular event is.

Take the Real Madrid vs Roma match above as an example.

Since the probability of Madrid winning is higher, the odds against them winning is just 1.40. A draw, which is more unlikely, has odds of 4.75.

And the odds of a highly unlikely Roma win in 7.00.



How do these numbers impact your bet amount and their returns?

Simple. In the above example, if you bet 1 pound on a Real Madrid win and win the bet, you get back a total of 1.40 pounds (inclusive of the 1 pound that you originally bet).

Which is why winning bets on more unlikely events (like a Roma victory) gets you bigger returns.

In this case, you would have got back 7 pounds for every pound you bet on Roma if they ended up winning.

Let us now see how do bookmakers calculate football betting odds using a simple Poisson Distribution equation.

What is Poisson distribution?

“Poisson distribution is the probability of the number of events that occur in a given interval when the expected number of events is known and the events occur independently of one another.

For instance, suppose you sit in a park for a few days and count the number of people who come to the park in a black T-shirt.

Using Poisson distribution, you can guess if the number of people coming to the park on a specific day in a black t-shirt will be 10, 11, etc.

But how does it relate to football betting odds prediction?

If you are able to calculate the average attack and defense strength of the teams in a match over a certain period and calculate the Poisson distribution, you will be able to predict the odds of one team performing over other.

But if the data is too long the data would be irrelevant, and if it's short, outliers might skew the data.

This means that not only external factors like transfers, home, and away from ground affect the odds, but also the duration of events which need to be taken into consideration for calculation.

Let’s see how football betting odds work using Poisson distribution

Before we apply Poisson, we need to get some mathematical figures.

Let’s use this method to calculate the odds for the Manchester United vs. Manchester City matches to be played on February 26, 2017.

First, we need to find the attack and defense strength of these teams.

Calculating Average Attack and Defense for prediction

Before we identify a particular team strength and weakness, we need to find the average strength and weakness of all teams in the last playing season.

This can be calculated by dividing the total goals scored in particular season by a total number of games played in a particular season.
  • Number of Goals Scored at Home / Number of Games = 203/380 = 0.534
  • Number of Goals Scored Away / Number of Games = 158/380 = 0.415
The difference from the values above gives the “Attack intensity” of a team.

We will also need an average of goals conceded to know the weakness, which is simply the inverse of goals scored.

The average number of goals conceded at Home = 0.415

The average number of goals conceded away = 0.534

This gives us the “ Defense intensity” of a team.

Now that we have the average strength and weakness of the teams, let's take a look at the stats for Manchester United and Manchester City in 2015.

Based on these stats, we can calculate the Poisson distribution for the teams playing in February 2017, where Manchester United is the away team and Manchester City is the home team.

[caption id="attachment_5249" align="aligncenter" width="3509"]Football betting odds, How are football betting odds calculated, Football betting explained using Poisson distribution, How football betting works ,Poisson distribution, How football betting is done, how is poisson equation used in football betting, Manchester united vs Manchester city, How do I bet on football, What are football odds 2015 Statistics - Manchester United vs Manchester City[/caption]

Predicting Manchester United Goals

Let’s see the possibility of Manchester United scoring at Manchester City’s home ground.

Number of Goals scored away = 22/19 = 1.15

Manchester United Goals = Number of goals scored/Season’s average goals scored away = 1.36/0.415 = 2.77

Manchester City Defense at home

This is calculated by dividing the number of goals conceded at home in the last season by the home team by the number of away games, which is 1.105 ( (21/19).

Manchester City Goals = Number of goals conceded/ Season’s average goals conceded = 1.105/0.415 = 2.66

Manchester United’s Goals = Manchester United’s Attack? Manchester City Defense? Average Number of Goals = 3.05

Predicting Manchester City Goals

Manchester City Attack at Home

Manchester City = Number of Goals scored home - 47/19 = 2.47

Manchester City Goals = Number of goals scored/Average goals scored in the last season =2.47/0.534 = 4.62

Manchester United Defense away

Take the number of goals conceded away last season by the away team and divide by the number of away games, which is equal to 1.05 ((20/19).

Manchester United Goals = Number of goals conceded/Average goals conceded in the last season =1.05/0.534 =1.966

Manchester City’s Goals = Manchester City’s Attack? Manchester United’s Defense? Average No. Goals = 1.10

Once we have the averages of Manchester United’s goals and Manchester City’s goals, we can use them to calculate the Poisson distribution for a number of goals scored by a particular team . (various goals possibilities).

Poisson Distribution betting – Predicting multiple match outcomes

The formula for Poisson distribution is:

P(x; ?) = (e-?) (?x) / x!

e = Euler’s constant = 2.718

! = Factorial

x = number of successes of the event

µ = mean distribution of the event

It can be coded as follows
#include <stdio.h>

#include <math.h>
double factorial(int n) {
int fact = 1;
for (int i = 1; i<=n; i++) fact *= i;
return fact;
}
float poisson(int r, float mean) {
return (exp((-1) * mean) * pow(mean,r))/factorial(r);
}
int main(int argc, char const *argv[])
{
printf("%f\n", poisson(1, 1.10));
return 0;
}

You can also use the Poisson Distribution Calculator for such equations.

Poisson Distribution prediction for match the between Manchester United and Manchester City

Goals 0 1 2 3 4 5
Manchester United 4.73% 14.44% 22.02% 22.39% 17.07% 10.41%
Manchester City 33.28% 36.61% 20.13% 7.38% 2.03% 0.44%
Probability 1.5 5.28 4.43 1.65 0.34 0.23

The possibility that Manchester United and Manchester City would score 1 goal each is 14.44% and 36.61% respectively.


From the above distribution table we can see that the possibility of Manchester city scoring no goal is 4.73 and that of Manchester United is 33.28.

Scoring 2 goals, each for Manchester United and Manchester City is 22.02% and 20.13% respectively.

The possibilities decrease as the number of goals increases to 4 and 5 goals by the individual team.

Taking these number into consideration, the odds of Manchester City winning is high if the number of goals in a match is 0 or 1. But if Manchester United is able to score 2 goals it’s the probability of winning the match increases.

So how is football betting odds made?

Based on the number by distribution table and the probability of these goals in a match, it is clear that a 1-1 draw has the highest possibility of 5.28, followed by 4.43 for a 2-2 draw. But the possibility of Manchester City winning with 1-0 or 2-1 also looks great.

Based on the previous match at Old Trafford, which is the home ground to Manchester United, Manchester City won by 2-1.

Not taking any sides (I support Algorithm), I would put my bet on 1-0 or 1-1 draw in favor of Manchester City.

The disadvantage of using the Poisson equation is that it doesn’t take into consideration external factors like the players/coach changed in transfer windows, the home ground factor, and injured players.

It helps you calculate the distribution only based on the averages of previous occurrences.

But then Elihu Feustel is one such person who makes a million dollars by betting using mathematical algorithms.

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December 9, 2016
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How I used VibeCode Arena platform to build code using AI and leant how to improve it

I Used AI to Build a "Simple Image Carousel" at VibeCodeArena. It Found 15+ Issues and Taught Me How to Fix Them.

My Learning Journey

I wanted to understand what separates working code from good code. So I used VibeCodeArena.ai to pick a problem statement where different LLMs produce code for the same prompt. Upon landing on the main page of VibeCodeArena, I could see different challenges. Since I was interested in an Image carousal application, I picked the challenge with the prompt "Make a simple image carousel that lets users click 'next' and 'previous' buttons to cycle through images."

Within seconds, I had code from multiple LLMs, including DeepSeek, Mistral, GPT, and Llama. Each code sample also had an objective evaluation score. I was pleasantly surprised to see so many solutions for the same problem. I picked gpt-oss-20b model from OpenAI. For this experiment, I wanted to focus on learning how to code better so either one of the LLMs could have worked. But VibeCodeArena can also be used to evaluate different LLMs to help make a decision about which model to use for what problem statement.

The model had produced a clean HTML, CSS, and JavaScript. The code looked professional. I could see the preview of the code by clicking on the render icon. It worked perfectly in my browser. The carousel was smooth, and the images loaded beautifully.

But was it actually good code?

I had no idea. That's when I decided to look at the evaluation metrics

What I Thought Was "Good Code"

A working image carousel with:

  • Clean, semantic HTML
  • Smooth CSS transitions
  • Keyboard navigation support
  • ARIA labels for accessibility
  • Error handling for failed images

It looked like something a senior developer would write. But I had questions:

Was it secure? Was it optimized? Would it scale? Were there better ways to structure it?

Without objective evaluation, I had no answers. So, I proceeded to look at the detailed evaluation metrics for this code

What VibeCodeArena's Evaluation Showed

The platform's objective evaluation revealed issues I never would have spotted:

Security Vulnerabilities (The Scary Ones)

No Content Security Policy (CSP): My carousel was wide open to XSS attacks. Anyone could inject malicious scripts through the image URLs or manipulate the DOM. VibeCodeArena flagged this immediately and recommended implementing CSP headers.

Missing Input Validation: The platform pointed out that while the code handles image errors, it doesn't validate or sanitize the image sources. A malicious actor could potentially exploit this.

Hardcoded Configuration: Image URLs and settings were hardcoded directly in the code. The platform recommended using environment variables instead - a best practice I completely overlooked.

SQL Injection Vulnerability Patterns: Even though this carousel doesn't use a database, the platform flagged coding patterns that could lead to SQL injection in similar contexts. This kind of forward-thinking analysis helps prevent copy-paste security disasters.

Performance Problems (The Silent Killers)

DOM Structure Depth (15 levels): VibeCodeArena measured my DOM at 15 levels deep. I had no idea. This creates unnecessary rendering overhead that would get worse as the carousel scales.

Expensive DOM Queries: The JavaScript was repeatedly querying the DOM without caching results. Under load, this would create performance bottlenecks I'd never notice in local testing.

Missing Performance Optimizations: The platform provided a checklist of optimizations I didn't even know existed:

  • No DNS-prefetch hints for external image domains
  • Missing width/height attributes causing layout shift
  • No preload directives for critical resources
  • Missing CSS containment properties
  • No will-change property for animated elements

Each of these seems minor, but together they compound into a poor user experience.

Code Quality Issues (The Technical Debt)

High Nesting Depth (4 levels): My JavaScript had logic nested 4 levels deep. VibeCodeArena flagged this as a maintainability concern and suggested flattening the logic.

Overly Specific CSS Selectors (depth: 9): My CSS had selectors 9 levels deep, making it brittle and hard to refactor. I thought I was being thorough; I was actually creating maintenance nightmares.

Code Duplication (7.9%): The platform detected nearly 8% code duplication across files. That's technical debt accumulating from day one.

Moderate Maintainability Index (67.5): While not terrible, the platform showed there's significant room for improvement in code maintainability.

Missing Best Practices (The Professional Touches)

The platform also flagged missing elements that separate hobby projects from professional code:

  • No 'use strict' directive in JavaScript
  • Missing package.json for dependency management
  • No test files
  • Missing README documentation
  • No .gitignore or version control setup
  • Could use functional array methods for cleaner code
  • Missing CSS animations for enhanced UX

The "Aha" Moment

Here's what hit me: I had no framework for evaluating code quality beyond "does it work?"

The carousel functioned. It was accessible. It had error handling. But I couldn't tell you if it was secure, optimized, or maintainable.

VibeCodeArena gave me that framework. It didn't just point out problems, it taught me what production-ready code looks like.

My New Workflow: The Learning Loop

This is when I discovered the real power of the platform. Here's my process now:

Step 1: Generate Code Using VibeCodeArena

I start with a prompt and let the AI generate the initial solution. This gives me a working baseline.

Step 2: Analyze Across Several Metrics

I can get comprehensive analysis across:

  • Security vulnerabilities
  • Performance/Efficiency issues
  • Performance optimization opportunities
  • Code Quality improvements

This is where I learn. Each issue includes explanation of why it matters and how to fix it.

Step 3: Click "Challenge" and Improve

Here's the game-changer: I click the "Challenge" button and start fixing the issues based on the suggestions. This turns passive reading into active learning.

Do I implement CSP headers correctly? Does flattening the nested logic actually improve readability? What happens when I add dns-prefetch hints?

I can even use AI to help improve my code. For this action, I can use from a list of several available models that don't need to be the same one that generated the code. This helps me to explore which models are good at what kind of tasks.

For my experiment, I decided to work on two suggestions provided by VibeCodeArena by preloading critical CSS/JS resources with <link rel="preload"> for faster rendering in index.html and by adding explicit width and height attributes to images to prevent layout shift in index.html. The code editor gave me change summary before I submitted by code for evaluation.

Step 4: Submit for Evaluation

After making improvements, I submit my code for evaluation. Now I see:

  • What actually improved (and by how much)
  • What new issues I might have introduced
  • Where I still have room to grow

Step 5: Hey, I Can Beat AI

My changes helped improve the performance metric of this simple code from 82% to 83% - Yay! But this was just one small change. I now believe that by acting upon multiple suggestions, I can easily improve the quality of the code that I write versus just relying on prompts.

Each improvement can move me up the leaderboard. I'm not just learning in isolation—I'm seeing how my solutions compare to other developers and AI models.

So, this is the loop: Generate → Analyze → Challenge → Improve → Measure → Repeat.

Every iteration makes me better at both evaluating AI code and writing better prompts.

What This Means for Learning to Code with AI

This experience taught me three critical lessons:

1. Working ≠ Good Code

AI models are incredible at generating code that functions. But "it works" tells you nothing about security, performance, or maintainability.

The gap between "functional" and "production-ready" is where real learning happens. VibeCodeArena makes that gap visible and teachable.

2. Improvement Requires Measurement

I used to iterate on code blindly: "This seems better... I think?"

Now I know exactly what improved. When I flatten nested logic, I see the maintainability index go up. When I add CSP headers, I see security scores improve. When I optimize selectors, I see performance gains.

Measurement transforms vague improvement into concrete progress.

3. Competition Accelerates Learning

The leaderboard changed everything for me. I'm not just trying to write "good enough" code—I'm trying to climb past other developers and even beat the AI models.

This competitive element keeps me pushing to learn one more optimization, fix one more issue, implement one more best practice.

How the Platform Helps Me Become A Better Programmer

VibeCodeArena isn't just an evaluation tool—it's a structured learning environment. Here's what makes it effective:

Immediate Feedback: I see issues the moment I submit code, not weeks later in code review.

Contextual Education: Each issue comes with explanation and guidance. I learn why something matters, not just that it's wrong.

Iterative Improvement: The "Challenge" button transforms evaluation into action. I learn by doing, not just reading.

Measurable Progress: I can track my improvement over time—both in code quality scores and leaderboard position.

Comparative Learning: Seeing how my solutions stack up against others shows me what's possible and motivates me to reach higher.

What I've Learned So Far

Through this iterative process, I've gained practical knowledge I never would have developed just reading documentation:

  • How to implement Content Security Policy correctly
  • Why DOM depth matters for rendering performance
  • What CSS containment does and when to use it
  • How to structure code for better maintainability
  • Which performance optimizations actually make a difference

Each "Challenge" cycle teaches me something new. And because I'm measuring the impact, I know what actually works.

The Bottom Line

AI coding tools are incredible for generating starting points. But they don't produce high quality code and can't teach you what good code looks like or how to improve it.

VibeCodeArena bridges that gap by providing:

✓ Objective analysis that shows you what's actually wrong
✓ Educational feedback that explains why it matters
✓ A "Challenge" system that turns learning into action
✓ Measurable improvement tracking so you know what works
✓ Competitive motivation through leaderboards

My "simple image carousel" taught me an important lesson: The real skill isn't generating code with AI. It's knowing how to evaluate it, improve it, and learn from the process.

The future of AI-assisted development isn't just about prompting better. It's about developing the judgment to make AI-generated code production-ready. That requires structured learning, objective feedback, and iterative improvement. And that's exactly what VibeCodeArena delivers.

Here is a link to the code for the image carousal I used for my learning journey

#AIcoding #WebDevelopment #CodeQuality #VibeCoding #SoftwareEngineering #LearningToCode

The Mobile Dev Hiring Landscape Just Changed

Revolutionizing Mobile Talent Hiring: The HackerEarth Advantage

The demand for mobile applications is exploding, but finding and verifying developers with proven, real-world skills is more difficult than ever. Traditional assessment methods often fall short, failing to replicate the complexities of modern mobile development.

Introducing a New Era in Mobile Assessment

At HackerEarth, we're closing this critical gap with two groundbreaking features, seamlessly integrated into our Full Stack IDE:

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Now, assess mobile developers in their true native environment. Our enhanced Full Stack questions now offer full support for both Java and Kotlin, the core languages powering the Android ecosystem. This allows you to evaluate candidates on authentic, real-world app development skills, moving beyond theoretical knowledge to practical application.

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Say goodbye to setup drama and tool-switching. Candidates can now build, test, and debug Android and React Native applications directly within the browser-based IDE. This seamless, in-browser experience provides a true-to-life evaluation, saving valuable time for both candidates and your hiring team.

Assess the Skills That Truly Matter

With native Android support, your assessments can now delve into a candidate's ability to write clean, efficient, and functional code in the languages professional developers use daily. Kotlin's rapid adoption makes proficiency in it a key indicator of a forward-thinking candidate ready for modern mobile development.

Breakup of Mobile development skills ~95% of mobile app dev happens through Java and Kotlin
This chart illustrates the importance of assessing proficiency in both modern (Kotlin) and established (Java) codebases.

Streamlining Your Assessment Workflow

The integrated mobile emulator fundamentally transforms the assessment process. By eliminating the friction of fragmented toolchains and complex local setups, we enable a faster, more effective evaluation and a superior candidate experience.

Old Fragmented Way vs. The New, Integrated Way
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Quantifiable Impact on Hiring Success

A seamless and authentic assessment environment isn't just a convenience, it's a powerful catalyst for efficiency and better hiring outcomes. By removing technical barriers, candidates can focus entirely on demonstrating their skills, leading to faster submissions and higher-quality signals for your recruiters and hiring managers.

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Vibe Coding: Shaping the Future of Software

A New Era of Code

Vibe coding is a new method of using natural language prompts and AI tools to generate code. I have seen firsthand that this change makes software more accessible to everyone. In the past, being able to produce functional code was a strong advantage for developers. Today, when code is produced quickly through AI, the true value lies in designing, refining, and optimizing systems. Our role now goes beyond writing code; we must also ensure that our systems remain efficient and reliable.

From Machine Language to Natural Language

I recall the early days when every line of code was written manually. We progressed from machine language to high-level programming, and now we are beginning to interact with our tools using natural language. This development does not only increase speed but also changes how we approach problem solving. Product managers can now create working demos in hours instead of weeks, and founders have a clearer way of pitching their ideas with functional prototypes. It is important for us to rethink our role as developers and focus on architecture and system design rather than simply on typing c

Vibe Coding Difference

The Promise and the Pitfalls

I have experienced both sides of vibe coding. In cases where the goal was to build a quick prototype or a simple internal tool, AI-generated code provided impressive results. Teams have been able to test new ideas and validate concepts much faster. However, when it comes to more complex systems that require careful planning and attention to detail, the output from AI can be problematic. I have seen situations where AI produces large volumes of code that become difficult to manage without significant human intervention.

AI-powered coding tools like GitHub Copilot and AWS’s Q Developer have demonstrated significant productivity gains. For instance, at the National Australia Bank, it’s reported that half of the production code is generated by Q Developer, allowing developers to focus on higher-level problem-solving . Similarly, platforms like Lovable or Hostinger Horizons enable non-coders to build viable tech businesses using natural language prompts, contributing to a shift where AI-generated code reduces the need for large engineering teams. However, there are challenges. AI-generated code can sometimes be verbose or lack the architectural discipline required for complex systems. While AI can rapidly produce prototypes or simple utilities, building large-scale systems still necessitates experienced engineers to refine and optimize the code.​

The Economic Impact

The democratization of code generation is altering the economic landscape of software development. As AI tools become more prevalent, the value of average coding skills may diminish, potentially affecting salaries for entry-level positions. Conversely, developers who excel in system design, architecture, and optimization are likely to see increased demand and compensation.​
Seizing the Opportunity

Vibe coding is most beneficial in areas such as rapid prototyping and building simple applications or internal tools. It frees up valuable time that we can then invest in higher-level tasks such as system architecture, security, and user experience. When used in the right context, AI becomes a helpful partner that accelerates the development process without replacing the need for skilled engineers.

This is revolutionizing our craft, much like the shift from machine language to assembly to high-level languages did in the past. AI can churn out code at lightning speed, but remember, “Any fool can write code that a computer can understand. Good programmers write code that humans can understand.” Use AI for rapid prototyping, but it’s your expertise that transforms raw output into robust, scalable software. By honing our skills in design and architecture, we ensure our work remains impactful and enduring. Let’s continue to learn, adapt, and build software that stands the test of time.​

Ready to streamline your recruitment process? Get a free demo to explore cutting-edge solutions and resources for your hiring needs.

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