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Esqueletos sin manos y pies descubiertos en un antiguo complejo militar nazi en Polonia
Los arqueólogos han descubierto los esqueletos de 🧾 cinco personas, que carecen de manos y pies, en una antigua base militar nazi en Polonia.
Fueron descubiertos en un centro 🧾 de mando nazi conocido como la Guarida del Lobo en Gierloz, en el noreste de Polonia, después de que el 🧾 grupo excavara un fragmento de cráneo humano durante una excavación el 24 de febrero y alertara a las autoridades locales, 🧾 que decidieron realizar excavaciones adicionales.
Los restos pertenecen a tres adultos, un adolescente y un bebé recién nacido, según un comunicado 🧾 de la Fundación Latebra, una organización histórica con sede en la ciudad polaca de Gdansk, publicado el jueves.
Los cinco cuerpos 🧾 estaban dispuestos unos cerca de otros, enfrentados en la misma dirección, afuera de una casa ocupada por el comandante nazi 🧾 Hermann Göring, un as de los pilotos de caza durante la Primera Guerra Mundial que se convirtió en uno de 🧾 los líderes nazis más poderosos en la Segunda Guerra Mundial y en un amigo cercano de Adolf Hitler.
Junto a ellos 🧾 había tablas quemadas y los restos de la infraestructura de alcantarillado, pero no había rastros de ropa, según el comunicado.
Adrian 🧾 Kostrzewa, miembro de la junta directiva de la fundación, le dijo a que el equipo inicialmente pensó que estaban desenterrando 🧾 un baño antiguo cuando encontraron tuberías bajo tierra.
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"Fue muy sorprendente", dijo.
La fundación está a la espera de los resultados de una investigación policial sobre 🧾 los restos, y plantean muchas preguntas sin respuesta.
"Hay muchas teorías (acerca de) por qué no tienen manos y pies", dijo 🧾 Kostrzewa. "En este momento, es muy difícil decirlo".
Una próxima etapa importante es determinar la edad de los restos utilizando la 🧾 datación por carbono, agregó.
Construido deliberadamente a millas de la civilización en los bosques del noreste de Polonia, la Guarida del 🧾 Lobo fue la sede del cuartel general del Este de los nazis de 6,5 kilómetros cuadrados (2,5 millas cuadradas).
La base 🧾 fue una de las más grandes de su tipo en Europa, según la fundación.
"La singularidad de este descubrimiento radica en 🧾 el hecho de que los cuerpos fueron encontrados en el sitio del complejo más fuertemente fortificado del Tercer Reich", indica 🧾 el comunicado.
Hitler pasó casi tres años allí en total.
El bastión fue el sitio del intento de asesinato de Operación 🧾 Valkyrie contra Hitler en julio de 1944, antes de que fuera destruido en enero de 1945 para evitar que cayera 🧾 en manos del ejército soviético en avance, según la fundación.
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In sports betting, there is always going to be an element of unpredictability, but that doesn’t mean you want to 5️⃣ waste your money placing random bets that have no real grounding behind them. You want methods and models that can 5️⃣ give you some insight into which way a game is likely to go, and one such strategy is known as 5️⃣ Poisson distribution.
Poisson distribution is a method that works best for calculating statistics in sports where scoring is rare and happens 5️⃣ in increments of one. This is why it is most widely used in association football, and occasionally in hockey, but 5️⃣ not really utilised elsewhere – at least, not successfully.
That’s why, in this article, we’re going to focus on the former 5️⃣ in particular, and why much of what we’ll write will be applicable to football alone. With that said, let’s begin…
What 5️⃣ Is Poisson Distribution?
Poisson distribution is a method of calculating the most likely score in a sporting event such as football. 5️⃣ Used by many experienced gamblers to help shape their strategies, it relies on the calculation of attack and defence strength 5️⃣ to reach a final figure.
A mathematical concept, Poisson distribution works by converting mean averages into a probability. If we say, 5️⃣ for example, that the football club we’re looking at scores an average of 1.7 goals in each of their games, 5️⃣ the formula would give us the following probabilities:
That in 18.3% of their games they score zero
That in 31% of their 5️⃣ games they score one
That in 26.4% of their games they score two goals
That in 15% of their games they score 5️⃣ three times
This would help the individual to make an educated guess with a good chance of delivering a profitable outcome 5️⃣ to their bet.
Calculating Score-line Probabilities
Most individuals use Poisson to work out the likeliest scoreline for a particular match, but before 5️⃣ they can do this, they first need to calculate the average number of goals each team ought to score. This 5️⃣ requires two variables to be taken into account and compared: ‘attack strength’ and ‘defence strength’.
In order to work out the 5️⃣ former, you’ll typically need the last season’s results, so that you can see the average number of goals each team 5️⃣ scored, both in home games and away games. Begin by dividing the total number of goals scored in home matches 5️⃣ by the number of games played, and then do the same for away matches.
Let’s use the figures for the English 5️⃣ Premier League 2024/2024 season:
567 goals divided by 380 home games = 1.492 goals per game
459 goals divided by 380 away 5️⃣ games = 1.207 goals per game
The ratio of the team’s individual average compared to the league average helps you to 5️⃣ assess their attack strength.
Once you have this, you can then work out their defence strength. This means knowing the number 5️⃣ of goals that the average team concedes – essentially, the inverse of the numbers above. So, the average number conceded 5️⃣ at home would be 1.207; the average conceded away 1.492. The ratio of the team average and the league average 5️⃣ thus gives you the number you need.
We’re now going to use two fictional teams as examples. Team A scored 35 5️⃣ goals at home last season out of 19 games. This equates to 1.842. The seasonal average was 1.492, giving them 5️⃣ an attack strength of 1.235. We calculated this by:
Dividing 35 by 19 to get 1.842
Dividing 567 by 380 to get 5️⃣ 1.492
Dividing 1.842 by 1.492 to get 1.235
What we now need to do is calculate Team B’s defence strength. We’ll take 5️⃣ the number of goals conceded away from home in the previous season by Team B (in this example, 25) and 5️⃣ then divide them by the number of away games (19) to get 1.315. We’ll then divide this number by the 5️⃣ seasonal average conceded by an away team in each game, in this case 1.492, to give us a defence strength 5️⃣ of 0.881.
Using these figures, we can then calculate the amount of goals Team A is likely to score by multiplying 5️⃣ their attack strength by Team B’s defence figure and the average number of home goals overall in the Premier League. 5️⃣ That calculation looks like this:
1.235 x 0.881 x 1.492 = 1.623.
To calculate Team B’s probable score, we use the same 5️⃣ formula, but replacing the average number of home goals with the average number of away goals. That looks like this:
1.046 5️⃣ (Team B’s attack strength) x 0.653 (Team A’s defence strength) x 1.207 = 0.824
Predicting Multiple Outcomes
If you fail to see 5️⃣ how these values might be of use to you, perhaps this next section might clarify things. We know that no 5️⃣ game is going to end with 1.623 goals to 0.824 goals, but we can use these numbers to work out 5️⃣ the probability for a range of potential outcomes.
If your head is already spinning at the thought, we’ve got some good 5️⃣ news for you: you won’t need to do this manually. There are plenty of online calculators and tools that can 5️⃣ manage the equation for you, so long as you can input the potential goal outcomes (zero to five will usually 5️⃣ work) and the likelihood of each team scoring (the figures we calculated above).
With these probabilities to hand, you can work 5️⃣ out the bets that are most likely to deliver a profit, and use the odds you get to compare your 5️⃣ results to the bookmaker’s and see where opportunities abound.
The Limitations of Poisson Distribution
Poisson distribution can offer some real benefits to 5️⃣ those who desire strong reasoning to support their betting decisions and improve the likelihood of a profitable outcome, but there 5️⃣ are limits to how far such a method can help you.
Key among these is that Poisson distribution is a relatively 5️⃣ basic predictive model, one that doesn’t take into account the many factors that can affect the outcome of a game, 5️⃣ be it football or hockey. Situational influences like club circumstances, transfers, and so on are simply not recognised, though the 5️⃣ reality is that each of these can massively impact the real-world likelihood of a particular outcome. New managers, different players, 5️⃣ morale… The list goes on, but none of these is accounted for within the remit of such a method.
Correlations, too, 5️⃣ are ignored, even pitch effect, which has been so widely recognised as an influencer of scoring.
That’s not to say that 5️⃣ the method is entirely without merit. Though not an absolute determiner of the outcome of a game, Poisson distribution certainly 5️⃣ does help us to create a more realistic picture of what we can expect, and can be an invaluable tool 5️⃣ when used alongside your existing knowledge, natural talent, and ability to listen and apply all that you hear, read, and 5️⃣ see.
FAQs
Why is Poisson distribution used for football?
The Poisson distribution is often used in football prediction models because it can model 5️⃣ the number of events (like goals) that happen in a fixed interval of time or space. It makes a few 5️⃣ key assumptions that fit well with football games:
Events are independent: Each goal is independent of others. The occurrence of one 5️⃣ goal doesn’t affect the probability of another goal happening. For example, if a team scores a goal, it doesn’t increase 5️⃣ or decrease the chances of them scoring another goal.
Events are rare or uncommon: In football, goals are relatively rare events. 5️⃣ In many games, the number of goals scored by a team is often 0, 1, 2, or 3, but rarely 5️⃣ more. This is a good fit for the Poisson distribution which is often used to model rare events.
Events are uniformly 5️⃣ distributed in time: The time at which a goal is scored is independent of when the last goal was scored. 5️⃣ This assumption is a bit of a simplification, as in reality, goals may be more likely at certain times (like 5️⃣ just before half-time), but it’s often close enough for prediction purposes.
Average rate is known and constant: The Poisson distribution requires 5️⃣ knowledge of the average rate of events (λ, lambda), and assumes that this rate is constant over the time period. 5️⃣ For example, if a team averages 1.5 goals per game, this would be the λ value used in the Poisson 5️⃣ distribution.
These assumptions and characteristics make the Poisson distribution a useful tool for modelling football goal-scoring, and for creating predictive models 5️⃣ for football match outcomes. However, it’s important to remember that it’s a simplification and may not fully capture all the 5️⃣ nuances of a real football game. For example, it doesn’t take into account the strength of the opposing teams, the 5️⃣ strategy used by the teams, or the conditions on the day of the match.
How accurate is Poisson distribution for football?
The 5️⃣ accuracy of the Poisson distribution in predicting football results can vary depending on the context, the specific teams involved, the 5️⃣ timeframe of the data used, among other factors. A recent study examined the pre-tournament predictions made using a double Poisson 5️⃣ model for the Euro 2024 football tournament and found that the predictions were extremely accurate in predicting the number of 5️⃣ goals scored. The predictions made using this model even won the Royal Statistical Society’s prediction competition, demonstrating the high-quality results 5️⃣ that this model can produce.
However, it’s important to note that the model has potential problems, such as the over-weighting of 5️⃣ the results of weaker teams. The study found that ignoring results against the weakest opposition could be effective in addressing 5️⃣ this issue. The choice of start date for the dataset also influenced the model’s effectiveness. In this case, starting the 5️⃣ dataset just after the previous major international tournament was found to be close to optimal.
In conclusion, while the Poisson distribution 5️⃣ can be a very effective tool for predicting football results, its accuracy is contingent on a number of factors and 5️⃣ it is not without its limitations.
What is the application of Poisson distribution in real life?
The Poisson distribution has a wide 5️⃣ range of applications in real life, particularly in fields where we need to model the number of times an event 5️⃣ occurs in a fixed interval of time or space. Here are a few examples:
Call Centres: Poisson distribution can be used 5️⃣ to model the number of calls that a call centre receives in a given period of time. This can help 5️⃣ in planning the staffing levels needed to handle the expected call volume.
Traffic Flow: It can be used to model the 5️⃣ number of cars passing through a toll booth or a particular stretch of road in a given period of time. 5️⃣ This information can be useful in traffic planning and management.
Medical Studies: In medical research, it can be used to model 5️⃣ rare events like the number of mutations in a given stretch of DNA, or the number of patients arriving at 5️⃣ an emergency room in a given period of time.
Networking: In computer networks, the Poisson distribution can be used to model 5️⃣ the number of packets arriving at a router in a given period of time. This can help in designing networks 5️⃣ and managing traffic.
Natural Phenomena: It’s also used in studying natural phenomena like earthquakes, meteor showers, and radioactive decay, where the 5️⃣ events occur randomly and independently over time.
Manufacturing: In manufacturing and quality control, the Poisson distribution can be used to model 5️⃣ the number of defects in a batch of products. This can help in process improvement and quality assurance.
Retail: In the 5️⃣ retail sector, it can be used to model the number of customers entering a store in a given period of 5️⃣ time, helping in staff scheduling and inventory management.
Remember that the Poisson distribution is based on certain assumptions, such as the 5️⃣ events being independent and happening at a constant average rate. If these assumptions don’t hold, other distributions might be more 5️⃣ appropriate.
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