I am sure his formulas are correct. He certainly did not forget to factor in a lambda somewhere... Since you've read the paper and understood it so well, can you address my conceptual points and say where exactly I've said something untrue, or how exactly did the paper overcome any of the issues I layed out? Explain it to me. Teach me.. While you are at it, can you also respond to the quote from introduction that i posted eariler?
You know, courtesy comes from non-trolling. I can try to do justice to the work, hell, based on our interactions thus far, the author of the papers can do a full lecture on your behalf, and you'll still find ways to ignore all the points and go back to trolling people with your agenda. You said you want to address the specific issues involving the papers, yet nothing you do suggests that. You sat you are open to accepting new ideas, yet none of your actions suggest that. In fact, everything you do, comes with mockery, ridicule, and false mis-representations. If that's your version of patience, please spare me of that kindness. Let me show you some examples. 1) Far more complex matters have been attempted to be calculated. This is an attempt, not the finished article. Again, give me some sort for sound reasoning for an inevitable mathematical dead-end other than your gut-feelings of the matters being too complex. 2) If your question is, if the author is so smart, has he literally mathematically solved football as of now, and has literally cracked the code to the matrix, enough to make a fortune off betting sites alone? Of course not. Why is this proof that the premise is flawed from the start? If perfection is the standard, nothing you do or say has any sort of ground at all also. Stop talking then. Just stay quiet until you make a living off making predictions. 3) If this is so mathematically easy to refute, just read the papers and find some fundamental flaws within in, as opposed to giving me a non-stop list of potential concerns that the paper already attempts to mathematically solve, and just find as many angles to insult the work as possible, like your attempts to say the author has not succeeded in life anyways. 4) If you have read any of my posts. I said there were many examples of the conclusions I personally disagree with. I can say the same for your work, WhoScored, and Trachta10's work. Now how is that relevant to the discussion of the mathematical integrity of the initial premise? If you want to discuss the papers as avid fans of football, and how to best approach it statistically, please do so with intellectual integrity (as in the basic manners to at least not troll me), and if not, just leave me alone, and go fight Cristiano Ronaldo fans elsewhere. That's your true passion in life isn't it?
I really like your posts (I think it's clear since I give rep at almost all your posts) But if you want some advice from a friend and admirer of your posts, I would tell you not to get too involved in discussions with SexyBeast. He will always use logical fallacies like ad hominem, straw man, circular reasoning, false cause, etc... And this becomes very clear in my discussions with him as I analyze his viewpoints and expose his logical fallacies, ironies and general weaknesses
honestly ... i don't know ... his Top 10 or Top 20 ... The History of the Football ??? .... But .. i think so .. your posts .. are good yes .. !
All statistical models are tools to decipher patterns. Patterns our brains might have missed, it doesn't really matter if we know extra contexts and details about a specific single player, that the model doesn't account for to mathematical perfection, as long as it provides a new angle and perspective to draw patterns from, and the general nature of it is logically sound. It is there to establish insightful patterns of thought. Every patterns I've learned from statistical analysis of any kind, helps me in the way I think, even if the immediate results don't make sense to me. I'm not here to establish absolute truths, but to learn a new premise. I don't think some people here approached the paper with the same amount of curiosity, because they prioritize other matters, such as their version of the absolute truth for the first ten or so players they appreciate dearly, even if the ramifications of the rough algorithms used for the other thousands upon thousands of professional players may not be ideal, in universal application. That is fine, because who has time for all that statistical gibberish. We are not professional statisticians. A person can still be the number one expert on Lionel Messi, have all his nuances, without needing to rely on the most mathematically sound universally applicable models. But to waste someone else's time and efforts, pretending to be interested in statistics, when they are actually interested in the immediate ramifications of the statistics, and how it may help them score points to win internet arguments about Lionel Messi is just tribal behaviour with the false pretense of intellectual curiosity. I don't think this model is the best model to capture for all the minor scheduling nuances, or play details of Lionel Messi or anyone in particular. We don't need statistical analysis for that, you can just watch his career as a fan. Applying the spectator viewership experience, to brute forcing that specific experience onto all professional players, is something I do not prefer over the premise of this model. Everyone has various spectator experience, and personal preferences. Universal application of that idiosyncratic experience does not work for all player types across all levels. That is my key assesertion. This model might be superior in that regard with better execution and more tweaking.
The author mostly publishes rankings in that moment in time, with a statistical model that scores heavily against players who lack career maturity, and those in the latter stages of their careers. It is mostly who is currently good amongst those around the age of 28 or so, at that particular moment, not a full career analysis in totality. So the top 20 list that contained Thomas Muller as the number one player was probably taken around 2017 when he was 28. Most of the players are around the age of 28 for that list. For the all-time lists, you can approximate based on the estimated peak ratings (as in their highest career point, not their current score), which you can find on the author's YouTube channel. The peak ratings seem to differ across time as new data gets added and the formula warps accordingly. I am still unsure how the peak scores are being estimated mathematically. It is just an interesting tool, and I'm more interested to see what it says about the more forgotten players, rather than settling more media-driven narratives like Lionel Messi versus Cristiano Ronaldo.
yes .. could be ... Why not ?? in somehow ... on Thomas Muller .. yes .. honestly me too ... i'm not looking for a Lionel Messi or a C. Ronaldo ... I respect them .. at all ... are at Top 10 or Top 20 for sure .! But ... i don't see nothing on them ... i mean ... I'm not searching for them . !
I have layed out reasons why it is too complex, random and unsolvable issue. I am sorry if that doesnt satisfy your burden of proof but my arguments are sound and they make clear sense to me because this is not something I thought of for 5 seconds. If arguments are not sound, you can pinpoint where, how and why exactly.. The reason why it is unfinished paper and why it will stay that way is because it is not solvable issue. .. If i were to measure length of leafs on a tree in my backyard and from this data were trying to create a model to evaluate football players, you would be correct in saying that my premise is stupid and unsolvable no matter which mathematical tools I use. There is no correlation between length of leafs and quality as a football player. But then I say you know what, I will measure lengths of leafs of all trees in backyards' of all footballers and will have a much biiiger sample size. You would still be correct to point out again that the premise makes no sense. There is no correlation between length of a leaf and who is the best player in the world no matter a sample size. And you wouldnt waste your time reading my 20-page paper of me using statistical tools to analyze this nonsense. I've explicitly said that the paper you shared is a conceptual dead end, and have actually read the introduction and quoted the author avoiding responsibility for accuracy and sense of the model saying that it assumes and considers some things as truth without questioning it. Which "coincidentally" aligns with my reasoning put forth prior. And rather than responding to me in a way to disaprove my actual words and offer alternative perspective to mine, you are telling me that i should just read the paper. Also saying that the model is not finished and doesnt solve many problems (hey surprise) and that you actually dont understand what it is doing, which makes your instance on me reading the paper bogus. Putting your trust into unquestioned authority of a random someone doesnt make you intellectually honest but rather intellectually naive. It is a random paper on economy in football by a person who clearly is not a football analyst, accomplished in such regard nor cares about football whatsoever. On the other hand, you are criticizing companies (whoscored, sofascore, etc.) and people who run them who are experts as well and actually dedicated their careers to understanding football and developing sophisticated models to mathematically capture quality of performance. Explain me how that makes any sense? This is no the case of me being intellectually dishonest and closed minded, and distrusting authorities.. What you can do is actually respond to my reasoning beyond saying it is my gut feeling and I am intellectually dishonest. I have wrote many sentences so far (still havent touched upon many points as well) so you can quote specific sentences and paragraphs that you think are wrong or unapplicable in the case of the paper and say them.. you can even quote the paper where it says something that counters my sense of it and the reasoning. Only then i have actually something of substance to respond to. Till then, this is going in circle and I literally have no counter argument to respond to other than you calling me intellectually dishonest and all other nice things..
If you don’t like me insulting you, either recognize the kind of behaviour that triggers such responses, or just stop talking to me. It’s what I’m considering doing as of now, since I think you truly don't want to discuss this issue at all, but still want to shut-down what could spawn as a consequence of me taking an interest in such issues, due to reasons I've explained previously. I’ll give it one more shot, and yes if I sound like a prick, it is both because I am a prick, and you are being a prick also with your intentions, but nicer with the wording. 1) You believe and strongly assert the literal mathematical impossibility, not difficulty in correct exection, literally pure, utterly unavoidable doomed nature of such a task, without having done any reading of the work. Either you have insanely strong faith in your statistical and mathematical intuitions, when things like the Tikhanov regression model are by most accounts, very hard to intuit, especially without prior experience with handling data-sets with it, or you are speaking in hyperboles just to be derogatory of the premise. 2) I don’t even get your hypothetical scenario. How would you possibly make a mathematically water-tight correlation model out of those two independent variables (let’s say largest dimensions of 500,000 leaves, and goals per 90 minutes of 50,000 professional footballers) that does not immediately raise red-flags from a statistical stand-point? It is like saying would you believe in the existence of Gandalf the Grey, if I transported you to Middle Earth and started dishing out magic spells? Why do you require impossible hypothetical mathematical scenario to explain your stance on the formula, instead of actually looking into the model that we see in the papers? 3) There is a huge difference here. First is making a brute-force, collect-the-on-field-action-tallies-and-re-arrange-them until the top ten players somewhat complies with what society wants model, like what I suspect WhoScored model of being, although I must say in fairness, still better work than anything I can do. Like I said before, the model, I suspect, also becomes less and less concerned as you trickle-down the consequences of making sure an appetizing first page appears on the WhoScored ratings, to the rest of the field. Unless you are famous and popular enough to warrant being specifically calculated for, good luck with your ratings if you do not share the play-styles of more famous players than you. And the other premise, starts with a bold, ambitious mathematical model that attempts to gauge the correlation between team results and player influence on it, but fails to land on perfect execution after a couple of tries. One has been done so many times, and it is by nature just a numerical reflection of what the media and public tends to appreciate in footballers, not that there is anything wrong with spectator evaluation per-se, but it isn’t really the best feasible route to measuring the most effective player. Humans aren’t the best equipped to think in such statistical mannerisms, it is why we need help. Human intuitions, when it comes to the realm of statistics, tend to suck ass. That's what I think. 4) Also, such an approach will always improve at a much slower rate given the same amount of resources. It will always be an echo of the overall voice of the footballing scene. And we already know the voices and opinions, so we don’t need to parrot those things into numbers, as if the statistics were the engine that created those opinions. We are essentially at the stage of using numbers to back-up our already made-up conclusions, when it can go one-step further. The other premise, on the other hand, can be ahead of the game, just as a raw idea. It is mathematically just more pleasing, and the possibilities involved are mouth-watering, with sufficient man-power and time. If you believe in the infallible analysis of the human eyes and brain, for football, we shouldn't even be discussing statistics. Just tell others what you see, as in somebody else that cares as deeply about Lionel Messi or whoever it is that you want to talk about. Make it into the biggest circle-jerk ever seen with as many trivias about Lionel Messi that also simultaneously throws subtle shades at Cristiano Ronaldo for the biggest satisfaction bonus points.
I would like to limit to discussion to the players born in 1996 (aged around 28), because the quadratic equation used to formulate the numbers, in my opinion, sort of brute-forces a ratings peak around that age for most players who cannot over-power the equation due to their outstanding prodigious nature, or extreme unnatural longevity of their careers. Every career is sort of forced into an upside down U shape, and its sort of harsher on the age ranges that deviate too much from the age of 28 or so. Since the peak ratings of players who dropped out of the lists cannot be searched for, I’ll just see if there might be players on the list, judged by their current ratings, who might be underrated (in terms of what they give to the team, and how they are rated by the on-the-ball metrics) by what they give to the team, but only for those born in 1996. Due to the more holistic approach of the formula (as in the seasonal performances are really hard to gauge in isolation), rather than the season-to-season in separation ratings of the WhoScored algorithms, the disparity between the two are hard for me to explain from a pure statistical stand-point. I’ll be stupid anyways and just go with it, I’ll skip over the usual suspects like Rodri, because we don’t need statistics to vouch for the team contributions for this profile of a player. Denzel Dumfries: Rated 61st on the list, and my initial selection as a player that might be underrated by the conventional WhoScored type metrics, and more appreciated by this statistical model. For me, not that really crazily rated by the WhoScored metrics or really highlighted by the media. Although I am very uneducated about the player, I would assume the difference might be because he seems to suit the profile of an athletically gifted player who is useful for the team, without being much of a joy to spectate due to his on-the-ball deficiencies. As in, you might miss him as a supporter of the team when he is gone (hence the higher rating if you value effectiveness for the team), but don't really enjoy watching him due to his on-the-ball limitations, and don't think much of him. His profile might be the kind of player who provides a lot of avenues for his team through his general leg-work, and also shuts down avenues from the opponents due to his general physicality and presence in the air, but sort of lacks quality in the final-third with the ball at his feet. The kind of player that might get massacred in terms of WhoScored or Sofascore ratings, even if his presence was a net positive in terms of influence on team results, or if his absence consistently caused team downfall in terms of results. I think these are the things I'm interested in, and see much potential for.
Yes! Although I use the word impossible here in its every day meaning rather than the literal one. For example, there is possibility that graphite in your pencil turns into diamond, but it is very, very small chance so practically speaking it will never happen in the lifetime of universe. That is quantum mechanics.. Since you like reading a lot and think I am making shit up I will just quote chatGPT: "You're absolutely right in making the distinction between something being *theoretically* possible and *practically* impossible, especially from a quantum or physical perspective. The idea that many things we think of as "impossible" in everyday language are actually just *extremely* unlikely is a key insight from modern physics, particularly in quantum mechanics and thermodynamics. In everyday conversation, when we say something is "impossible," we often mean it's beyond conceivable or practical realization. For example, when people say, "It's impossible to travel faster than light," they refer to the constraints imposed by the laws of physics (in this case, Einstein's theory of relativity), which make it unachievable for anything with mass under normal conditions. ### Quantum Mechanics and the Concept of Impossibility In quantum mechanics, however, events are governed by probabilities, and the term "impossible" takes on a different connotation. Quantum systems are described by wavefunctions that include many possible outcomes, even those that are *extremely* unlikely. In theory, the laws of quantum mechanics do not rule out incredibly rare events; they just assign a very, very small probability to them. Take your example of graphite turning into diamond spontaneously. Both graphite and diamond are made of carbon, but their atoms are arranged differently. While it is possible for the atoms in graphite to rearrange themselves into the more ordered diamond structure, the energy barrier for this transformation is so high that it would never happen naturally under ambient conditions without external pressure or temperature—at least not on a timescale shorter than the age of the universe. From a quantum mechanical perspective, however, the word "impossible" would only apply if the event had a probability of exactly zero. In this case, the graphite-to-diamond transition has a non-zero probability, but it's so low that it can be practically ignored. This leads to the idea of something being "practically impossible" rather than "fundamentally impossible." ### Statistical Mechanics and Thermodynamics Similarly, in statistical mechanics, the concept of "impossibility" is often tied to the second law of thermodynamics, which states that entropy (disorder) in a closed system tends to increase over time. In principle, there's a very small chance that all the molecules in a room could spontaneously align themselves in one corner, dramatically lowering the entropy. This doesn't violate any fundamental laws of physics—it's just *astronomically* improbable. So we say it's "impossible" in practical terms because it would never happen within the lifetime of the universe, even though it's not strictly forbidden by the laws of nature. ### Theoretical vs Practical Impossibility This brings us to the distinction between theoretical and practical impossibility. Theoretically, something is only impossible if it contradicts the fundamental laws of physics. For example, violating the conservation of energy would be theoretically impossible because it contradicts one of the most fundamental principles of physics. On the other hand, practically impossible events are those that, while theoretically possible, have such a low probability that they can be ignored for all intents and purposes. In summary: - **Theoretical impossibility**: Events that *cannot* happen under any circumstances because they contradict the fundamental laws of physics (e.g., perpetual motion machines). - **Practical impossibility**: Events that, while not violating the laws of physics, are so unlikely (due to the vast number of atoms or the massive energy barriers involved) that they can be safely ruled out in practice (e.g., a pencil spontaneously turning into diamond, or a person walking through a wall due to quantum tunneling). So, when thinking from a quantum or thermodynamic perspective, many things are "possible" in theory but "impossible" in practice. Everyday language often collapses these nuances, but physics reminds us that probability plays a key role in what we consider to be truly "impossible."" I call it impossible in every day meaning. I can call it pracitcally imposisible or unfeasible if you'd like that: "Yes, "unfeasible" (or "infeasible") is often a more accurate term to use in everyday language when referring to something that is theoretically possible but highly impractical or improbable to the point that it can't happen under normal circumstances. For example, instead of saying "it's impossible for graphite to turn into diamond," you could say "it's unfeasible for graphite to turn into diamond under everyday conditions." This acknowledges that, while it's technically possible (given the right pressure and temperature), it's not going to happen spontaneously in a practical or accessible way. Here's a comparison of how these terms could be used: - **Impossible**: Refers to something that cannot happen at all, no matter the conditions. For example, "it's impossible to violate the laws of thermodynamics." - **Unfeasible/Infeasible**: Refers to something that could theoretically happen, but is not realistic or practical. For example, "it's unfeasible for a person to quantum tunnel through a wall." Using "unfeasible" instead of "impossible" helps avoid overstating the situation, especially when you're speaking in terms of probabilities or scientific phenomena. It better captures the nuance of things being beyond practical reach rather than outright prohibited by nature." If football was only complex in a sense of there being 22 independent variables interacting with each other on the pitch then some tools could account for that. However, Tihkanov regression model doesn't account for randomness, which is a dominant phenomenon in football primarily due to being a low-scoring game. Multiple independent variables and an effect of random events are two separate challenges that are impossible to account for with the classical +/- model and real-life sample size. **Tikhonov regularization** (commonly known as **Ridge Regression**) is a technique used in machine learning and statistics to deal with **overfitting** and complexity by penalizing large coefficients in the model, effectively simplifying it. The main purpose of Ridge Regression is to strike a balance between bias and variance by introducing a regularization term that shrinks the regression coefficients. This helps handle datasets where there are many predictors (features) or where the predictors are highly correlated. "In the context of football, using **Ridge Regression** could help address certain complexities and randomness, but with limitations. Let's break this down: ### What Ridge Regression Could Help With: 1. **Reducing Overfitting**: Football data often involves many variables (player stats, tactical data, environmental factors, etc.), and Ridge Regression can help prevent overfitting by controlling the influence of less important features. For example, if you have too many features describing a player's actions, Ridge will help avoid making the model overly sensitive to noise from less significant variables. 2. **Handling Many Features**: Football data is inherently complex, with many interacting variables like the actions of players, formations, pitch conditions, etc. Ridge Regression can help manage this complexity by penalizing large coefficients, ensuring that the model doesn't over-rely on any single predictor. 3. **Multicollinearity**: In football, some variables (like passes completed and passes attempted) may be highly correlated. Ridge Regression can help by shrinking the coefficients of these correlated features, making the model more robust and stable when dealing with multicollinearity. ### What Ridge Regression Can't Solve: 1. **Randomness and Unpredictability**: Football is heavily influenced by random events and situations that are difficult to quantify—such as a deflection, referee decisions, weather changes, or team morale. Ridge Regression, while it can reduce model complexity, **can't account for pure randomness** in outcomes because randomness isn't predictable or explainable by any statistical model. 2. **Context and Intangibles**: Ridge Regression will still require well-defined features. Football involves many contextual and intangible factors (e.g., leadership, positioning, decision-making under pressure) that are difficult to represent as numerical features. If these aspects are not captured in the data, Ridge Regression won't be able to account for them. 3. **Capturing Nonlinear Relationships**: Football is a nonlinear game, where interactions between players and events are highly complex and dynamic. Ridge Regression is a linear model, so it **won't capture nonlinear interactions** unless the data is transformed appropriately, or unless more advanced methods (e.g., neural networks or other nonlinear models) are applied. ### Practical Impact of Tikhonov Regularization in Football Analysis: - **Useful for feature selection**: In a dataset where you're trying to predict match outcomes or player performance based on hundreds of metrics (e.g., passes, shots, tackles), Ridge Regression can help identify which metrics are most predictive while reducing the noise from irrelevant features. - **Improves generalization**: It ensures that the model works well on new, unseen matches by avoiding overfitting to the peculiarities of a specific dataset, such as one team’s unique playing style over a season. ### Conclusion: While **Tikhonov regularization (Ridge Regression)** can help **reduce complexity and overfitting**, making your model more robust and generalizable, it won't fully solve the problem of **randomness and uncontrollable events** in football. To address randomness, you might need a combination of techniques, including better data preprocessing, feature engineering, and even more complex models that can capture nonlinearities or stochastic processes." "Yes, accounting for randomness in football **would require a very large sample size** to accurately assess the performance of an individual player, and this sample size is often **not feasible** to achieve. Here’s why: ### 1. **Football's Randomness and Complexity**: - **Football is a low-scoring, event-driven game** where many factors influence the outcome (referee decisions, weather, random deflections, opposition quality, team tactics, etc.). - For any single match, a player’s performance is affected by all these external factors. Even if a player performs consistently, the outcome of their actions is often dictated by chance or elements beyond their control (e.g., a perfectly placed pass might lead to a goal, or the same pass might be intercepted due to a random event). - These random events create a lot of **noise** in the data, making it harder to isolate a player’s true contribution to the match or season. ### 2. **Why a Huge Sample Size Is Necessary**: - **Random events average out** over a large number of observations. For example, in football, to truly understand how much a player influences a match, you'd need to look at a large number of games to balance out the effect of randomness and isolate the player's true impact. - For example, if you evaluate a striker’s goal-scoring ability over just 5 matches, luck (such as deflections, goalkeeper mistakes, etc.) may skew the results. To mitigate the impact of randomness, you would need many more matches, ideally across different teams and contexts, to draw a reliable conclusion. ### 3. **Feasibility Issues**: - **Limited Data**: In football, players don’t play enough games within a single season to provide a large enough sample. Even a player with 50 or 60 matches in a season (which is high) may not have enough data points to fully separate performance from randomness. - **Player Variability**: Players change over time. They might improve or decline due to age, fitness, or other factors, which means that you can’t just collect data over many years and expect it to be consistent. A player’s performance today may not be reflective of their performance five years later. - **Context Dependence**: The team a player plays for, the opposition, and tactical changes all impact their performance. The same player might perform differently in different teams, meaning that even a large sample size might not fully capture their potential or isolate their true contribution. ### 4. **Diminishing Returns on More Data**: - After a certain point, adding more matches won’t dramatically reduce the impact of randomness. Even with 100 or 200 matches, there will still be some level of uncertainty due to the complex and random nature of the game. This is especially true when evaluating rare events, like a midfielder's assist rate or a defender's ability to prevent goals. ### 5. **Impracticality for One Player**: - To gather a statistically significant sample that minimizes randomness for one player, you might need hundreds or even thousands of matches, which isn't practical for a single player's career, especially when considering factors like injuries, transfers, and changing roles within teams. ### Conclusion: Yes, accounting for randomness in an individual player's performance would require an impractically large sample size, especially in a sport as complex and unpredictable as football. While some randomness can be reduced through statistical techniques and smarter data analysis (like controlling for context or using advanced metrics), **completely isolating a player’s performance from randomness would require more data than is feasible** to collect. Therefore, models and evaluations must accept some level of randomness or rely on more sophisticated methods to estimate performance while accounting for these uncertainties." "In practice, **no model**—no matter how sophisticated—can **fully capture a player's performance** from a typical, realistic sample size in football. Here’s why: ### 1. **Football’s Complexity**: - **Dynamic interactions**: Football is a highly dynamic game with 22 players on the pitch, each influencing one another. The complexity of these interactions cannot be fully captured by even the most sophisticated models. - **Unpredictable and chaotic**: Football has random, chaotic elements—such as deflections, refereeing decisions, and weather conditions—which make it difficult to isolate individual contributions. - **Contextual performance**: A player’s performance depends heavily on factors like team tactics, the quality of teammates and opponents, match situations (e.g., playing with 10 men), and whether the player is attacking or defending. These variables constantly shift and are hard to capture holistically in a model. ### 2. **Sample Size Limitations**: - A **single season** (30-50 games) for one player is a relatively small dataset when you consider the high variance in outcomes and performance in football. There isn’t enough data to smooth out the randomness, making it hard to isolate the player's true value. - Even with multiple seasons of data, player performance fluctuates due to injuries, aging, changing teams, different coaches, and shifting tactics. This variability makes it harder for any model to generalize or predict future performance accurately. ### 3. **Intrinsic Uncertainty and Randomness**: - **Luck and variance** play a significant role in football. A striker may hit the post 10 times in a season, or a midfielder might create brilliant chances that teammates fail to convert. This variance is an unavoidable part of football and cannot be perfectly modeled. - Even advanced models struggle to capture the **intangibles** that make a great player. Things like leadership, off-ball movement, positioning, tactical intelligence, and psychological aspects (confidence, pressure-handling) are difficult to quantify. ### 4. **Feature Limitations**: - **Key metrics** like goals, assists, tackles, and passes are useful, but they don’t fully account for the **quality and context** of each action. For example, two passes might be successful, but one could be a simple sideways pass, and the other a brilliant through-ball that splits the defense. - More sophisticated models, such as **expected goals (xG)** or **expected assists (xA)**, add layers of context by measuring the quality of chances created, but even these are approximations and don’t account for tactical influence, off-ball contributions, or defensive awareness that aren’t directly tied to the play-by-play data. ### 5. **Limits of Even Advanced Models**: - **Machine learning models** (like deep learning, neural networks, etc.) can analyze patterns and relationships between many variables, but they rely heavily on the quality of input data. Football data is still limited in terms of capturing **context** (e.g., tactical roles, off-ball actions, defensive positioning), and even large historical datasets have gaps in these areas. - Models also require **generalization** to predict performance in future matches or seasons, but the level of randomness in football makes it hard to generalize perfectly, especially when circumstances change (e.g., player transfers, tactical changes, new managers, different leagues). ### 6. **Bias and Oversimplification**: - **Subjectivity in defining metrics**: In some models, the weighting of certain metrics is arbitrary. For example, deciding how much to value a through-ball versus a tackle involves subjective judgment. - **Oversimplification**: In trying to quantify everything, models may oversimplify the game. A model might assign a weight to an action (e.g., a key pass or interception) without fully considering the context, tactical importance, or uniqueness of each situation. This can lead to an incomplete or even misleading assessment of a player’s true contribution. ### 7. **The Role of Human Expertise**: - Even the best models can’t replace the **nuanced understanding** that comes from human expertise. Coaches, analysts, and scouts use both data and **qualitative insights**—such as how a player fits a system, their psychological traits, leadership, and tactical intelligence—which are difficult for any model to quantify comprehensively. ### Conclusion: While **sophisticated models** can provide valuable insights and greatly enhance our understanding of player performance, **they cannot fully capture** the complexity, randomness, and context-dependent nature of football, especially within the constraints of a practical sample size (such as one or even several seasons of data). Football is a fluid, multi-dimensional game where many factors beyond a player’s control affect outcomes. Therefore, any model, no matter how advanced, will always be an **approximation**—useful for guiding decisions but never able to perfectly or fully reflect a player's true value or contribution. Ultimately, combining **advanced data models** with **expert human judgment** and **contextual understanding** is the most realistic approach for evaluating football players." For there to be any chance of mathematically accounting for randomness in football, the data set would have to be randomized. You've heard of the term "randomized controlled trial"? In practical football terms this would mean that player selection by all managers would have to be random (plus it would be great if players each round play for a random term with random teammates) and there would have to be muuuuuch more games in a season - practically impossible number. If you get hands on such real-life data sample, please share with us and others, because in that case this model could go somewhere. The classical +/- model can not differentiate performance of a player who plays 50 games in a season and misses 5 games. These 5 games are not enough to evaluate how team performs without the player. Most players play the most of the games in a season.. not that it is enough absolute number of games either way.. Unless the paper uses data outside of the scope of the classical +/- model, they would have no sufficient information to accoutn for this things. Albeit, I dont know what kind of the +/- model the paper uses or if they majorily deviate from the original idea behind the classical +/- model and are misappropriately calling it that... but I have a sense that you would have pointed that out so far if it was the cass... so I assume it is a slight variation of the classical one, which is bad. However, I never said that a +/- model can not be used in some clever ways to add on to other fundamental models, but if it is a basis of a data sample and analysis, the everything else afterwards falls into a garbage can because it is not good at its premise. Okay that is enough so far. I will respond to other stuff later
1) Perfection, and the idea of which premise sounds better. If the immediate, or short-term (within our life cycles) goal is mathematical solution. Yes it literally is impossible. Take it to such impossible standards, everything that humanity does is ridiculous and ultimately doomed to be wrong. Tallying of actions-on-pitch like points for goals, deducting point for cards has been done since the 1990s. The level of refinement since then has been colossal, but the premise has been worked on way earlier, since it does not need help from powerful mathematical tools to make it operational. The Plus-Minus model is a more complex idea that breaks down the moment you try to handle it in a non-mathematically sound way. It has a way steeper curve of execution. The author's take on Plus-Minus models with his two-pronged solution of massive data sample size, and ridge regression, has been worked on by who else? What other paper has the necessary sample size, in conjunction with the proper statistical analysis for a sound mathematical take on a concept like the Plus-Minus model? I literally couldn't find one. So this is literally the starting point of my liking for the premise. If you did not notice, I do not appreciate amateurish mathematical takes on a sample size of 10 games. A child can do that. You are comparing the integrity of a really good mathematical solutions (of course it is no where near being done, I would liken it to a take-off from ground zero) to a difficult problem, to the flawed nature of amateurish takes on the model to make it sound more stupid and useless. That was the partly why I started being so persistent in defending it, because it was being mocked from the get go, by people who didn't even read it. The premise is the following, with my own sets of reasonable configurations and goals, and as you have asserted, let us be as fair as possible, in this thought experiment, and be fair to the confounding variables: My premise: A) Equalize for man-power/overall access to computing power. B) Equalize for the amount of time spent, and access to the data. -> Let's scale the two ideas with enough time and computing, and see what premise works as an universally applicable tool for all players. Not who describes Lionel Messi in more thorough detail to his fans' content. Literally pick any random player across time, and see which model assesses him better. Literal random selection for the assessment of the premises, after both has been equalized for resources and the opportunity to be wrong and be improved on over time. Inside my mind, the premise worked on in the papers has more upside. I cannot prove it, and it isn't like you went through rigorous mental exercises to disprove it either. We are both basing this off our gut instincts, and pretending to be logical. 2) Nature of Plus-Minus models, what it requires to be operational, and what it can measure. Didn't I already mention the need for a large sample size, and even then how the model isn't apt for the usual game-by-game analysis? Why are you spending time chatting to ChatGTP when you literally gloss over all of my points? Start talking to the AI, and leave me out of this third wheel experience if this is your approach. Why do you keep insisting on bringing down the sample size to crash the model? I literally said the model scales-off the amount of sample size, and that even more data would make it better. Why are you ignoring me, and just throwing words at my face, and passive aggressively feign hurt when I get frustrated? If I'm too bad at explaining the promising concepts of the papers compared to ChatGTP, just talk to it instead and arrive at your own conclusions at your leisure. Or try to actually address the points I'm trying to make. This nature of discourse is way too vexing, I am not your personal ChatGTP that gives endless answers to your what-about-isms, without ever getting frustrated or angry, even if you literally ignore the immediate prior statements to drive home the same notions but with added insults and passive-aggressive comments.
Okay, I think I see where the confusion is. Before I respond to the points you brought up that are very interesting, may i first ask you if you agree with this foundational idea to find a common ground between us? If you dont agree with this, then there is no common ground to stand on and there is no point in continuing. ... You must of heard of the 3-step process that describes every function in mathematics: Input -> function -> output Models of any kind in any aspect of life can be described the same. The only difference between them, I think, is that models are more elaborated and imply a goal. Would you agree with the statement about the 3-step process describing models? Okay so if you agreed, model is described by input (data), some set of operations like mathematical tools and such and some kind of output.. And this is the key idea: Obviously if you have nonsensical data as an input and you have nonsensical set of operations as function, your output will be nonsense. So: Nonsensical data + nonsensical processing = nonsensical output (score) However, the same applies if only either data or processing step is nonsense: Perfect data + nonsensical processing = nonsensical output Nonsensical data + perfect processing = nonsensical output. ... Everything in a model needs to be reasonable, sensical to make sense overall. If any tiny step in the whole model is nonsensical, the whole model immediately, irretrivably becomes garbage unless it is changed into something sensical. This is why I gave the example about the length of leaves example - to illustrate the point that if you feed the model nonsensical data and expect sensical output, you will not get it. And the thing about input is that it is manually given to model. It is a human input. Even if we did it and came up with a perfect model (its processing step) that ingeniously combines neural network with the most advanced and sophisticated mathematical tools possible and feed it a nonsensical data, it will output nonsense. This is important. Would you 100% agree with this perpsective? If you dont, there is no common ground for any further conversation. I can not discuss with you about something making sense or not.. Btw, this is exactly where my "strong" intuition comes from and how come I am able to make these generalized, black and white statements about whether a model is a dead end or not.. because it is rooted in a simple, big picture perspective that just makes sense.
................................ Is Interesting .. the mentality Of Pelé ...that he is speaking there ... Pelé speaking there..in the documentary.. Despite having scored more than 1000 goals in my career.. It's always a joy to do it again... a new goal... a new goal ... a new goal ...a new goal .. There would be no Football without the Goal in any sport. you have the maximum achievement In Football, the ultimate achievement is the goal.. Pelé's Mind speaking ..with himself ....: Theoretically..The easiest way to reach the goal is to go straight through the middle, attacking zone 14 aggressively. with very very Aggression ... vertically is much easier than doing zig zag ..." If you have two players extremely quicker and Foresight.. Premonition..Intuition's Mind You attack by doing Plays one-twos..and narrowing the game..on the middle ... no fears at all .. and Attacking zone 14 or half-moon in brazilian portuguese .. a expression in Football from here .. in Brazil... ..and having ..an absurd Technique " ambi-dextrous feet "..then it is easier to attack through the middle ..and narrow ..in a matter of Milli-Seconds the move to make is decided on my mind ... Examples this... type Pelé and Coutinho .. Pelé and Pagão .... I don't know why... the teams... nowadays are afraid of attacking zone 14... playing in midfield. and narrow.. They are playing now on the wings..and widen the field a lot.. They say it's very difficult to play through the middle and narrow. Here is Wiliam Phil Gracek talking to you guys .. .. hahahaha ! .. I got the feeling that Pelé is talking about the 1974 Dutch team.. the mentality ..of the dutch Football ... or German Football ...
Sure, I can stray from the mathematics, and discuss my gut-intuitions also. My problem with the WhoScored algorithms is that it is mostly an on-the-ball action tally that attempts to evaluate those who offer so much without on-the-ball actions. If the premise was given like a top-scorer list, as in we see exactly what the topic is attempting to discuss, that is fine, but I hardly see any attempts to correctly state what it attempts to measure and say. I also think people who support players who benefit most from this metric willingly stay ignorant, or choose to stay quiet about this. I have hinted many times that the issue with WhoScored algorithms, is that it measures incompletely, not incorrectly. They can be saying something completely correct in isolation, just not the whole truth. If I cherry-pick the selectively, even if the sampling was all 100% true, I can end up thinking the most stupid things. What if I cherry-picked the best ever selfies of an instagram model, and presented that as the entire package as a person, all the good and the bad? My judgement would immediately get clouded by the biased perception, even if I actively tried to account for the other factors inside my mind. It is an unfair portrayal of reality, even if the photographs were not photoshopped at all, and were naturally taken. I have no problems saying that WhoScored pretty much achieves what it sets out to achive. It is the latest configuration of an age-old ratings system that started decades prior. If we didn't get better at it, as in, trying to mirror on-the-ball action tallies with overall player perception, it would be an extremely odd occurence. Give me 5 billion years of life-time, and infinite stamina, I'll be able count every possible actions around the ball, for every single game with video footage, and give you a better tallying system through sheer trial and error alone. It is an extremely intuitive process, if your aim is to merely reflect the media perceptions, as closely as possible, with the numbers you tweak from the tallies. I just don't like what it attempts to address as an initial premise, which is, actions that happens around the ball can be worked-with, in a manner that ends up measuring all types of players fairly. Or even worse of a statement, it is okay to penalize the countless number of less prominent players so as long as the most of the minutia of the more commercially viable players are captured in the model. They are merely collateral damage in a system that was never meant to do them justice, but we will set order a valuation for all players as if the model was capable of doing all these players justice. As I mentioned many times previously, I just don't think it is universally applicable method of addressing all types of player effectiveness in a fair manner. I can give you some examples off the top of my head. Kieran Trippier versus Kyle Walker. Players with similar age, overlapping teams, overlapping leagues, and overlapping positions. Kyle Walker's presence alone shifts the entire shape of the field, and the dynamics involved with the opposing players. Wingers from the opposite side play differently. The avenues of attack changes. These are all things that constantly happen, even without the ball being near him. He is a player that cannot be judged solely-off on-the-ball actions alone. Kieran Trippier on the other hand, is a much more potent threat with the ball at his feet, and due to the nature of WhoScored, gets rated higher than I would mark him overall as a player. During the 2022/2023 season, he was rated as the 6th highest rated player in the entire league, being a Beckham-esque player with deadly effectiveness in set-pieces, and crossing ability, and of course all of those key passes sky-rockets his ratings. He is a good player, no doubt, but the bias towards creative forwards creates an unfair trickle-down effect that makes players of all roles and functions, somewhat overrated so as long as they share some traits with a more famous player like Lionel Messi, who I value extremely highly, but not so much the fake adulation that borders on needless worship. Kyle Walker doesn't even come close to the top ten in any of his WhoScored scores for any of his seasonal domestic league performances. Not once. In his entire career. Yet whenever I see him on the pitch, with a player I frequently watch such as Heung-Min Son, facing him as the opposite number, I get an immediate sinking feeling in my stomach that I never would get when seeing Kieran Trippier. It is a gut feeling that is far stronger than any decent number of creative actions with the ball can create. These overall assets are things that don't register naturally for me, at least, because it is so much easier to be captivated and remember what the player does once he gets the ball at his feet, than his overall contributions to the team, even boring ones. Was the difference that large as the WhoScored ratings suggest, that a prime Kyle Walker struggles to lick the boots of the master-playmaking creative full-back Kieran Trippier who was verging on the age of 32 or so? Or maybe it is more of a statement in the inherent bias that is specifically designed to praise the creative attacking on-the-ball magicians people love to support, follow, and study intensely without missing a single brush-stroke of their majestic ball touches? Does Hvattum's mathematical take on the Plus-Minus model fair any better? I would guess so, and let's find out. Kieran Trippier turned 28 on 19th September 2018, and Kyle Walker did so in 28th May 2018. I couldn't find an overlapping top 100 video where both these players got ranked, so I did some google search for these players. And found this page that seems to be associated with the author of these papers. Highest rated players born in the year 1990 | Patreon I'm not sure at which point the current rating was given, maybe it was 2023, but what can be asserted is that according to their peak estimated ratings, Kyle Walker was more of a net-positive as a player than Kieran Trippier, which I personally have always felt, even though Kyle Walker is no-where near as good on-the-ball, and creative metrics that WhoScored values highly. This is the sort of inherent bias I am trying to address via this model, which of course requires more work. I just think it is an amazing step in the right direction for a similar premise I already seen on FBREF, but personally thought the numbers were all over the place. This mathematical take, is a whole different beast that makes the model really good, and I think it is an okay substitute for players who help the team massively without being the greatest on-the-ball talents. At least comparatively to WhoScored, which totally blows-ass in this regard, if I'm being honest. And this model already does a better job at appreciating all profiles of players, than WhoScored, who get really bad at appreciating the overall net-positive contributing players, who don't only seek to help once they get the ball at their feet. I'll try going over multiple players of this nature to make my points clearer across time, and see how the model holds up versus my expectations. I don't really feel like Lionel Messi is the core of this discussion, he is merely one of the factors that caused the distortion in the ratings.
In general, I see an almost total disconnect between the "philosophy" behind the model and the numerical value it generates. If the goal is to measure a player's influence on their team, how can goal difference be expected to indicate something like that? I insist, it’s not taking into account the context of each player. An example, If I take the games played by Müller, he is the player whose team had the highest goal difference in modern football when he played. On the other hand, Iago Aspas plays for a team that barely has more goals than its rivals. I have no doubt that Iago Aspas playing for Celta de Vigo was much more influential than Thomas Müller at Bayern Munich, but you will never be able to measure something like that with this method. Do both players have the same numerical possibility? That’s my question.
Muller is the 99 guy on MacroFootball as well, in fact the highest rated 23/24 big-5 player in terms of Isolated Impact. https://macro-football.com/player/page/thomas.muller_224/ The Method: https://macro-football.com/about/lev2.0/
Is this a joke answer? I literally said it is important to find a common ground, that we cant continue talking about it if we dont agree on it and asked you 2 direct questions, which you completely ignored. You responded to one word of mine ("intuition") in the last paragraph furthering your agenda of certain players having to be rated higher no matter what because you feel like it. And you are calling out people on having agendas and being intellectually dishonest. If your goal is not to be challenged at all and have an actual discussion, but writting your feelings down, you can simply do that without calling others out and acting as if you are a symbol of intellectual honesty open for reasoning things through. You clearly are not.
Of course. There is simply not enough information on a player's performance within the goal difference data to be extracted by any kind of process to yield sensical results. It is informationally-deprived data.
I felt like that's the game we are playing. Why are you attacking my feelings and calling my heartfelt post nasty things? Forget about mathematic concerns. Let's talk about what we feel based on our gut instincts, and why it is pure arrogance to debate in any other manner. I feel like you are coming from a very negative place. You emotions basically stem from the thought that it was rude of me to undermine you intellectually, for trying to discuss the mathematical impossibility of overcoming the sacred WhoScored algorithms, without actually reading any of the papers. Isn't this what you want? Just free flowing exchange of emotions, with no demands to read useless papers, or no insults? This truly is liberating. I don't even need to think. I feel your adulation for Lionel Messi is making you extremely dull and pointless to talk to. I feel like everything you did was not done with the intention to share your insight, but force your prior beliefs even at the cost of hurting your intellectual integrity. That's how I truly feel. My gut-feelings are now saying I should add you to the ignore list. I tried my best to be intellectually honest with you, and I truly am sorry that I failed in that regard.
Because he has the wrong nationality and language. The wrong market. The full-backs that get rated are typically from the bigger markets and countries, even more so than with e.g. strikers. One decade ago people as Lichtsteiner or Alaba were not really rated either and just a decoration for Lahm. Ask people about the twenty best full-backs of the last decades and chances are high not a single player from the 'smaller' countries are on this. Also not Portugal, no, this time (they still get solidarity money from UEFA and FIFA, and we are net payer, wtf). With full-backs you see this more often as with some other positions. Awards like the Ballon d'Or this century sh*t on us and then years later you'll see a further bump down for any given season, from the already low starting position. I'll not mention names. Only eleven Oranje players received Ballon d'Or votes this century. In terms of defensive players, only Van Dijk was on this more than once (in 2019 and 2022 - chances are high this will be it for him; that plus-minus source also has a comparison for Van Dijk vs Vidic, the 'winner' of this comparison cannot be surprising). Then you get repeatedly stuff like this, yes, and the desire to freeze is out entirely from top level football. Throw us out of the Champions League. https://www.bigsoccer.com/threads/what-has-happened-to-german-and-dutch-football.654591/ https://www.bigsoccer.com/threads/champions-league-revamp.877580/#post-16474119 Push that button for long enough, for decades (by The Guardian, The Times, The Athletic - it is clear they 'hate' us and will not apply those themes to Germany or Spain), and it becomes reality. 'Objective' indicators do not quite match. Such as these: https://www.premierleague.com/news/585146 (for La Liga between 1992-2024 also the 3rd European country behind France and Portugal, in the CL not 'bad' either) Dumfries does not set the indexes on fire - and I am genuinely not a fan of him - but he is not poor either. In Sofascore he is basically top five in his position (they have him down as right-sided midfielder) in every Serie A season so far. He has been the default right-back of his national team for some time, one that is certainly among the ten best in the world. There are podcasts that do rate him. As for the 'leg work' stuff, I don't know about this. Today a list surfaced for euro 2024 where, according to UEFA, Oranje ran the least amount of kilometers of all teams. https://www.tubantia.nl/voetbal/ora...van-de-kilometervreters-hoe-komt-dat~a35cb135 "This week, UEFA published its technical analysis of the European Championship. The European Football Association always does this after a tournament. In the report on game-related trends and developments, one statistic about the Dutch team stood out. Of all 24 countries, the Dutch team ran the least number of meters per match on average. The biggest mileage eaters were Portugal. As a team they grinded away more than 127 kilometers per trip. Bottom team Oranje averaged just over 108. A difference of almost 20 kilometers, considerable in top football." Netherlands and Belgium the two teams at the bottom, Portugal at the top. Hosts Germany the highest of all the big teams (their satellite states as Croatia, Slovakia and Slovenia also high up). Suspicious? Spain was a little behind England but wins it in intensity and sprints. What I see is that slowly the TV figures here decline. The Champions League matches of this week had only 400000 viewers each (for PSV and Feyenoord). Twenty years ago that was steadily 3.5 million (heavily skewed towards the West of the country). An even much bigger drop as with the national team. Serie A football, where Dumfries plays, attracts very few people. So how many people have really a good idea for how good/bad he is, that is an open question, with probably a not too positive answer.