其實ESPN給的勝率 在REDDIT上面引起討論 於是一名Reddit鄉民--Noirradnod 就對ESPN的建模進行研究 以下翻譯 The mathematical reason why ESPN's playoff model is so bad. https://tinyurl.com/bdzncdxx After seeing u/wormhole222's post highlighting the fact that, despite being currently up 2-0, ESPN only gives the Heat a 35% of winning their series against the Celtics, I decided to do some investigation, and I think I figured out why this model is so risibly fallacious. I believe that, at the start of the playoffs, they created a set of probability values P for each team winning a single game against each other team and from that extrapolate performance for the entire playoffs. My evidence is as follows. 根據u/wormhole222的貼文，指出儘管目前2-0領先，ESPN僅給予熱火隊35%贏得與賽爾提 克隊系列賽的機會，我決定進行一些調查，並找出這個模型為何如此荒謬地錯誤。我相信 ，在季後賽開始時，他們為每支隊伍在對陣其他隊伍時贏得單場比賽的機率創建了一組概 率值P，並從中推斷整個季後賽的表現。我的證據如下。 At 0-0, they gave the Heat a 3.2% chance of winning their series. If they are deriving this value in the way I believe, then it can be found by solving the equation https://imgur.com/DTtEsKS , or as written out, the 7th degree polynomial https://imgur.com/iyfwr5b = 0.032. This has one real solution in the interval [0, 1], 0.197625,so from this we can assume that ESPN's model gives the Heat around a 20% chance of winning any given game against the Celtics. 在0-0的情況下，他們給予熱火隊3.2%的贏得系列賽的機會。如果他們是按照我所認為的 方式推導出這個值，則可以通過解方程 https://imgur.com/DTtEsKS = 0.032 來解它， 或者寫成https://imgur.com/iyfwr5b = 0.032 在區間[0, 1]中，這個方程有一個實數解，為0.197625，因此我們可以推斷 ESPN的模型給予熱火隊大約20%的機會贏得與賽爾提克隊的任何一場比賽。 How can we test this hypothesis to see if it's true? The Heat are now up 2-0 against them, and ESPN now gives them a 35% chance of winning the series. We can calculate the probability of a team winning two games before its opponent wins 4 given a constant probability value for it winning a single game. The formula for this is 1-(3*(1-p)4 (p)+(1-p)4 ), and sure enough when you plug in p=0.2, this expression evaluates to 0.344, a 34.4% chance of winning, very close to ESPN's assigned value and within the margin of error for their reported significant figures. 我們如何測試這個假設是否成立？熱火隊目前以2-0領先，而ESPN現在給予他們35%的贏得 系列賽的機會。我們可以計算在對手贏得4場比賽之前，一支球隊贏得兩場比賽的概率， 假設贏得單場比賽的概率保持不變。這個公式為https://imgur.com/8QeDcCn， 當你將p=0.2代入這個表達式時，得到的值為0.344，即34.4%的機會贏得系列賽，非常接 近ESPN給出的數值，並且在其報告的有效位數範圍內。 In effect, ESPN has taken the laziest approach for statistical modeling and run with it. This approach can work for simplistic systems and would be fine if basketball tournaments were a fixed Markov process, but they are not. They are not updating probabilities for individual g ame victories based on team's recent performances, especially in head-to-head matchups. More complex analysis would also factor in game location, as the NBA has demonstrable home court advantages, and could also draw on historical trends from series results given the current record to try to capture the concept of momentum. 事實上，ESPN採用了最懶惰的統計建模方法並加以運用。這種方法對於簡單的系統可能是 有效的，如果籃球是一個固定的馬可夫過程，那麼這種方法可能是可以接受的。然而，現 實情況並非如此。尤其在籃球比賽中，他們沒有根據球隊最近的表現，來更新單場比賽勝 利的概率。更複雜的分析應該還會考慮到比賽場地，因為NBA有明顯的主場優勢，並且可 以根據目前的戰績，和從系列賽結果的歷史趨勢中獲取資訊，去獲得比賽走向。 As it is, in the same way their reporting, talking heads, and game broadcasts are often subpar, so too is their statistical modeling and it shouldn't be used for any realistic assessment of a team's playoff odds. 和ESPN他們新聞報導、評論以及比賽轉播一樣，他們的統計建模也是如此欠佳，完全 不能用於對球隊季後賽勝率進行任何實際評估。 -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 220.137.177.83 (臺灣) ※ 文章網址: https://webptt.cc/bbs/NBA/M.1684676397.A.176.html ※ 編輯: love1500274 (220.137.177.83 臺灣), 05/21/2023 21:52:34