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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.



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.



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。



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※ 作者: love1500274 2023-05-21 21:39:54
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