Sports Related Math Question

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AndrewWiggins22

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Hello, i have a Math Question related to sports. If home teams in NBA win 60% of the time and you have a team who has won 60% of their home games playing at home against a team that has won 40% of their road games. What percentage should that home team win at in that situation using those numbers?
 
AndrewWiggins22 said:
Hello, i have a Math Question related to sports. If home teams in NBA win 60% of the time and you have a team who has won 60% of their home games playing at home against a team that has won 40% of their road games. What percentage should that home team win at in that situation using those numbers?
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What are your thoughts?

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These are my thoughts... I think the home team would win at 60%. If on average home teams win 60% of the time then by definition road team lose 60% of the time (or win 40% of the time). In other words, the hypothetical 40% road game team is a perfectly average team playing a perfectly average home team. It should be 60% in my opinion.
 
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I am not good at math so I don't know what equations to use with this question/problem. I just feel that in my mind it is common sense.
 
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My older brother, who is way better at math than me, claims that the home team will in this scenario win more than 60% of the time. His claim is that they will win close to 70%. He has tried explaining it to me but I just don't understand his logic whatsoever.
 
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Actually, you have already answered you own question! The question was "What percentage should that home team win at in that situation using those numbers?" and the answer is "60%".
 
HallsofIvy said:
Actually, you have already answered you own question! The question was "What percentage should that home team win at in that situation using those numbers?" and the answer is "60%".
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Is there a mathematical equation to use to prove that the answer is 60%? My brother swears up and down that the answer isn't 60% so I would like to prove it to him with something other than what I think is just common sense.
 
My brother is now telling me that I asked the question wrong.. He is saying I needed to add at the end " what is the probability given these conditions that the home team will win the game."

I don't think it changes the answer but I don't know.
 
AndrewWiggins22 said:
My brother is now telling me that I asked the question wrong.. He is saying I needed to add at the end " what is the probability given these conditions that the home team will win the game."

I don't think it changes the answer but I don't know.
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You are correct - the answer does not change.

However, may be you should ask your brother to write down his "thought-process" as to why he thinks the answer should be different and post it here for review.
 
AndrewWiggins22 said:
Thanks, just did....
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This is the brother:

first of all - league average is irrelevant information to the question. What you are trying to determine is what is the probability that a team that wins 60% of the time will beat a team that wins 40% of the time.

to determine this, you need to figure out the probability of all theoretical outcomes.

theoritical outcome 1: team 1 (60%) wins and team 2 (40%) loses
.6 * .6 = .36

theoretical outcome 2: team 1 loses and team 2 wins

.4 * .4 = .16

Theoretical outcome 3: team 1 wins and team 2 wins

.6 * .4 = .24

theoretical outcome 4 : team 1 loses and team 2 loses

.4 * .6 = .24

To check your math - sum all the results = .36 + .16 + .24 + .24 = 1.00 ; or 100% of all theoretical outcomes.

however we know 2 of those outcomes (3 and 4) are impossible in the real world - so we are left with .36 and .16 as valid outcomes.

so if the home team will win 36 out of 52 time (36 + 16); that means that the home team has a 69.23% probability of winning that game.

now to help those people who are struggling with the "common sense" portions of this: a team that wins 60% of the time is not going to stay at the league average win rate or even their own average win rate against a team that loses over 50% of the time. The probability is their losses will come against superior competition - i.e. To get to 60% they are beating the teams they are supposed to beat (sub 50%) and losing to the teams they are supposed to lose to (teams above .500). Here is the other thing - ask yourself how you would figure this out for any other win percentages - if your conclusion is that you would use my methodology, then why would you stop using it because two teams happen to be at the league average - trust the math.
 
AndrewWiggins22 said:
This is the brother:

first of all - league average is irrelevant information to the question. What you are trying to determine is what is the probability that a team that wins 60% of the time will beat a team that wins 40% of the time.
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I think this is the real question. Is the league average relevant or irrelevant when trying to figure this out.
 
Is this problem just too hard to solve for everyone? Just want to know if that's the case and I should stop asking for help. My thread has the most views and least replies.
 
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