A Basketball Question (2)

Macjack452

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Ok a followup basketball question but unrelated to the original.

Q: If Team A averages 110 points per game on offense and Team B allows 100 points per game on defense in a league where the average points scored is 100, how many points is Team A expected to score vs Team B?

Two models. First is multiplicative linear where Expected points = (Team A * Team B)/league avg = (110*100)/100 = 110

second additive where (Team A - league average) + (Team B - league average) so (110-100) + (100-100) = 110

BUT these assume offense and defense are weighted equally and each control 50% of expected points. What if 66% of the expected points are weighted to be from the offense and defense only controls 33%?

I’m struggling how to use this weight in the equations. I have for example Team A*0.66 * Team B*0.33 / league average in the first equation but get 106.67 which is less than if they had equal weights.

sorry for long post.
 

BigBeachBanana

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Ok a followup basketball question but unrelated to the original.

Q: If Team A averages 110 points per game on offense and Team B allows 100 points per game on defense in a league where the average points scored is 100, how many points is Team A expected to score vs Team B?

Two models. First is multiplicative linear where Expected points = (Team A * Team B)/league avg = (110*100)/100 = 110

second additive where (Team A - league average) + (Team B - league average) so (110-100) + (100-100) = 110

BUT these assume offense and defense are weighted equally and each control 50% of expected points. What if 66% of the expected points are weighted to be from the offense and defense only controls 33%?

I’m struggling how to use this weight in the equations. I have for example Team A*0.66 * Team B*0.33 / league average in the first equation but get 106.67 which is less than if they had equal weights.

sorry for long post.
I suggest you make a new thread before @Subhotosh Khan deletes this post. Forum rule: one thread one question.
 

BigBeachBanana

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Is this a real/practical question or is this a fictitious scenario (e.g a homework question)?
 

Macjack452

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I’m actually trying to develop a basketball scoring model. I have most parameters, just needed help with a couple equations.

I’m in high school but it’s not a “homework” question per se
 

BigBeachBanana

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A couple of questions:
1) Do you have an average for A's defence and B's offence?
2)What's the probability that A/B play defence vs offence? For example, out of 100 games, how many games A plays offence/defence?
how many points is Team A expected to score vs Team B?
3) You're looking for a ratio i.e [imath]\frac{\text{expected A's score}}{\text{expected B's score}}[/imath]
 
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Macjack452

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I should have clarified:

I only want to know what Team As offense would be expected to score vs Team Bs defense if we know what Team A averages on offense, what Team B allows on average on defense, and the league average score.

for example Team A averages 110 points on offense. Team B allows 100 points average on defense. League average points scored is 100.

I know how to calculate it if offense and defense are weighted 1:1 but what is it when what Team A is expected to score is weighted 66% by their offensive average and 33% by Team Bs defensive average?
 

Macjack452

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From the first post, where in this example Team A offense averages 110 points per game, Team B defenses averages 100 allow and league average is 100 per game:

Two models. First is multiplicative linear where Expected points = (Team A * Team B)/league avg = (110*100)/100 = 110

second additive where (Team A - league average) + (Team B - league average) so (110-100) + (100-100) = 110
 

BigBeachBanana

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From the first post, where in this example Team A offense averages 110 points per game, Team B defenses averages 100 allow and league average is 100 per game:

Two models. First is multiplicative linear where Expected points = (Team A * Team B)/league avg = (110*100)/100 = 110

second additive where (Team A - league average) + (Team B - league average) so (110-100) + (100-100) = 110
That's not how you calculate average?
Suppose I were to ask you the average (midpoint) between 110 and 100. What do you do?
Also, how did you get the league average is 100/game in the first place?
 

Macjack452

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The 100 league average is hypothetical.

But if a team averages 110 points on offense against the league and now plays a team that gives up the league average on defense (in this case 100) they should be expected to score 110 points if the offense and defense are weighted equally and the league average is 100.

Playing a defense that is the same as the league average is not going to change a teams points when they average 110 vs the league of offense and defense are weighted equally. The average WOULD be 105 if the league average was not considered.

I just want to know if offense is weighted 66% what would the 110 point team average vs the same defense that allows 100 with a league average of 100.
 

BigBeachBanana

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But if a team averages 110 points on offense against the league and now plays a team that gives up the league average on defense (in this case 100) they should be expected to score 110 points if the offense and defense are weighted equally and the league average is 100.
I think what you meant is: Expected points for A = 110(100%)+100(0%)=110
Ergo, if the weights is 66% then:Expected points for A = 110(66%)+100(100-66)%= 106.67
Notice if they were 1:1 i.e, 50%, then Expected points for A = 110(50%)+100(100-50)%= 105.
 
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Macjack452

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See the first equation here: http://www.rawbw.com/~deano/articles/kalman/methdesc.html

Dean is weighting offense and defense THE SAME. Using my example and his equation you get 110 expected points for the offense. But I want offense to matter twice as much as defense. But 66% to 33% to give a 106.67 average just doesn’t make sense when the equation assumes they are equal and gives 110. It should be HIGHER than 110 with 66% slanted to the offense.

I’m sorry I’m bad explaining what I’m trying to get at. Thank you for your patience.
 

BigBeachBanana

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OK, you're trying to build a predictive statistic model for rating points with a particular method that's very different from ordinary descriptive statistics of the expected score. They're not the same thing. I'm unfamiliar with its use, so I can't offer much more help. However, I assumed you read the paper, but do you understand the underlying assumptions and see whether that applies to your scenario? For example:

"Mathematically, this relationship says that Utah's offensive performance is linearly related to both the average Utah offense and to the opposing defense. "Linearly" means that if the average Jazz offense improves by 10%, then the Jazz offense vs Team B's defense also improves by 10%, not 8% or 50%. I only introduce this because a Kalman Filter is strictly only "optimal" if this relationship is linear."

"Keep in mind that a, b, and c are, or points per 100 possessions. Replacing these with Points Per Game values A, B, and C is not strictly true but is a good approximation. That is what makes equation 2 OK."

However, if I were to guess...if the weights are 66% then: Expected A= 66%(100+110)=140
 
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Macjack452

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Ok. That was helpful. I will read through the paper again and try to grasp better.

I really appreciate your help!
 
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