Pranav, you should not expect to see a multiplicative event, due to the fact that team 1 being selected in the top four and team 2 not being selected in the top four is not independent. That’s a key item to note here. For instance knowledge of the 1 seed being in the top four picks changes the probability of the 2 seed being in the top four!

To compute the probability of the 2nd seed with the fifth pick, we first look at every option of Team 2 not being selected first. The crux of the work is being performed in the line secondProbs = [x + y for x,y in zip(secondProbs, ConditionalProbs)]. That’s updating the total probability of being selected second after the first pick is made. That is not creating a new vector each time. It is accumulating probability mass as the probability space is partitioned by Team 1 selected first, Team 2 selected first, Team 3 selected first, etc.

Now, we repeat this process for the first four picks. This will identify a nested loop of i,j,k,l of the first four picks. From there, we use the findFixedTeams probability. For the second team to be picked fifth, you need to walk through each combination to identify all partitions of Team 1 being selected in the Top 4 and Team 2 being selected outside of the Top 4. The code walks through each inner loop of the process.

I don’t supply the code explicitly because an Eastern conference team had an interview question asking to program this problem and asked me to not make this code available. I also don’t maintain a GitHub because of security clearance reasons: having an active GitHub requires continual pre-publication reporting.

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]]>Could you please explain the math behind the 2nd seed having a 27.8% chance of getting the 5th pick? I can’t wrap my head around your code. The way I was thinking about it is the probability that the 2nd seed gets the fifth pick is the probability the first seed gets pick 1,2,3, or 4 AND the 2nd seed doesn’t get pick 1,2,3, or 4. However when I try to multiply those probabilities out, I don’t get 27.8%. Also, is your code available anywhere in github? Thank you so much, please let me know what you think!

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]]>I’ve seen the Phoenix stuff before and I’d be really interested in execution of the promise of millimeter resolution from sensorless collection. It’s never been done before, so my skepticism arises that’s there’s a product that promises it.

I think the integration will be much smoother using the 5G capabilities but if I’m a player being told that a flex of a tendon needs addressing from only four cameras; I may want a second opinion.

Other than that, the sentiment is there: understanding the body mechanics is a must to improve importance beyond the video age. The current systems use RF sensors, which are intrusive to players; to the point where some players fight back using them.

]]>I think the first steps have been taken, from an infrastructure standpoint, to be able to obtain this data. The Phoenix Suns’ new Verizon 5G Performance Center is advertised to have state of the art tracking cameras. This article (https://www.forbes.com/sites/timnewcomb/2020/11/18/phoenix-suns-unveil-nba-first-technologically-advanced-practice-facility-owner-calls-it-special/?sh=a0aeeaf62730) details how the coaching staff could point to an instance of Devin Booker’s right shoulder collapsing as a sign of fatigue, a subtlely that may go unnoticed by Second Spectrum’s arena cameras. I think this technology can be readily applied to my original goal of measuring rhythm to more accurately estimate shot probabilities.

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]]>“Leveraging the 750 number, we find that at league average levels, the actual margin of error associated with 750 attempts (bounded by probability) is really 1.8%.”

Is this line saying that at 750 attempts, 95% of the time the “true” 3P% will lie within +/-1.8% of the reported value? When you say “at league average levels”, do you mean if the reported 3P% is ~35%? How does this change if the shooter is a 40% shooter? And then finally, how did you arrive at the 1.8% number from the 750 number?

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]]>You’re right: It was 3-for-2. The emphasis was that there was three foul shots available. Which looking back, does make it sound like a possibility for three points. Sorry about that, but thanks for making the footnote here in the comments in case other readers see it that way.

The TOV% is indeed pretty good. Teams today range between 11-to-14% so this is indeed on the better end of the spectrum. These two teams were both actually incredibly good at handling the ball. The other Celtics-Lakers games I have from this year (not many to be honest) the rates are effectively the same. One Nationals-Hawks game had a much higher TOV rate, but another Celtics-Royals game is considerably good (~10%).

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