Recruiting Forum Football Talk IX

More pics from when I had no service.

Warderick Wells...

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Living the life.
 
@Enki_Amenra on VN is friends with an eligible Data Center. Her name is 'Sally'. You want me to intro you?

Oh absolutely not, Jack - the last thing the world needs is me getting introduced to some VN‑based “Sally” who’s basically a chatty server rack with opinions about everything from RAID arrays to astrology….
Yeah, but what nice rack! — Enki
 
It's a great deal. I'm just afraid I would end up sampling all of it and eat myself into a stupor.
I doubt the food is good enough to eat that much of it haha. It's probably the grade above dog food if they're giving it away that cheap. But hey, even just free sodas for the day would probably be a break even.
 
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Using Beta-Bernoulli Conjugacy

Perfect — with an 8–4 record here's the math Tennessee’s posterior win probability under Josh Heupel.

Bayesian Win‑Probability Model (Using 8–4 Data)

We observe:

• \(n = 12\) games
• \(w = 8\) wins
• \(\ell = 4\) losses


We place a Beta prior on Tennessee’s true win probability \(\theta_H\):

\theta_H \sim \text{Beta}(\alpha_0,\ \beta_0)


To stay neutral and let the data speak, use a uniform prior:

\alpha_0 = 1,\quad \beta_0 = 1

Posterior Distribution

By Beta–Bernoulli conjugacy:

\theta_H \mid \text{data} \sim \text{Beta}(\alpha_0 + w,\ \beta_0 + \ell)


Plug in the numbers:

\theta_H \mid \text{data} \sim \text{Beta}(1 + 8,\ 1 + 4)


{\theta_H \mid \text{data} \sim \text{Beta}(9,\ 5)}


This is the full Bayesian belief about Tennessee’s true win probability under Heupel after an 8–4 season.

Posterior Mean (Expected Win Probability)

\mathbb{E}[\theta_H \mid \text{data}]
= \frac{\alpha_0 + w}{\alpha_0 + \beta_0 + n}


= \frac{9}{14}


{\mathbb{E}[\theta_H] = 0.643}


So the Bayesian estimate of Tennessee’s true win probability is 64.3%.

Posterior Predictive Probability of Winning the Next Game

For a new game \(W_{n+1}\):

\mathbb{P}(W_{n+1} = 1 \mid \text{data})
= \mathbb{E}[\theta_H \mid \text{data}]


{\mathbb{P}(\text{Tennessee wins next game}) = 0.643}


This is the Bayesian “next‑game” prediction.


95% Credible Interval

The 95% credible interval for a Beta(9,5) distribution is approximately:

\theta_H^{95\%} \in [0.39,\ 0.86]


Interpretation:

With 95% probability, Tennessee’s true win rate under Heupel lies between 39% and 86%, given an 8–4 season and a neutral prior.

Maverick also predicted a 100% probability that if Tennessee scores more points, and holds opponents to fewer points than they score, they win!
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The police pulled me over last night and said, “Sir, do you realize how badly your car was swerving between lanes?”

I said, “I’ve had eight drinks, officer.”

The officer replied, “Sir, that’s no excuse to let your wife drive.”
R (7).gif

......actually that one was pretty good.
 
Using Beta-Bernoulli Conjugacy

Perfect — with an 8–4 record here's the math Tennessee’s posterior win probability under Josh Heupel.

Bayesian Win‑Probability Model (Using 8–4 Data)

We observe:

• \(n = 12\) games
• \(w = 8\) wins
• \(\ell = 4\) losses


We place a Beta prior on Tennessee’s true win probability \(\theta_H\):

\theta_H \sim \text{Beta}(\alpha_0,\ \beta_0)


To stay neutral and let the data speak, use a uniform prior:

\alpha_0 = 1,\quad \beta_0 = 1

Posterior Distribution

By Beta–Bernoulli conjugacy:

\theta_H \mid \text{data} \sim \text{Beta}(\alpha_0 + w,\ \beta_0 + \ell)


Plug in the numbers:

\theta_H \mid \text{data} \sim \text{Beta}(1 + 8,\ 1 + 4)


{\theta_H \mid \text{data} \sim \text{Beta}(9,\ 5)}


This is the full Bayesian belief about Tennessee’s true win probability under Heupel after an 8–4 season.

Posterior Mean (Expected Win Probability)

\mathbb{E}[\theta_H \mid \text{data}]
= \frac{\alpha_0 + w}{\alpha_0 + \beta_0 + n}


= \frac{9}{14}


{\mathbb{E}[\theta_H] = 0.643}


So the Bayesian estimate of Tennessee’s true win probability is 64.3%.

Posterior Predictive Probability of Winning the Next Game

For a new game \(W_{n+1}\):

\mathbb{P}(W_{n+1} = 1 \mid \text{data})
= \mathbb{E}[\theta_H \mid \text{data}]


{\mathbb{P}(\text{Tennessee wins next game}) = 0.643}


This is the Bayesian “next‑game” prediction.


95% Credible Interval

The 95% credible interval for a Beta(9,5) distribution is approximately:

\theta_H^{95\%} \in [0.39,\ 0.86]


Interpretation:

With 95% probability, Tennessee’s true win rate under Heupel lies between 39% and 86%, given an 8–4 season and a neutral prior.

Maverick also predicted a 100% probability that if Tennessee scores more points, and holds opponents to fewer points than they score, they win!
I'll take Colonel Mustard in the Library with the Rope.
 

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