Recruiting Forum Football Talk IX

#141,813
#141,813
Glitch said:
My wife and middle daughter on in Japan right now for a graduation gift for our daughter. They say how absolutely incredible it is there. They are having a great time.
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My daughter and SIL are flying back now after first anniversary trip. They loved it and felt very safe.
 
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#141,818
#141,818
Jackcrevol said:
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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So we could be anywhere from 4-8 to 10-2.Thats some fine projecting there.

Also if that’s the floor and the bar, 🤮
 
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