Recently I had to take my dog in for surgery. Over nearly 20 years of owning multiple dogs, this isn't new. But this is the first time design actually played a helpful role for my pet's post-op care.

At every other veterinary practice I've been to—over a half-dozen, from Manhattan to the rural countryside—they hand you med vials with the dosage instructions printed on them. The font on the labels is tiny (requiring reading glasses, for me) and it's impossible to read a full sentence without rotating the vial.

This time, however, this new vet handed me this simple chart:

I was really impressed by the low-tech efficacy of the design. The days are delineated by tonal differences, and a pink highlighter was used on all but one of the boxes, to remind me that one of the drugs was not to be administered on the morning of 2/7 (due to lingering medication from the surgery, I was verbally told). Two of the drugs are meant to be administered for 7 days in a row, and the third for 14 days in a row; the vet tech was easily able to modify the chart to indicate this.

All of this information is on the three barely-legible labels on the vials. But by consolidating it into one chart, the vet practice made the information much easier to grasp and track.

I do wonder why, having been to so many vets, this is the first time I'd seen such a chart. It should be standard practice.

If you have studied probability, you might be familiar with fractional odds, which represent the ratio of the probability something happens to the probability it doesn’t. For example, if the Seahawks have a 75% chance of winning the Super Bowl, they have a 25% chance of losing, so the ratio is 75 to 25, sometimes written 3:1 and pronounced “three to one”.

But if you search for “the odds that the Seahawks win”, you will probably get moneyline odds, also known as American odds. Right now, the moneyline odds are -240 for the Seahawks and +195 for the Patriots. If you are not familiar with this format, that means:

• If you bet $100 on the Patriots and they win, you gain $195 – otherwise you lose $100.
• If you bet $240 on the Seahawks and they win, you gain $100 – otherwise you lose $240.

If you are used to fractional odds, this format might make your head hurt. So let’s unpack it.

Suppose you think the Patriots have a 25% chance of winning. Under that assumption, we can compute the expected value of the first wager like this:

def expected_value(p, wager, payout):
    return p * payout - (1-p) * wager

expected_value(p=0.25, wager=100, payout=195)

-26.25

If the Patriots actually have a 25% chance of winning, the first wager has negative expected value – so you probably don’t want to make it.

Now let’s compute the expected value of the second wager – assuming the Seahawks have a 75% chance of winning:

expected_value(p=0.75, wager=240, payout=100)

15.0

The expected value of this wager is positive, so you might want to make it – but only if you have good reason to think the Seahawks have a 75% chance of winning.

Implied Probability

More generally, we can compute the expected value of each wager for a range of probabilities from 0 to 1.

ps = np.linspace(0, 1)
ev_patriots = expected_value(ps, 100, 195)

ps = np.linspace(0, 1)
ev_seahawks = expected_value(1-ps, 240, 100)

Here’s what they look like.

plt.plot(ps, ev_patriots, label='Bet on Patriots')
plt.plot(ps, ev_seahawks, label='Bet on Seahawks')
plt.axhline(0, color='gray', alpha=0.4)

decorate(xlabel='Actual probability Patriots win',
        ylabel='Expected value of wager')

To find the crossover point, we can set the expected value to 0 and solve for p. This function computes the result:

def crossover(wager, payout):
    return wager / (wager + payout)

Here’s crossover for a bet on the Patriots at the offered odds.

p1 = crossover(100, 195)
p1

0.3389830508474576

If you think the Patriots have a probability higher than the crossover, the first bet has positive expected value.

And here’s the crossover for a bet on the Seahawks.

p2 = crossover(240, 100)
p2

0.7058823529411765

If you think the Seahawks have a probability higher than this crossover, the second bet has positive expected value.

So the offered odds imply that the consensus view of the betting market is that the Patriots have a 33.9% chance of winning and the Seahawks have a 70.6% chance. But you might notice that the sum of those probabilities exceeds 1.

p1 + p2

1.0448654037886342

What does that mean?

The Take

The sum of the crossover probabilities determines “the take”, which is the share of the betting pool taken by “the house” – that is, the entity that takes the bets.

For example, suppose 1000 people take the first wager and bet $100 each on the Patriots. And 1000 people take the second wager and bet $240 on the Seahawks.

Here’s the total expected value of all of those wagers.

total = expected_value(ps, 100_000, 195_000) + expected_value(1-ps, 240_000, 100_000) 

plt.plot(ps, total, label='Total')
plt.axhline(0, color='gray', alpha=0.4)

decorate(xlabel='Actual probability Patriots win',
        ylabel='Total expected value of all wagers')

The total expected value is negative for all probabilities (or zero if the Patriots have no chance at all) – which means the house wins.

How much the house wins depends on the actual probability. As an example, suppose the actual probability is the midpoint of the probabilities implied by the odds:

p = (p1 + (1-p2)) / 2
p

0.31655034895314055

In that case, here’s the expected take, assuming that the implied probability is correct.

take = -expected_value(p, 100_000, 195_000) - expected_value(1-p, 240_000, 100_000) 
take

14244.765702891316

As a percentage of the total betting pool, it’s a little more than 4%.

take / (100_000 + 240_000)

0.04189636971438623

Which we could have approximated by computing the “overround”, which is the amount that the sum of the implied probabilities exceeds 1.

(p1 + p2) - 1

0.04486540378863424

Don’t Bet

In summary, here are the reasons you should not bet on the Super Bowl:

• If the implied probabilities are right (within a few percent) all wagers have negative expected value.
• If you think the implied probabilities are wrong, you might be able to make a good bet – but only if you are right. The odds represent the aggregated knowledge of everyone who places a bet, which probably includes a lot of people who know more than you.
• If you spend a lot of time and effort, you might find instances where the implied probabilities are wrong, and you might even make money in the long run. But there are better things you could do with your time.

Betting is a zero-sum game if you include the house and a negative-sum game for people who bet. If you make money, someone else loses – there is no net creation of economic value.

So, if you have the skills to beat the odds, find something more productive to do.

The post Don’t Bet on the Super Bowl appeared first on Probably Overthinking It.

In the early 20th century, scientists sought to get to the bottom of a mysterious disease that caused thousands of deaths per year in the United States. By 1912 in South Carolina alone, more than 30,000 cases were reported with a fatality rate of 40 percent.

This ailment is known as pellagra, and it was discovered as early as the 18th century when it inflicted Spanish peasants. At the time, it was commonly confused with leprosy as it can cause skin sores. The condition also triggers symptoms throughout the body including diarrhea, neurological issues like tremors, and even dementia. In 1869, Italian criminologist Cesare Lombroso suggested that pellagra comes from spoiled corn, as it often affects people with corn-heavy diets.

Lombroso’s theory entered the conversation when pellagra became epidemic throughout the Southern U.S. Some eugenicists suggested that it stemmed from racial or hereditary factors. A 1912 investigation of a South Carolina mill village reported that the disease was infectious, a finding that guided doctors for years.

Around this time, Congress asked the Surgeon General to investigate pellagra. He tapped Joseph Goldberger, a medical officer in the U.S. Public Health Service, to take the reins. Goldberger was already recognized for his work on epidemics such as typhus and yellow fever.

Goldberger suspected that the disease was linked to a diet lacking key nutrients, not infection—a possibility also raised by researchers in Europe. In the early 20th century, low-income people in the South mostly ate cornmeal, meat, and molasses. Due to the region’s thriving cotton industry, little land remained to grow vegetables.

It was already known that wealthy people were far less likely to develop pellagra, and Goldberger had observed the condition among patients and residents at the mental hospitals and orphanages he visited, yet not the staff. 

Following his intuition, he carried out an experiment on male inmates at a Mississippi prison that began on this day in 1915. These men received pardons for their participation, an unethical exchange that wouldn’t be approved today. He observed how they fared on their usual diet, which included dairy products and vegetables grown at the farm they worked at, versus a typical Southern diet at the time. Eleven subjects stayed on this diet until late October 1915, six of whom experienced pellagra symptoms. “I have been through a thousand hells,” one participant remarked. All of these individuals eventually recovered.

Read more: “Fruits and Vegetables Are Trying to Kill You”

Goldberger had also studied populations at orphanages and asylums in the South, and came to the conclusion that an unbalanced diet can trigger pellagra. In fact, some asylum patients with dementia saw such drastic improvements on an improved diet that they were discharged.

Still, Goldberger’s advice mostly went unheeded. Southern politicians and doctors tended to reject his theory linking the condition to poverty in their region, insisting pellagra was an infectious disease or that it stemmed from moldy corn. This prompted Goldberger to organize “filth parties,” where people took pills containing skin, urine, and other samples taken from individuals with pellagra, yet attendees didn’t go on to develop the condition. 

Despite Goldberger’s breakthroughs, he couldn’t pinpoint the exact ingredient required to prevent pellagra. In 1927, he found that a daily dose of brewer’s yeast offered an effective treatment, and a year later he asserted that pellagra likely results from a vitamin deficiency. The next year, though, pellagra reached its peak in the South and killed nearly 7,000 people.

Before Goldberger could get to the bottom of it, he died from kidney cancer in 1929. But less than a decade later, scientists landed on that specific vitamin: niacin. Biochemist Conrad Elvehjem arrived at this discovery after administering small amounts of niacin to dogs with the canine equivalent of pellagra, and the treatment ended up working for humans, too. Corn does contain niacin, but in a form that our bodies can’t absorb well—Indigenous people in the Americas have rendered niacin easier to digest for centuries by soaking corn kernels in limewater.

Today, pellagra is rare in many countries thanks to flour fortified with niacin, a practice that ramped up in the U.S. during World War II. It’s considered a massive public health success story, effectively wiping out one of the most devastating nutritional deficiency diseases ever documented in the country.

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Lead image: hartono subagio / Pixabay

Building in consumer hardware as a software engineer

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Bob and I have spent many years as Python devs, and 6 years coaching with Pybites and we can safely say that being a Senior Developer is only about 1/3 Python knowledge.

The other 60% is the ecosystem. It’s the tooling. It’s all of the tech around Python that makes you stand out from the rest.

This is the biggest blind spot keeping developers stuck in Tutorial Hell. You spend hours memorising obscure library features, but you crumble when asked to configure a CI/CD pipeline. (That’s not just made up by the way – many of you in dev roles will have seen this with colleagues at some point or another!)

These are the elements of the Python ecosystem you should absolutely be building experience with if you want to move from being a scripter to an engineer:

• Dependency Management: Stop using pip freeze. Look at uv.
• Git: Not just add/commit. Learn branching strategies and how to fix a merge conflict without panicking.
• Testing: print() is not a test. Learn pytest and how to write good tests.
• Quality Control: Set up Linters (Ruff) so you stop arguing about formatting, and ty for type checking.
• Automation: Learn GitHub Actions (CI/CD). Make the robots run your tests for you.
• Deployment: How does your code get to a server? Learn basic Docker and Cloud.
• The CLI: Stop clicking buttons and get comfortable in the terminal. Learn Makefiles and create a make install or make test command to save your sanity.

It looks like a lot. It is a lot. But this is the difference between a hobbyist and a professional.

Does this make you feel overwhelmed? Or does it give you a roadmap of what to do this year?

I’m curious! Feel free to hit me up in the Community with your thoughts.

And yes, these are all things we coach people on in PDM. Use the link below to have a chat.

Julian

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