Value Example: Salmon

Salmon

Salmon on a bed of pasta is my favorite meal in the world. Salmon on a bed of rice is for some reason the thing that I eat more frequently.

My standard dinner is salmon with Costco stir-fry vegetables (frozen) sometimes with a cup of rice. (A dietician recently told me this is too much salmon/mercury.)

A Restaurant Incident

Because I eat salmon multiple times a week, I tend to go for other items at restaurants. There are two major exceptions:

The Cheesecake Factory makes an excellent salmon meal (albeit farmed)
Fish restaurants often have special kinds of salmon

In 2021, I went to a fish restaurant in the Chicago suburbs. I had eaten there pre-COVID and was excited for the large portions. Prices had gone up from the tremendous pre-COVID value, but still seemed reasonable.

As of August 2024, the prices are the following. All include a “14-16 oz portion, homemade roasted vegetables, and wild rice”.

Scottish Salmon: $32.99
Wild Alaskan Salmon: $37.99
New Zealand Organic Salmon: $39.99

Considering that these types of salmon would generally cost $15-30/lb in a supermarket, this still seems like a solid deal.

Wild Salmon Interlude via Claude

Species	Quality	Farmed/Wild	Important Characteristics
Chinook (King)	High	Mostly wild	Largest salmon; rich, fatty flesh; high in omega-3s
Coho (Silver)	Good	Mostly wild	Milder flavor; firm texture; popular for grilling
Sockeye (Red)	High	Mostly wild	Deep red color; strong flavor; high in omega-3s
Pink (Humpback)	Lower	Mostly wild	Lightest color and flavor; often canned
Chum (Dog)	Lower	Mostly wild	Pale flesh; milder flavor; often smoked or canned
Atlantic	Good	Mostly farmed	Mild flavor; adaptable to farming; controversial due to environmental concerns
Kokanee	Good	Wild	Landlocked Sockeye; smaller size; popular for fishing

Some additional important points:

Wild salmon generally have better flavor and nutritional profiles compared to farmed salmon, but they’re often more expensive.
Farming practices vary widely, affecting quality and environmental impact. Some farms are working on more sustainable practices.
Salmon quality can vary based on the specific run and location, even within the same species.
Conservation status is a concern for some wild salmon populations, particularly in certain regions.
The taste and texture of salmon can be influenced by their diet and the waters they inhabit.
King salmon has limited farming, mainly in New Zealand and very small operations elsewhere.

While a little odd that a fish restaurant wouldn’t be more specific about the type of its “Wild Alaskan Salmon”, I proceeded to order that dish.

Size Problems

When it arrived, it looked way too small.

Previous portion at same restaurant (sides shown)

By standard restaurant serving sizes, this would be perfectly acceptable, but the menu claimed 14-16 oz. As a frequent salmon consumer, I knew something was wrong.

I mentioned the size issue to the food runner who escalated the matter to the waiter. The waiter told me that this was in fact the correct size. I said no I don’t think so and he said yes and then left without resolving the issue.

Unsatisfied, I again brought it up and he then said that it must have shrunk a bit from the cooking.

Cooked vs. Uncooked Weight Interlude

Apparently the restaurant norm is to advertise the uncooked weight of food, e.g. a quarter pounder hamburger will be a quarter pound (4 oz) frozen and closer to 3 oz cooked.

Size Specifics

In the case of salmon, Claude claims that we should expect a weight loss of “15-25%”. ChatGPT says “10-20%”. We’ll therefore say a 17.5% average loss. Given this, let’s look at some estimates for the size of fish that we could expect.

Largest without shrinkage: A 16 oz piece

Largest with shrinkage: Start with a 16 oz piece, with 10% shrinkage:

\text{Resulting size} = 16*0.9 = 14.4 \text{oz}

Average with shrinkage: Start with a 15 oz piece, with 17.5% shrinkage:

\text{Resulting Size} = 15*0.825 = 12.38 \text{oz}

Smallest with shrinkage: Start with a 14 oz piece, with 25% shrinkage:

\text{Resulting Size} = 14*0.75 = 10.5 \text{oz}

Hmm, so technically even a 10.5 oz piece would have been in the acceptable range. Admittedly, I think I would have (lightly) complained about approximately anything <12 oz, but this size seemed even smaller.

After a brief and polite conversation raising my previous time at this restaurant and my deep general salmon experience, I insisted that we go to the kitchen to solve this the right way: on the scale.

After weighing the plate with the salmon and a separate empty plate, we concluded that the salmon size was about 9 oz!

Recall from above that we have 10.5 oz as the minimum size and 12.4 oz as the average size. And 15 oz would be the average size without any shrinkage. This means this was too small by minimum 1.5 oz and on average over 3 oz and often over 4 oz, a substantial percentage!

Results

They gave me an extra small piece for my troubles. While blatantly too small and annoying that it got that far, at least it wasn’t on a date. That would’ve been a real conundrum.

Salmon Size Interactive

imagePath = FileAttachment("assets/salmon/plate.png").url()

viewof rawWeight = Inputs.range([14, 16], {step: 0.1, label: "Raw Weight (oz)", value: 15})
viewof shrinkagePercent = Inputs.range([10, 25], {step: 0.1, label: "Shrinkage (%)", value: 20})
viewof actualCookedWeight = Inputs.range([9, 16], {step: 0.1, label: "Actual Cooked Weight (oz)", value: 9})
cookedWeight = rawWeight * (1 - shrinkagePercent / 100)

md`The expected cooked weight is approximately ${cookedWeight.toFixed(2)} oz.`

md`The actual cooked weight is ${actualCookedWeight} oz.`

function createChart() {
  const minRawWeight = 9;
  const maxRawWeight = 18; // Increased to accommodate larger actual weights
  const data = [];
  for (let weight = minRawWeight; weight <= maxRawWeight; weight += 0.1) {
    data.push({
      x: weight,
      y: weight * (1 - shrinkagePercent / 100)
    });
  }

  const currentPoint = {
    x: rawWeight,
    y: cookedWeight
  };

  const actualPoint = {
    x: actualCookedWeight / (1 - shrinkagePercent / 100),
    y: actualCookedWeight
  };

  const margin = {top: 20, right: 30, bottom: 30, left: 40};
  const width = 640 - margin.left - margin.right;
  const height = 400 - margin.top - margin.bottom;

  const x = d3.scaleLinear()
    .domain([minRawWeight, Math.max(maxRawWeight, actualPoint.x)])
    .range([0, width]);

  const y = d3.scaleLinear()
    .domain([Math.min(d3.min(data, d => d.y), 9) * 0.9, 
             Math.max(d3.max(data, d => d.y), actualCookedWeight, rawWeight) * 1.1])
    .range([height, 0]);

  const line = d3.line()
    .x(d => x(d.x))
    .y(d => y(d.y));

  const svg = d3.create("svg")
    .attr("viewBox", [0, 0, width + margin.left + margin.right, height + margin.top + margin.bottom])
    .attr("width", width + margin.left + margin.right)
    .attr("height", height + margin.top + margin.bottom);

  const g = svg.append("g")
    .attr("transform", `translate(${margin.left},${margin.top})`);

  // Add the plate images along y = 9
  const imgWidth = 40;
  const imgHeight = 30;
  const numPlates = Math.floor(width / (imgWidth * 1.5));
  for (let i = 0; i < numPlates; i++) {
    g.append("image")
      .attr("xlink:href", imagePath)
      .attr("x", i * imgWidth * 1.5)
      .attr("y", y(9) - imgHeight / 2)
      .attr("width", imgWidth)
      .attr("height", imgHeight);
  }

  // Add a dashed line at y = 9
  g.append("line")
    .attr("x1", 0)
    .attr("y1", y(9))
    .attr("x2", width)
    .attr("y2", y(9))
    .attr("stroke", "red")
    .attr("stroke-dasharray", "5,5");

  g.append("g")
    .attr("transform", `translate(0,${height})`)
    .call(d3.axisBottom(x).ticks(width / 80).tickSizeOuter(0))
    .append("text")
      .attr("x", width)
      .attr("y", -6)
      .attr("fill", "#000")
      .attr("text-anchor", "end")
      .text("Raw Weight (oz)");

  g.append("g")
    .call(d3.axisLeft(y))
    .append("text")
      .attr("transform", "rotate(-90)")
      .attr("y", 6)
      .attr("dy", ".71em")
      .attr("fill", "#000")
      .text("Cooked Weight (oz)");

  g.append("path")
    .datum(data)
    .attr("fill", "none")
    .attr("stroke", "steelblue")
    .attr("stroke-width", 1.5)
    .attr("d", line);

  // Add expected weight point (red)
  g.append("circle")
    .attr("cx", x(currentPoint.x))
    .attr("cy", y(currentPoint.y))
    .attr("r", 4)
    .attr("fill", "red");

  // Add actual weight point (green)
  g.append("circle")
    .attr("cx", x(actualPoint.x))
    .attr("cy", y(actualPoint.y))
    .attr("r", 6)
    .attr("fill", "green");

  // Add legend
  const legend = g.append("g")
    .attr("font-family", "sans-serif")
    .attr("font-size", 10)
    .attr("text-anchor", "end")
    .selectAll("g")
    .data(["Expected Weight", "Actual Weight"])
    .enter().append("g")
    .attr("transform", (d, i) => `translate(0,${i * 20})`);

  legend.append("rect")
    .attr("x", width - 19)
    .attr("width", 19)
    .attr("height", 19)
    .attr("fill", (d, i) => i === 0 ? "red" : "green");

  legend.append("text")
    .attr("x", width - 24)
    .attr("y", 9.5)
    .attr("dy", "0.32em")
    .text(d => d);

  return svg.node();
}

md`### Salmon Weight Comparison`

createChart()

Salmon Photo Gallery

Purchases from the excellent Tanner’s Alaskan Seafood:

Great and rare Whole Foods value on King salmon:

Farmed salmon looks beautiful (avoid!):

Sashimi in the Amsterdam Airport and the rare Whole Foods smoked salmon freeroll: