Z-score pilot's guide

Or: How to mathematically prove that your favorite takeoff is actually worth the drive

What the Hell is a Z-Score Anyway?

You know that friend who always brags about their "epic" sites, but you're pretty sure they're just full of hot air? Z-scores are the mathematical BS detector you've been waiting for.

The Short Version: A z-score tells you how unusual a data point is compared to the rest of your data. It's basically asking: "Is this site actually special, or am I just remembering that one good day?"

The Formula (don't run away):

Z-Score = (Your Value - Average) / Standard Deviation

Translation for Pilots: How many "standard deviations" away from average is this thing?

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Breaking It Down (Because We're Not All Math Nerds)

The Setup

Imagine you've flown from 10 different takeoff sites over the season. You want to know which ones are your actual go-to spots vs. which ones you just happened to visit once on an epic day.

Here's your data (average flight duration from each site):

Average across all sites: 2.77 hours Standard Deviation: 0.91 hours

The Calculation

Let's calculate the z-score for Bassano (because 5.0 hours is suspiciously good):

Z-Score = (5.0 - 2.77) / 0.91
Z-Score = 2.23 / 0.91
Z-Score = 2.45

What does 2.45 mean?

• Bassano's average duration is 2.45 standard deviations above the mean
• In the pilot cockpit, this shows up as your Performance Score
• This is statistically significant (|z| > 2 = outlier territory)
• Translation: Bassano isn't just good, it's legitimately exceptional

Now let's check Pokhara (1.8 hours, feels short):

Z-Score = (1.8 - 2.77) / 0.91
Z-Score = -0.97 / 0.91
Z-Score = -1.07

What does -1.07 mean?

• Pokhara is about 1 standard deviation below average
• Not terrible, but not great either
• Maybe you caught it on bad days, or maybe it's just a sled ride site

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The Z-Score Decoder Ring

Here's how to interpret your z-scores:

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Why Z-Scores Matter (The Pilot's Perspective)

Problem 1: The "Remember That One Time?" Trap

You: "Dude, I LOVE flying from [Random Site]. It's amazing!" Your Brain: Remembering that ONE epic 6-hour XC from 3 years ago while conveniently forgetting the 15 sled rides

Z-Score Solution: If the site's z-score is negative or close to zero, your brain is lying to you. The data doesn't lie - you're mostly bombing out there.

Problem 2: Sample Size Shenanigans

You've flown Bassano once (5 hours, epic), and you've flown your local hill 47 times (average 2.1 hours).

Which is better? Hard to say without context, right?

Z-Score Solution: The z-score accounts for the whole dataset, so you can compare apples to oranges. It asks: "Compared to ALL my sites, how does this one stack up?"

Problem 3: The Validation Station

You want to justify that 4-hour drive to your partner/boss/"I'm working from home today" excuse.

Z-Score Solution: Print out your cockpit stats showing a z-score of +2.8 for that site. "See honey, it's not just fun, it's STATISTICALLY SIGNIFICANT fun. This is science."

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How We Use Z-Scores in We-Fly

In the Cockpit Dashboard

When you look at your By Takeoff stats, you'll see a Performance Score for each site. This is the z-score, and it's calculated from your average flight duration per site (the ratio of total hours to number of flights).

// From src/lib/utils.ts
export function computeZScore(dataSerie: chartData[]) {
  // For each takeoff site
  for (let indexx = 0; indexx < dataSerie.length; indexx++) {
    // Calculate the average ratio (avg hours per flight) across all sites
    let avg_ratio = 0;
    for (let index = 0; index < dataSerie.length; index++) {
      avg_ratio += dataSerie[index].ratio;
    }
    avg_ratio = avg_ratio / dataSerie.length;

    // Calculate the standard deviation
    let sum_deviations = 0;
    for (let index = 0; index < dataSerie.length; index++) {
      sum_deviations += Math.pow(dataSerie[index].ratio - avg_ratio, 2);
    }
    let deviation = Math.sqrt(sum_deviations / dataSerie.length);

    // Calculate z-score: (this site's ratio - average) / std deviation
    dataSerie[indexx].z = deviation === 0
      ? 0
      : (dataSerie[indexx].ratio - avg_ratio) / deviation;
  }
}

What We're Actually Measuring

• Value: Average hours per flight for each takeoff site
• Mean: Your overall average flight duration across all sites
• Standard Deviation: How spread out your flight times are
• Z-Score: How exceptional (or terrible) each site is

Outlier Detection

The code comments say: "Values with |z| > 2 are considered statistical outliers."

This means:

• z > +2: This site is an outlier in a GOOD way (you're staying up way longer than average)
• z < -2: This site is an outlier in a BAD way (you're landing way earlier than average)

Real Example from Your Cockpit

Let's say you check "By Takeoff" and see:

What this tells you:

1. Mont Blanc (z = +2.84): Holy crap, this site is a statistical unicorn. Every time you fly here, you're almost guaranteed a long flight. Book the Airbnb NOW.

2. Local Hill (z = -0.52): Slightly below average, but not terrible. It's convenient, and you're building hours. Keep using it for practice, but don't expect epics.

3. That One Time (z = +0.41): Mildly above average, but you've only flown it once. Could be luck. Need more data before you know if it's actually good.

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The Fine Print (Edge Cases & Gotchas)

When Z-Scores Break Down

1. Small Sample Sizes

• Flew a site once for 6 hours? Z-score might be +3.0, but that's just luck
• Fix: Look at the flight count. If it's low (< 5 flights), take the z-score with a grain of salt

2. All Values Are The Same

• If every site averages exactly 2.5 hours, the standard deviation is zero
• Can't divide by zero, so z-score = 0 for everything
• Fix: The code handles this: deviation === 0 ? 0 : (value - avg) / deviation

3. Seasonal Bias

• You only fly Site A in summer, Site B in winter
• Z-scores might reflect season more than site quality
• Fix: Use filters! Filter by season or date range to compare apples to apples

4. Different Flight Styles

• Site A is great for XC (long flights)
• Site B is perfect for acro (short flights)
• Z-score will favor Site A, but that doesn't make Site B "bad"
• Fix: Filter by flight type if that data is available

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Z-Scores in Other Contexts (Because We're Not Done Yet)

By Glider

Which wing gives you the longest flights?

• Glider A: z = +1.8 → Above average, probably a good XC wing
• Glider B: z = -0.3 → Slightly below average, maybe your old beater wing

By Month

When should you book your vacation?

• July: z = +2.1 → Consistently epic month, book time off
• November: z = -1.5 → Skunky month, stay home and fix your gear

By Country

Which flying destination is worth the plane ticket?

• France: z = +1.2 → Above average flight times
• That Random Island: z = -2.0 → Beautiful, but you're not flying much

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Real-World Decision Making

Scenario 1: The Road Trip Debate

Your buddy wants to drive 5 hours to a new site. You check your cockpit:

• New site: 1 flight, 4.5h avg, z = +1.5 (but only 1 flight!)
• Nearby site: 23 flights, 3.2h avg, z = +1.8

Decision: The nearby site has a higher z-score AND more data. It's the safer bet for a good day. Save the 5-hour drive for when you have more data on the new site.

Scenario 2: Wing Shopping

You're deciding between two wings based on your logged flights:

• Current Wing: 89 flights, 2.1h avg, z = -0.4 (slightly below your average)
• Friend's Wing (borrowed twice): 2 flights, 3.5h avg, z = +1.2

Decision: Don't buy the friend's wing based on 2 flights. The z-score looks good, but sample size is too small. Could be luck, could be the friend is a better pilot than you.

Scenario 3: Proving You're Not Crazy

Your partner: "You drive 2 hours to that site every weekend. Is it even worth it?"

You: "Check this out. Z-score of +2.3. I average 4.2 hours there vs. 2.1 hours at the local hill. That's statistically significant. I'm flying TWICE as long for a 2-hour drive. The math checks out."

Result: Your partner still thinks you're crazy, but at least now you have DATA.

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The Bottom Line (TL;DR for Impatient Pilots)

What is a z-score? A measure of how unusual a value is compared to your average. It's normalized by standard deviation so you can compare different things.

Why do we use it? To identify which takeoff sites (or gliders, or months, or countries) are actually exceptional vs. just lucky one-offs.

How do I read it?

• Positive z-score: Above average (good!)
• Negative z-score: Below average (meh)
• |z| > 2: Statistical outlier (extreme!)
• |z| < 1: Pretty normal (average)

Where do I see it? In your Cockpit Dashboard, under "Performance Score" for takeoffs, gliders, months, etc.

What should I do with it? Use it to make smarter decisions about where to fly, what gear to use, and when to plan trips. The z-score is your data-driven wingman.

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Appendix: The Math (For the Nerds in the Back)

Full Worked Example

Dataset: Average flight hours per site

Sites: [2.5, 3.8, 2.2, 5.0, 2.4, 2.6, 1.8, 2.7, 2.3, 2.4]

Step 1: Calculate Mean

Mean = (2.5 + 3.8 + 2.2 + 5.0 + 2.4 + 2.6 + 1.8 + 2.7 + 2.3 + 2.4) / 10
Mean = 27.7 / 10 = 2.77 hours

Step 2: Calculate Variance

Variance = Σ(x - mean)² / N

For each value:
(2.5 - 2.77)² = 0.073
(3.8 - 2.77)² = 1.061
(2.2 - 2.77)² = 0.325
(5.0 - 2.77)² = 4.973  ← Bassano
(2.4 - 2.77)² = 0.137
(2.6 - 2.77)² = 0.029
(1.8 - 2.77)² = 0.941
(2.7 - 2.77)² = 0.005
(2.3 - 2.77)² = 0.221
(2.4 - 2.77)² = 0.137

Sum = 7.902
Variance = 7.902 / 10 = 0.790

Step 3: Calculate Standard Deviation

Std Dev = √Variance = √0.790 = 0.889 hours

Step 4: Calculate Z-Scores

Z(Bassano) = (5.0 - 2.77) / 0.889 = +2.51 🌟
Z(Pokhara) = (1.8 - 2.77) / 0.889 = -1.09 👎
Z(Annecy) = (2.5 - 2.77) / 0.889 = -0.30 🤷

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One Last Thing: Z-Scores Don't Lie, But Context Matters

A z-score tells you what is unusual, not why it's unusual.

• High z-score site? Could be great conditions, or you only fly it on perfect days
• Low z-score month? Could be bad weather, or you were injured that month
• High z-score glider? Could be a better wing, or you're more confident on it

Always look at:

1. Sample size (more flights = more reliable z-score)
2. Context (filters, date ranges, flight types)
3. Your own memory (does this FEEL right?)

Z-scores are a tool, not the truth. But they're a damn good tool for cutting through the BS and finding the signal in the noise.

Now get out there and fly! And when your friends ask why you're driving 3 hours to that one site, you can confidently say: "Because the z-score is +2.6, bro. SCIENCE."

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"In statistics we trust, but in thermals we must." - Every data nerd pilot