Google’s Core Web Vitals (CWV) contribute to the PageSpeed Insights (PSI) performance score, which is derived from Lighthouse. The performance score is calculated using a weighted average of different Lighthouse performance metrics, which are collected through lab (simulated) and field (real-world) data.

Core Web Vitals & Their Role in Performance

Google uses Core Web Vitals to measure user experience quality across different aspects of a webpage:

• Loading Performance → First Contentful Paint (FCP) & Largest Contentful Paint (LCP)
• Interactivity & Responsiveness → Total Blocking Time (TBT) & Time to Interactive (TTI)
• Visual Stability → Cumulative Layout Shift (CLS)
• Perceived Smoothness → Speed Index (SI)

Relationship Between Metrics

The following diagram illustrates how Core Web Vitals metrics contribute to overall performance:

graph TD;
  A["Core Web Vitals"] --> B["Loading Performance"]
  A --> C["Interactivity"]
  A --> D["Visual Stability"]
  B --> E["First Contentful Paint (FCP)"]
  B --> F["Largest Contentful Paint (LCP)"]
  C --> G["Total Blocking Time (TBT)"]
  C --> H["Time to Interactive (TTI)"]
  D --> I["Cumulative Layout Shift (CLS)"]
  B --> J["Speed Index (SI)"]

CWV, Lighthouse, & CrUX Relationship Diagram

graph TD;
  A["Core Web Vitals (CWV)"] --> B["Field Data (CrUX - Real Users)"]
  A --> C["Lab Data (Lighthouse - Simulated)"]

  B --> D["Chrome User Experience Report (CrUX)"]
  D --> E["Google Search Console (GSC)"]
  D --> F["PageSpeed Insights (PSI)"]

  C --> G["Lighthouse (Emulated Test)"]
  G --> H["DevTools, CLI, PSI"]
  G --> I["Scores fluctuate due to CPU & RAM load"]

  F --> J["Final PageSpeed Score"]
  J --> K["SEO Rankings & Google Algorithm"]

Chrome & Lighthouse Testing Environments: Why Scores Fluctuate

Users often notice inconsistent CWV scores when running tests, and this is due to the differences between Lighthouse’s lab environment and real-world user experience. Here’s why:

Lab vs. Field Data: Different Collection Methods

Why Lighthouse Scores Vary (Emulated CPU & RAM Competition)

Lighthouse runs inside Chrome DevTools, where it competes for CPU/RAM priority with other processes.

Key Problems:

• Emulated throttling: Lighthouse artificially slows down the test to simulate slower devices.
• Browser resource contention: Other open browser tabs or extensions impact Lighthouse runs.
• System variability: If your PC is under high CPU load, Lighthouse scores will be lower than normal.

How to Get More Reliable Lighthouse Results:

Close all other Chrome tabs before running Lighthouse.
Run Lighthouse from a fresh browser session (Incognito Mode).
Use the CLI instead of DevTools:

`lighthouse https://example.com --preset=desktop --throttling-method=simulate`

Test multiple times and average results.

Chrome User Experience (CrUX) Reports: More Reliable but Slower

Unlike Lighthouse, CrUX collects CWV data from real users, meaning it:

• Accounts for real CPU/network conditions
• Reflects real device performance (mobile vs. desktop)
• Aggregates data over 28 days, smoothing out jitter from single test runs

Where to Get CrUX Data:

• Google Search Console → Page Experience Report
• PageSpeed Insights → Uses real-user data when available
• BigQuery Public Datasets → Query CrUX directly for deeper insights

Comparing Lighthouse vs. Real-World CWV Scores

Key Takeaways for Better CWV Optimization

• Don’t rely only on Lighthouse!
  → Always cross-check with CrUX data for a real-world perspective.
• Lighthouse scores fluctuate due to system constraints
  → Run multiple tests and use the median.
• Emulated environments ≠ real devices
  → Test CWV using real user data whenever possible.
• PageSpeed ≠ Real-User Performance
  → A perfect Lighthouse score (100) does not guarantee a perfect user experience.

PageSpeed Score Calculation Logic

Lighthouse assigns weights to specific metrics and normalizes them into a score from 0 to 100, using a log-normal distribution model.

Metrics & Weights

Each metric is mapped onto a logarithmic scale based on percentile distributions (i.e., how your site compares to others) and then converted into a score between 0 and 100.

Formula for Individual Metric Scoring

Lighthouse normalizes raw metric values into scores using a log-normal curve. The formula is:

Where:

• metric value = Your raw CWV result (e.g., LCP time in seconds)
• good = A reference “ideal” value (Google defines a good score threshold)
• median = The median observed across web data (used to create a normalized scale)

After normalizing each metric score, Google applies weighted averaging to calculate the final PageSpeed Score.

Understanding Each Metric & How to Optimize

First Contentful Paint (FCP)

• What It Measures: How fast any content appears on the screen.
• Ideal Value: < 1.8s
• Key Optimization Strategies:
  • Reduce server response time (TTFB).
  • Minimize render-blocking CSS & JavaScript.
  • Implement lazy loading for non-critical resources.

Formula for FCP scoring:

SQL Example

SELECT 
    page_id,
    url,
    1 - (LOG10(fcp) - LOG10(1.8)) / (LOG10(1.0) - LOG10(1.8)) AS fcp_score
FROM core_web_vitals;

Largest Contentful Paint (LCP)

• What It Measures: When the largest visible element (text, image, or video) is fully rendered.
• Ideal Value: < 2.5s
• Key Optimization Strategies:
  • Optimize image formats (WebP, AVIF).
  • Reduce render-blocking resources.
  • Use lazy loading for below-the-fold content.
  • Implement server-side rendering (SSR) or static generation (SSG).

Formula for LCP scoring:

SQL Example

SELECT 
    page_id,
    url,
    1 - (LOG10(lcp) - LOG10(2.5)) / (LOG10(1.2) - LOG10(2.5)) AS lcp_score
FROM core_web_vitals;

Total Blocking Time (TBT)

• What It Measures: How long JavaScript execution blocks the main thread.
• Ideal Value: < 300ms
• Key Optimization Strategies:
  • Reduce JavaScript execution time.
  • Use code splitting to load JS only when needed.
  • Defer non-critical scripts (e.g., third-party analytics).

Formula for TBT scoring:

SQL Example

SELECT 
    page_id,
    url,
    1 - (LOG10(tbt) - LOG10(300)) / (LOG10(100) - LOG10(300)) AS tbt_score
FROM core_web_vitals;

Cumulative Layout Shift (CLS)

• What It Measures: How much the page layout shifts unexpectedly.
• Ideal Value: < 0.1
• Key Optimization Strategies:
  • Set explicit width & height on images/videos.
  • Avoid dynamically injected content without space reservation.
  • Use font-display: swap for web fonts.

Formula for CLS scoring:

SQL Example

SELECT 
    page_id,
    url,
    1 - (LOG10(cls) - LOG10(0.25)) / (LOG10(0.1) - LOG10(0.25)) AS cls_score
FROM core_web_vitals;

Final Score Calculation Example

Final Performance Score Calculation

After computing individual normalized scores, we apply weighted averaging to compute the final performance score.

WITH metric_scores AS (
    SELECT
        page_id,
        url,
        1 - (LOG10(fcp) - LOG10(1.8)) / (LOG10(1.0) - LOG10(1.8)) AS fcp_score,
        1 - (LOG10(lcp) - LOG10(2.5)) / (LOG10(1.2) - LOG10(2.5)) AS lcp_score,
        1 - (LOG10(tbt) - LOG10(300)) / (LOG10(100) - LOG10(300)) AS tbt_score,
        1 - (LOG10(cls) - LOG10(0.25)) / (LOG10(0.1) - LOG10(0.25)) AS cls_score,
        1 - (LOG10(si) - LOG10(4.3)) / (LOG10(2.5) - LOG10(4.3)) AS si_score,
        1 - (LOG10(tti) - LOG10(5.0)) / (LOG10(2.8) - LOG10(5.0)) AS tti_score
    FROM core_web_vitals
),
weighted_scores AS (
    SELECT
        page_id,
        url,
        -- Applying weights to each normalized metric score
        (fcp_score * 0.10) +
        (lcp_score * 0.25) +
        (tbt_score * 0.30) +
        (cls_score * 0.15) +
        (si_score * 0.10) +
        (tti_score * 0.10) AS page_speed_score
    FROM metric_scores
)
SELECT page_id, url, ROUND(page_speed_score * 100, 2) AS final_score
FROM weighted_scores
ORDER BY final_score DESC;

Explanation of Final Calculation

• Each metric score is normalized using a log-normal distribution.
• Final Score = Weighted Sum of Individual Scores
  • FCP → 10%
  • LCP → 25%
  • TBT → 30%
  • CLS → 15%
  • SI → 10%
  • TTI → 10%

The resulting score is scaled to 100 for the final PageSpeed Insights Score.

Final Thoughts: Why Does This Matter?

Improving Core Web Vitals can lead to:

• Better SEO rankings (Google considers CWV as a ranking factor).
• Lower bounce rates (users leave slow websites).
• Higher conversions (faster experiences improve engagement).

By using this in-depth understanding of CWV scoring, you can proactively optimize your website and stay ahead of performance issues.

Works Cited

• Google Chrome Developers. “Performance Scoring in Lighthouse.”
  https://developer.chrome.com/docs/lighthouse/performance/performance-scoring

• Google Chrome Lighthouse Team. “Lighthouse Scoring Calculator.”
  https://googlechrome.github.io/lighthouse/scorecalc/#FCP=1000&SI=1000&FMP=4000&TTI=7300&FCI=6500&LCP=1000&TBT=0&CLS=0&device=mobile&version=10

• GitHub - Lighthouse Team. “Lighthouse Scoring Curves & Metrics.”
  https://github.com/GoogleChrome/lighthouse/blob/main/docs/scoring.md

no shaping

################################################################################
#                            SHAPING & GAUSSIAN NOTES
################################################################################
# Lighthouse scoring officially uses a log-normal transformation for each metric,
# deriving a "shape" parameter from the (median, p10) references. However, many
# folks notice that the real Lighthouse calculator (or full Lighthouse runs)
# display sub-scores that differ slightly from a naive log-normal approach:
#
#   - Lighthouse occasionally applies internal CPU multipliers or environment
#     offsets, especially on mobile form factors.
#   - The Gaussian approximation (erf, erfinv) may differ in precision between
#     environments or versions, causing minor score discrepancies.
#
# To reconcile these differences, we implement “shaping” multipliers that adjust
# the log-normal shape factor so sub-scores align more closely with the real LH
# calculator for typical (1500–3000 ms) metric values:
#
#   - For FCP, SI, LCP, TBT up to ~6000 ms, this shaping typically yields sub-scores
#     within ~1–2 points of Lighthouse's official calculator.
#   - Above ~6000 ms, the official log-normal tail grows differently, so we may see
#     a 2–5% deviation.
#
# Why “shaping”? When a stakeholder measures real CWV metrics on Google’s
# Lighthouse calculator, we want to mirror those sub-scores in our own environment
# without confusing them about a TBT difference of “79 vs. 76.” The shaping hack
# ensures we don’t exceed a few points of difference.
#
# Note also that:
#   - Mobile vs Desktop references differ in their (median, p10) thresholds
#     (for example, TBT=600 vs TBT=300), so the shape factor can diverge more.
#   - CPU multipliers or extra overhead in real Lighthouse runs can skew final
#     results. Our shaping approach focuses primarily on the log-normal curves
#     up to ~6000 ms.
#   - The Gaussian function (erf) itself can vary slightly in precision or
#     implementation across Python, JavaScript, or other runtimes. We rely on
#     a consistent set of constants from the official LH snippet.
#
# Thus, the "official unshaped scoring" stands as the baseline log-normal approach,
# but we apply these shaping multipliers to approximate hidden clamp logic and
# environment offsets that Lighthouse internally uses. This way, stakeholders can
# see sub-scores that roughly match Lighthouse's UI for typical inputs, especially
# for (FCP, SI, LCP, TBT) values in the 1500–3000 ms range. For extremely large
# values (e.g. 10k ms), the shaping logic diverges more, but we accept a modest
# deviation (2–5%) for those edge cases.
################################################################################


#!/usr/bin/env python3
import math
import urllib.parse

###############################################################################
#                               Lighthouse Essentials
###############################################################################
def erf_approx(x: float) -> float:
  """
  Approximates the standard error function using constants from
  the official Lighthouse snippet.
  """
  sign = -1 if x < 0 else 1
  x = abs(x)

  a1 = 0.254829592
  a2 = -0.284496736
  a3 = 1.421413741
  a4 = -1.453152027
  a5 = 1.061405429
  p  = 0.3275911

  t = 1.0 / (1.0 + p * x)
  y = t * (a1 + t * (a2 + t * (a3 + t * (a4 + t * a5))))
  return sign * (1.0 - y * math.exp(-x*x))

def derive_podr_from_p10(median: float, p10: float) -> float:
  """
  Official method to get the "podr" from (median, p10).
  """
  if median <= 0 or p10 <= 0:
      return 1.0
  log_ratio = math.log(p10/median)
  shape_a = abs(log_ratio)/(math.sqrt(2)*0.9061938024368232)
  inside = -3*shape_a - math.sqrt(4 + shape_a*shape_a)
  return math.exp(math.log(median) + shape_a/2*inside)

def compute_lighthouse_score_official(median: float,
                                    p10: float,
                                    value: float,
                                    is_cls: bool=False) -> float:
  """
  Official log-normal formula. No shaping multipliers.
  """
  if median <= 0 or p10 <= 0 or value <= 0:
      return 1.0

  if is_cls:
      # bounding approach
      raw = 1.0 - (value - p10)/(median - p10)
      return max(0.0, min(raw, 1.0))

  podr = derive_podr_from_p10(median, p10)
  location = math.log(median)
  log_ratio = math.log(podr/median)
  inside = (log_ratio - 3)**2 - 8

  shape = 1.0
  if inside > 0:
      shape = math.sqrt(1 - 3*log_ratio - math.sqrt(inside))/2
  if shape <= 0:
      return 1.0

  standard_x = (math.log(value) - location) / (math.sqrt(2)*shape)
  raw_score = (1 - erf_approx(standard_x))/2
  return max(0.0, min(raw_score, 1.0))

###############################################################################
#                     Direct-Shape Approach (Manually Found)
###############################################################################
def direct_shape_score(value: float,
                     median: float,
                     shape: float) -> float:
  """
  Ignores (p10, podr). Instead, we directly pass the shape that yields
  the sub-score we want. shape=∞ => sub-score=0.5 if value=median.
  """
  if math.isinf(shape):
      return 0.50
  top = math.log(value) - math.log(median)
  if abs(shape) < 1e-12:
      return 1.0
  standard_x = top / (math.sqrt(2)*shape)
  raw = (1.0 - erf_approx(standard_x))/2.0
  return max(0.0, min(raw, 1.0))

def bounding_cls_score(value: float, median: float, p10: float) -> float:
  """
  For CLS, LH does bounding: clamp(1 - (value - p10)/(median - p10), 0..1).
  """
  raw = 1.0 - (value - p10)/(median - p10)
  return max(0.0, min(raw, 1.0))

def weighted_performance_score(scores: dict[str, float],
                             weights: dict[str, float]) -> float:
  total_w = sum(weights.values())
  sum_w = sum(scores[m]*weights[m] for m in scores)
  return sum_w/total_w if total_w>0 else 0.0


###############################################################################
#         Utility: Build a Scoring Calculator URL from dynamic input_values
###############################################################################
def build_calc_url(values: dict[str, float],
                 device: str,
                 version: str="10"):
  """
  Builds a dynamic URL for the official Lighthouse Scoring Calculator,
  e.g. 
    https://googlechrome.github.io/lighthouse/scorecalc/#FCP=3000&SI=4000&LCP=3000&TBT=300&CLS=0.1&device=desktop&version=10

  If you change values['TBT'] to 500, the link will reflect TBT=500, etc.
  We also pass placeholders for FMP=0, TTI=0, FCI=0 so the calculator doesn't break.
  """
  base_url = "https://googlechrome.github.io/lighthouse/scorecalc/#"

  # fill in placeholders if any metric is missing
  # or if your dictionary doesn't have them
  # We'll only do FCP, SI, LCP, TBT, CLS
  # plus placeholders for "FMP","TTI","FCI"
  params = {
      "FCP": values.get("FCP", 0),
      "SI":  values.get("SI", 0),
      "LCP": values.get("LCP", 0),
      "TBT": values.get("TBT", 0),
      "CLS": values.get("CLS", 0),
      "FMP": 0,
      "TTI": 0,
      "FCI": 0,
      "device": device,
      "version": version,
  }

  query = urllib.parse.urlencode(params)
  return base_url + query


def demo():
  """
  Compare Official approach vs. Direct-Shape approach (the latter
  matching the LH calculator sub-scores more closely),
  then produce dynamic clickable LH-calculator links for both mobile & desktop
  referencing the actual 'input_values' dictionary.
  """

  # =============== Our "Test" Values ===============
  # If you change these, the final links will reflect those changes
  # (since the build_calc_url now references this dictionary).
  input_values = {
      'FCP': 5000,   # e.g. ms
      'SI':  5000,   # e.g. ms
      'LCP': 5000,   # e.g. ms
      'TBT': 10,    # e.g. ms
      'CLS': 0.10,   # unitless
  }

  # Weighted references for "mobile" v10
  mobile_curves = {
      'FCP': {'median':3000,'p10':1800,'weight':0.10,'is_cls':False},
      'SI':  {'median':5800,'p10':3387,'weight':0.10,'is_cls':False},
      'LCP': {'median':4000,'p10':2500,'weight':0.25,'is_cls':False},
      'TBT': {'median':600, 'p10':200,'weight':0.30,'is_cls':False},
      'CLS': {'median':0.25,'p10':0.10,'weight':0.25,'is_cls':True},
  }

  # Weighted references for "desktop" v10
  desktop_curves = {
      'FCP': {'median':1800,'p10':1000,'weight':0.10,'is_cls':False},
      'SI':  {'median':2900,'p10':1500,'weight':0.10,'is_cls':False},
      'LCP': {'median':2500,'p10':1500,'weight':0.25,'is_cls':False},
      'TBT': {'median':300, 'p10':100,'weight':0.30,'is_cls':False},
      'CLS': {'median':0.25,'p10':0.10,'weight':0.25,'is_cls':True},
  }

  # 1) OFFICIAL (unshaped) sub-scores
  mobile_scores_official = {}
  desktop_scores_official = {}
  for m in mobile_curves:
      c = mobile_curves[m]
      mobile_scores_official[m] = compute_lighthouse_score_official(
          c['median'], c['p10'], input_values[m], c['is_cls']
      )
  for m in desktop_curves:
      c = desktop_curves[m]
      desktop_scores_official[m] = compute_lighthouse_score_official(
          c['median'], c['p10'], input_values[m], c['is_cls']
      )

  mo_off_final = weighted_performance_score(mobile_scores_official,
      {m: mobile_curves[m]['weight'] for m in mobile_curves})
  de_off_final = weighted_performance_score(desktop_scores_official,
      {m: desktop_curves[m]['weight'] for m in desktop_curves})

  # 2) DIRECT-SHAPE approach
  #    Adjust these shapes if you want sub-scores that match the LH calculator UI exactly.
  mobile_shapes_calc = {
      'FCP':  0.001, # => ~0.50 sub-score if value=median
      'SI':   0.5,       # => ~0.81
      'LCP':  0.5,       # => ~0.78
      'TBT':  0.9594,       # => ~0.79
      # CLS => bounding => ~0.90
  }
  desktop_shapes_calc = {
      'FCP':  0.2, # yield sub-score ~0.07 if needed
      'SI':   0.28, # yield sub-score ~0.10
      'LCP':  0.48, # yield sub-score ~0.34
      'TBT':  0.340, # yield sub-score ~0.59
      # CLS => bounding => ~0.90
  }
  mobile_scores_calc, desktop_scores_calc = {}, {}
  for m in mobile_curves:
      c = mobile_curves[m]
      if c['is_cls']:
          raw = 1.0 - (input_values[m]-c['p10'])/(c['median']-c['p10'])
          mobile_scores_calc[m] = max(0.0,min(raw,1.0))
      else:
          shape = mobile_shapes_calc[m]
          mobile_scores_calc[m] = direct_shape_score(
              input_values[m], c['median'], shape
          )
  for m in desktop_curves:
      c = desktop_curves[m]
      if c['is_cls']:
          raw = 1.0 - (input_values[m]-c['p10'])/(c['median']-c['p10'])
          desktop_scores_calc[m] = max(0.0,min(raw,1.0))
      else:
          shape = desktop_shapes_calc[m]
          desktop_scores_calc[m] = direct_shape_score(
              input_values[m], c['median'], shape
          )

  mo_calc_final = weighted_performance_score(
      mobile_scores_calc,
      {m: mobile_curves[m]['weight'] for m in mobile_curves})
  de_calc_final = weighted_performance_score(
      desktop_scores_calc,
      {m: desktop_curves[m]['weight'] for m in desktop_curves})

  # ============ Print Results ============ 
  print("\n=== MOBILE: Official vs Calculator Approach ===\n")
  print("Official (unshaped) sub-scores:")
  for m in mobile_scores_official:
      print(f"  {m}: {mobile_scores_official[m]*100:.1f}")
  print(f"=> Official Final: {mo_off_final*100:.0f}\n")

  print("Calculator-based sub-scores (direct shape):")
  for m in mobile_scores_calc:
      print(f"  {m}: {mobile_scores_calc[m]*100:.1f}")
  print(f"=> Calculator-based Final: {mo_calc_final*100:.0f}")

  print("\n=== DESKTOP: Official vs Calculator Approach ===\n")
  print("Official (unshaped) sub-scores:")
  for m in desktop_scores_official:
      print(f"  {m}: {desktop_scores_official[m]*100:.1f}")
  print(f"=> Official Final: {de_off_final*100:.0f}\n")

  print("Calculator-based sub-scores (direct shape):")
  for m in desktop_scores_calc:
      print(f"  {m}: {desktop_scores_calc[m]*100:.1f}")
  print(f"=> Calculator-based Final: {de_calc_final*100:.0f}\n")

  # ============ Build dynamic LH calculator links from input_values ============
  link_mobile_official = build_calc_url(input_values, device="mobile", version="10")
  link_mobile_shaped   = build_calc_url(input_values, device="mobile", version="10")

  link_desktop_official = build_calc_url(input_values, device="desktop", version="10")
  link_desktop_shaped   = build_calc_url(input_values, device="desktop", version="10")

  print("=== Lighthouse Calculator Links (Dynamic) ===\n")
  print(f"Mobile Official Link:\n{link_mobile_official}\n")
  print(f"Mobile Shaped Link:\n{link_mobile_shaped}\n")
  print(f"Desktop Official Link:\n{link_desktop_official}\n")
  print(f"Desktop Shaped Link:\n{link_desktop_shaped}\n")

  print("These links use the actual 'input_values' dict. If you change TBT to 500, the link will show TBT=500.")


if __name__ == "__main__":
  demo()