What share of the full daily range does MES's first 30 minutes typically account for

et = to_et(bars)
rth = rth_session(et)
rth = rth.copy()
rth['trading_date'] = trading_date(rth)

# daily full range
daily = rth.groupby('trading_date').agg(day_high=('high','max'), day_low=('low','min'))
daily['day_range'] = daily['day_high'] - daily['day_low']

# first 30 minutes window
mask30 = within_minutes_of_open(rth, 30)
first30 = rth[mask30]
f30 = first30.groupby('trading_date').agg(f30_high=('high','max'), f30_low=('low','min'))
f30['f30_range'] = f30['f30_high'] - f30['f30_low']

merged = daily.join(f30[['f30_range']], how='inner')
merged = merged[merged['day_range'] > 0]

shares = merged['f30_range'] / merged['day_range']
shares = shares.replace([np.inf, -np.inf], np.nan).dropna()

n = len(shares)
if n > 0:
    result = {
        'sample_size': int(n),
        'mean_share': float(shares.mean()),
        'median_share': float(shares.median()),
        'std_share': float(shares.std()) if n > 1 else 0.0,
        'min_share': float(shares.min()),
        'max_share': float(shares.max()),
    }
else:
    result = {
        'sample_size': 0,
        'mean_share': None,
        'median_share': None,
        'std_share': None,
        'min_share': None,
        'max_share': None,
    }