Does a narrow daily range day on MES tend to be followed by a wider range day

bars_et = to_et(bars)
rth = rth_session(bars_et)
td = trading_date(rth)

daily = rth.groupby(td).agg(high=('high','max'), low=('low','min'))
daily['range'] = daily['high'] - daily['low']
daily = daily.dropna()

median_range = daily['range'].median()
daily['narrow'] = daily['range'] < median_range

# next day range
daily['next_range'] = daily['range'].shift(-1)
daily = daily.dropna(subset=['next_range'])

narrow_days = daily[daily['narrow']]
wide_days = daily[~daily['narrow']]

avg_next_after_narrow = narrow_days['next_range'].mean() if len(narrow_days) > 0 else None
avg_next_after_wide = wide_days['next_range'].mean() if len(wide_days) > 0 else None

# fraction of narrow days followed by a wider day than themselves
if len(narrow_days) > 0:
    followed_wider = (narrow_days['next_range'] > narrow_days['range']).mean()
else:
    followed_wider = None

corr = daily['range'].corr(daily['next_range']) if len(daily) > 1 else None

result = {
    'sample_size': int(len(daily)),
    'n_narrow_days': int(len(narrow_days)),
    'n_wide_days': int(len(wide_days)),
    'median_daily_range': float(median_range) if pd.notna(median_range) else None,
    'avg_next_day_range_after_narrow': float(avg_next_after_narrow) if avg_next_after_narrow is not None else None,
    'avg_next_day_range_after_wide': float(avg_next_after_wide) if avg_next_after_wide is not None else None,
    'frac_narrow_followed_by_wider': float(followed_wider) if followed_wider is not None else None,
    'corr_range_to_next_range': float(corr) if corr is not None and pd.notna(corr) else None,
}