CRPS and fan chart/simulated futures


Question regarding CRPS:
The CRPS averages the quantile scores over all values of p i.e. the whole the forecast distribution. But exactly what is the whole the forecast distribution? Because if I do an autoplot of a fan chart with level = 100, the fan is all the way from the top to the bottom; does this mean the CRPS is a measure for 100% prediction interval's ? Or is the CRPS a measure of the whole distribution given the parameters of the model i.e. a fan chart as one would plot from 10,000 simulated futures?


# Re-index based on trading days
google_stock <- gafa_stock |>
  filter(Symbol == "GOOG", year(Date) >= 2015) |>
  mutate(day = row_number()) |>
  update_tsibble(index = day, regular = TRUE)

# Filter the year of interest
google_2015 <- google_stock |> filter(year(Date) == 2015)

# forecast OOS
google_2015 |>
  model(NAIVE(Close)) |>
  forecast(h = 10) |>
  autoplot(google_2015, level = c(80, 95, 100)) +
  labs(title="Google daily closing stock price", y="$US" )


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