._.

User.php

    public function getUsernameAvailableAt() : Carbon
    {
        $playCount = array_reduce(array_keys(Beatmap::MODES), function ($result, $mode) {
            return $result + $this->statistics($mode, true)->value('playcount');
        }, 0);

        if ($this->group_id !== 2) {
            //reserved usernames
            return Carbon::now()->addYears(10);  //This will always be in the future, which is wanted
        }

        if ($this->user_type === 1) {
            // restricted user
            return $this->user_lastvisit
            // This is a exponential decay function with the identity 1-e^{-$playCount}. 
            // The constant multiplier of 1580 causes the formula to flatten out at around 1580 days (~4.3 years). 
            // $playCount is then divided by the constant value 5900 causing it to flatten out at about 40,000 plays. 
            // Furthermore the formula has a 0.35 multiplier on $playCount, causing it to flatten out more slowly (closer to 80,000 plays).
            // A linear bonus of 6x/5900 is added to reward long-term play.
            ->addDays(intval(1580 * (1 - pow(M_E, -0.35 * $playCount / 5900)) + (3 * 8 * $playCount / (4 * 5900))));
        }

        return $this->user_lastvisit
            ->addDays(static::INACTIVE_DAYS) // base inactivity period for all accounts
            // Same formula as above, but with the 0.35 multiplier removed and a linear bonus of 8x/5900 instead.
            ->addDays(intval(1580 * (1 - pow(M_E, -$playCount / 5900)) + (8 * $playCount / 5900)));
    }