I'll assume you have the Chase Sapphire Reserve and get 1.5 cents per Ultimate Reward point.

The following would be my decision process:

• Take the cash price of the ticket you want (as listed in the Chase portal) and divide by the number of United miles required to purchase that ticket.
• If the result is more than 1.5 cents per mile, then use United miles to purchase it, because it costs less UR points to book in that manner. Otherwise, book using the Chase portal.

The above has you use as few UR points as possible. However, you could amend the 1.5 cents per mile figure upward or downward depending on your view of other considerations. For example:

• If you think there is a decent chance of needing to cancel/change the reservation, award tickets offer (relatively) low change fees. Thus, you might purchase an award ticket if the cash price is more than 1.4 cents per mile.
• If you account for award miles earned by booking (an essentially "cash" ticket) through the Chase portal, then maybe the threshold is 1.6 cents per mile.
• If you care about earning elite status, the threshold might be 1.8 cents per mile.

United economy saver is 45,000 United miles round trip; economy standard award is 90,000 miles round trip. (Those may change with dynamic award pricing, which is rolling out.) Finding round trip flights priced at 45,000 United miles that align well with your schedule would require some luck, and you should view 45,000 United miles as the best case scenario.

45,000 UR points equates to $675 of spend on the Chase portal; 90,000 UR points equates to $1350 on the Chase portal.

Based on your user name, I'll assume you are flying out of Denver. Practically speaking, I think you're likely to get a better deal by booking using UR points in the Chase portal. Non-stops from Denver priced at $650-$700 are frequently available, which would require approximately 45,000 UR points. Even if you can find saver economy award tickets (which also would cost at least 45,000 UR points) for that time period, there might not be non-stops available, and you will not earn award miles or credit towards elite status.