Sunday, January 13, 2013

Using High School Algebra to Figure Out the Best Starwood Redemption Option

Starwood is my primary hotel program, and mid-level properties are where I often find the best redemption values, as I laid out a few months ago. Stays of exactly 5 nights are also a great option, as the 5th award night is always free.


For award stays at category 3 and 4 properties of exactly 5 nights, Starwood's Nights & Flights is also an attractive option, offering 50,000 airline miles in addition to your room redemption. Unfortunately, United is not an option - but you can get AA, BA, Delta, USAir, and many other airlines. See here for full details.

The question then, is which option is best for stays of exactly 5 nights at category 3 and Category 4 properties? The answer depends on how you value your Starwood points and airline miles. Let's do some math:

First, our options for 5 night stays:
  • A 5th Night Free Award ("5N") at a category 4 hotel is 40,000 points (category 3 is 28,000)
  • Cash and Points ("CP") at a category 4 for 5 nights is 20,000 points + $300 (category 3 is 14,000 and $225)
  • Nights and Flights ("NF") at a category 4 for 5 nights is 70,000 points - and you get 50,000 airline miles in addition to your 5 nights (category 3 is 60,000 and again, you get 50,000 airline miles)

What we're trying to figure out is which option costs the least - where the cost is some combination of points and dollars (and in the case of Nights and Flight is offset somewhat by the airline miles you get). Let's see what the break evens are for category 4 awards:
  • 5N = CP where 40,000 Starpoints = 20,000 Starpoints + $300
    • i.e. where 20,000 Starpoints = $300
    • i.e. where 1 Starpoint = $300 / 20,000 = $.015
    • So if you value 1 Starpoint at $0.015, these options are equally "costly". If you value them higher than that, then Cash and Points is a better deal; if you value them lower, regular awards are a better deal
  • 5N = NF where 40,000 Starpoints = 70,000 Starpoints - 50,000 airline miles (which you essentially "get back")
    • i.e. where 30,000 Starpoints - 50,000 airline miles = 0
    • i.e. where 30,000 Starpoints = 50,000 airline miles
    • i.e. where 1 Starpoint = 5/3 = 1.67 airline miles
    • So if you value 1 Starpoint at 1.67 airline miles, these options are equally "costly". If you value them higher than that, then regular awards are a better deal; if you value them lower, Nights and Flights is a better deal
  • CP = NF where 20,000 Starpoints + $300 = 70,000 Starpoints - 50,000 airline miles
    • i.e. where 50,000 Starpoints - 50,000 airline miles = $300
    • i.e. where 1 Starpoint - 1 airline miles = $300 / 50,000 = $0.006
    • So if you value Starpoints to be worth exactly $0.006 more than airline miles, these options are equally "costly". If you value them higher than that, then Cash and Points is a better deal; if you value them lower, Nights and Flights is a better deal


Add those all together and we get something that looks like this:

"Cheapest" redemption options as a function of Starpoint and airline mile valuations

Which you can simplify as follows:

"Cheapest" redemption options as a function of Starpoint and airline mile valuations

Translation: 5th Night Free (aka the standard award) is only the best option if you have a very low valuation of both Starpoints and airline miles. For most people, it's really about the difference between what you consider a single Starpoint to be worth and what you consider a single airline mile to be worth. If a Starpoint is worth more than $0.006 more to you than an airline mile, then Cash and Points is your best bet, otherwise it's Nights and Flights. Interestingly enough, if you happen to value Starpoints at exactly $0.015 and airline miles at exactly $0.009, then the three options are exactly the same.

The calculations are the same for category 3 hotels, and while the line move slightly, the overall outcome is very similar.

Me personally? I value Starpoints at about $0.025 and most airline miles at about $0.015, so I will always grab Cash and Points when it happens to be available.

Where do your valuations fall on the plot?


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