Iguana's case was meant more as a qualitative and pseudo-quantitative example I think to show his point. Let's use some easy examples with actual costs.
1. Let's take the example where I'm 10 miles away from a kid (HV = $302, CV = $801) and I'm battling vs. a team just over 200 miles away and into the next cost structure (HV = $415, CV = $1,025).
Let's say he has $10,250 to spend and chooses all CVs. That's 10 CVs.
Now, for the same $10,250, I can do all HVs (33.9 HVs) or all CVs (12.8 CVs).
If I go with all CVs, then I have 28% more effort into the kid.
If I go with all HVs, then we have to convert that into CVs to be able to get an apples/apples comparison. But what ratio do we use? If we use the 2.65x ratio of HV to CV, then my 33.9 HVs = 12.8 CVs, which is the same as if I had gone with all CVs. If we use 2.00x as the ratio, then I have 16.95 CVs, which is clearly better than if I had gone with all CVs. But, you see, it's ratio dependent.
2. Another example, let's say I'm at 190 miles (HV = $338, CV = 823) and the other guy is just over 200 miles (same as above). Same $10,250 to spend. He gets 10 CVs. I can get 30.3 HVs or 12.5 CVs. Converting my 30.3 HVs at 2.65 = 11.4 CVs, which is a bit less than the 12.5 CVs I would have if I had spent it all on CVs. Using a 2.00x ratio makes my 30.3 HVs = 15.2 CVs, so clearly this would be more advantageous if I think the ratio is 2.00 and not 2.67.
3. Another example, let's say I'm just over 200 miles (HV = 415, CV = $1,025), he's just over 360 miles and into the next cost level (HV = $748, CV = $1,264). To keep the numbers simple, let's say we have $12,640 each to spend. He gets 10 CVs. I can either get 30.5 HVs or 12.3 CVs. Converting my HVs at 2.67x, they turn into 11.4 CVs, which is less than the 12.3 CVs I could've had if I bought them directly. Using 2.00x, my 30.5 HVs = 15.3 CVs, in which case I come out ahead by buying all HVs.
4. Another example. let's say I'm at 10 miles (HV = 302, CV = 801) and he's just over 360 miles and into the next cost level (HV = 748, CV = 1264). For $12,640, he gets 10 CVs. I can get 41.9HVs or 15.8 CVs. The 41.9 HVs can be converted into 15.7 CVs at a 2.65x ratio or into 21 CVs at a 2.00 ratio. At a 2.65 ratio, it's a wash. At a 2.00 ratio, again going with strictly HVs would make more sense.
5. I'm at 190 miles, or just before the next cost level (HV = 338, CV = 823) and he's just over 360 miles and into the next cost level (HV = 748, CV = 1264). For, $12,640 he gets 10 CVs. I can get 37.4 HVs or 15.4 CVs. My HVs translate into 14.1 CVs at 2.65x ratio or 18.7 CVs at 2.00x ratio. At 2.65x ratio, CVs win, at 2.00 ratio, HVs win.
So, how confident are each of us in what we think the golden ratio is? I always use 2.65, which would dictate that I should go with CVs in nearly every case (though I readily admit to sometimes going all HVs at times, despite what the numbers say). Worst case I break even it seems. If you use something closer to 2.00x as the ratio, then you should always go with HVs. If it's something in between, then work out the numbers for yourself and see which is best.
7/12/2011 11:23 PM (edited)