Well, as long as you understand it!
If the order is important, it'd be interesting to have two identical cars, power mileage, service history etc., and to do the oil and engine restorations in opposite orders and see what falls out (I'd predict that doing the oil first gives a 5% higher power in the "in-between" stage than doing the engine restore first).
To me, though, a
5% (
5/100) maximum loss of overall engine power due to oil deterioration implies multiplying the "base" horsepower (including any engine deterioration, or high mileage deterioration -
5% is a relative measure) by
0.95, i.e.
1 - 0.05 or
(100 - 5) / 100.
Note that the inverse process, dividing
1401 by
0.95, yields
1475 also.
1401 is not the base power, it is the oil-deteriorated power. Now:
1401 * 1.05 is only
1471 ish - that is not the correct inverse function in this case, and gives an error of over
5% in the increase i.e.
4/74, as stated.
The same applies to the engine deterioration:
1549 / 0.95 = 1630 (ignoring rounding issues and going by the numbers the game gave you).
It just makes more sense to me that the engine power modifications would be applied multiplicatively, and compoundly, e.g. as in the following potential candidate for the "governing equation":
C
urrentHp = stockBrandNewHp * oilFactor * engineFactor * mileageFactor
oilFactor exists in the range
0.95 to
1.05.
engineFactor in the range
0.95 to
1.00.
mileageFactor in the range
1.00 or lower (to some unknown limit, if present).
So in the case of oil, engine and ignoring the mileage deterioration, we have:
1401 = stockBrandNewHp * 0.95 * 0.95 * mileageFactor
Where
stockBrandNewHp and
mileageFactor are constants for our purposes here, and their product can be represented as
P.
i.e.:
1401 = 0.95 * 0.95 * P
After the oil change:
1549 = 1.05 * 0.95 * P
After the engine restore:
1630 = 1.05 * 1.00 * P
We can verify this representation accordingly by doing the calculations:
1.05 * 1401 / 0.95 = 1549
1.00 * 1549 / 0.95 = 1630
Or by noting that
P should be constant in each line:
P = 1401 / (0.95 * 0.95) = 1401 / 0.9025 = 1552
P = 1549 / (1.05 * 0.95) = 1549 / 0.9975 = 1552
P = 1630 / (1.05 * 1.00) = 1630 / 1.0500 = 1552
The stock un-boosted power was
1556 hp, so the mileage factor would appear to be about
0.9975 at this point. That's about
2.6% per
100 000 km, which is close to the value you suggest:
(19 568.3 - 10 000) / 100 000 * 2.6% = 0.25% decrease, or
99.75% of the initial. Using more precision in the calculation, i.e. 0.997429..., yields
2.7%. The more miles someone puts on a car, the more accurate we can be (and I appreciate the great effort in that regard.)
The hp rounding issue is massive here: if the power were actually
1551, that would be
3.4% per
100 000 km;
1553 and it's only
2.0% per
100 000 km.
Somewhere between two and four percent seems certain - that could be narrowed further by looking at other points in your data.
Edit: actually, it's between about
2.35 and
3%, because "
1552" is at minimum
1551.5 and at most
1552.49... But looking at more numbers will still help.
What's interesting is that it doesn't appear that you're wrong overall (I used your first post to define the "equation" I just tested), just that you might be attributing actual hp value changes in the wrong proportion to each effect, or that you're just summing things differently from the way I see it. It's clear that we need to be working in relative differences rather than absolute horsepower differences.
But I appreciate I could still just be being thick!
