Percentage from negative target - percentage

Question

I have these set of targets and actuals:
Actual: "-20" / Target: "-10"
Actual" "50" / Target: "-5"
Actual: "-10" / target: "30"
Target values are anticipated values for each of the 3 categories and actual values are year to date actual values.
On the first category; in was anticipated that there would be -10 sales compared to the previous period. It turned out to be -20 at the end of the current period. The answer could be -100% or -200%. None of these percentages make sense since percentage completed shouldn't be a negative amount. Another reason that makes the percentages unreasonable is that I cannot perceive the difference between 100% and -100% in this case.
On the 2nd category, it was anticipated that there would be 5 less sales in the current period but turns out there was actually 50 sales in the current period. The answer should be +1100% if we agree that every amount of 5 is a 100%.
EDIT: Same as above, the answer for the third category should be -133%
I want to see how much of the target is fulfilled. If actual=target then the answer is 100% although this doesn't make sense if both the actual and the target are negative amount.
If I use (actual/target)*100 negative amounts are always wrong. I need a general formula to calculate the correct answer. I don't mind if the formula has many conditional definitions. How can I do this?

Answer 1

When involving negative amount, you should always know what it is that you are looking for.
example 1:
if you use the absolute value, you should agree that target=10 and actual=-5 is and should be 50%. however, the 'pure' mathematical way to look at it is -50%.
A logical explanation for this is that actual=0 is, as logic predicts, 0%, -5 is even worse! since not only no progress was made, but rather a regression occurred, hence -50% is an understandable result.
example 2:
When both are negative then for target=-10 and actual=-20, since anchoring point is 0, the 'pure' mathematical result is 200% - and is correct (depending on your point of view of course) since you wanted a decrease of 10 and got a decrease of 20.
Note:if you want to define your wanted output differently, do so and we will try and come up with a 'custom' percentage calculation method.
Edit:
What you could try in your case (Although I must say I don't agree with this approach):
if target>0 and actual > 0 : (the usual) :
(actual/target)*100
if target < 0 and actual < 0 : (the usual negative) :
if (target>actual) - actual is worse than expected :
-(actual/target)*100
if (target < actual) - actual is better than expected :
(actual/target)*100
if target>0 and actual < 0 :
((actual-target)/target)*100
corresponds with target=50 , actual = -100 -> result = -300%
if target<0 and actual > 0 :
(abs(target)+actual)/abs(target))*100
so that for target = -50 , but actual = 100 -> result = 300%
I believe that covers your options and suits your needs.
Edit:
A good approach to your issue from my point of view is to look at absolute values (rather than differential values):
Lets say your sales in month A is 200, and you want a 10% increase in month A+1 -> set your target at 220 and then compare the actual to it, you can also compare it month's A actual and overall a report would use the absolute values for comparison, those are always positive, and can be understood more clearly.
now this:
target = -10% , actual +5% and base value of last month 100
will simply be this:
target = 90 actual =105 => Overall performance of 105/90 , or (105/90)-1 higher than expected.

Answer 2

If you want to treat Actual “-50” / Target “50” as 100% fulfilled, you should use the absolute value function in your formula.
| ((actual / target) * 100) |
How you use it in your code depends on the language. In JavaScript, your formula would be like this:
Math.abs((actual / target) * 100)
If this is not how you want your scoring to work, please provide an example of what the score should be when the target or actual is negative.

Answer 3

Based on your edit with more details about what you want, here is some JavaScript that implements that formula:
function percent_difference(target, actual) {
if (target === 0 || actual === 0) {
if (actual > target) {
return 100;
} else if (actual < target) {
return -100;
} else {
return 0;
}
}
var relative_to = Math.min(Math.abs(actual), Math.abs(target));
var distance_from_target_to_actual = actual - target;
var fraction_difference = distance_from_target_to_actual / relative_to;
return 100 * fraction_difference;
}
I tried to avoid unnecessary if statements to keep the code simple.
The function passes these tests:
function test_percent_difference() {
console.log("percent_difference(-10, -20)", percent_difference(-10, -20), "should be", -100);
console.log("percent_difference(-5, 50)", percent_difference(-5, 50), "should be", 1100);
console.log("percent_difference(30, -10)", percent_difference(30, -10), "should be", -400);
console.log("percent_difference(15, 0)", percent_difference(15, 0), "should be", 100);
console.log("percent_difference(0, 0)", percent_difference(0, 0), "should be", 0);
}
You can run it for yourself in your browser in this jsFiddle.

Answer 4

Here is the solution with R.
Assume your data is sample with Target and Actual columns:
sample<-structure(list(Actual = c(-20L, 50L, -10L), Target = c(-10L,
-5L, 30L)), .Names = c("Actual", "Target"), row.names = c(NA,
-3L), class = "data.frame")
sample<-
Actual Target
1 -20 -10
2 50 -5
3 -10 30
#first I compute the percentage deviation as ((Actual-Target)/Actual)*100
#then I will use following two conditions:
# if Actual<0 and Target>0 multiply by -1
#if Actual<0 and Target<0 and if absolute(Actual)>absolute(Target) multiply by -1 else leave as original percent
sample$diff<-with(sample,((Actual-Target)/Actual)*100)
> sample
Actual Target diff
1 -20 -10 50
2 50 -5 110
3 -10 30 400
sample$percent<-with(sample,ifelse((Actual<0 & Target>0),diff*(-1),ifelse((Actual<0 & Target<0),ifelse((abs(Actual)>abs(Target)),diff*-1,diff),diff)))
> sample
Actual Target diff percent
1 -20 -10 50 -50
2 50 -5 110 110
3 -10 30 400 -400
#delete diff column
sample$diff<-NULL
#your final output
> sample
Actual Target percent
1 -20 -10 -50
2 50 -5 110
3 -10 30 -400
Updated:
To match your answers:
sample$diff<-with(sample,((Actual-Target)/Target)*100)
sample$percent<-with(sample,ifelse((Actual<0 & Target>0),diff,ifelse((Actual<0 & Target<0),ifelse((abs(Actual)>abs(Target)),diff*(-1),diff),diff*(-1))))
> sample
Actual Target diff percent
1 -20 -10 100.0000 -100.0000
2 50 -5 -1100.0000 1100.0000
3 -10 30 -133.3333 -133.3333