Mixing
Percentage with negative numbers
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I have several competitors in an economic market, each one with a score of a strength indicator. Scores can vary in [-inf,inf]. For a subset of competitors, I need to calculate their relative importance.
With all positive scores (like in CASE A), I've been calculating relative importance using the following formula (like in percentages):
CASE A
Score 1 = 1 -- > r = 0.1111
Score 2 = 2 --> r = 0.2222
Score 3 = 6 --> r = 0.6667
How can I replicate my intent in CASE B, where I have some negative scores? Here, the above-mentioned formula does not reach my goal anymore.
CASE B
Score 1 = 1 -- > r = ?
Score 2 = 2 --> r = ?
Score 3 = 6 --> r = ?
Score 4 = -100 --> r = ?
percentages ratio
asked 5 hours ago
Forinstance
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I have several competitors in an economic market, each one with a score of a strength indicator. Scores can vary in [-inf,inf]. For a subset of competitors, I need to calculate their relative importance.
With all positive scores (like in CASE A), I've been calculating relative importance using the following formula (like in percentages):
CASE A
Score 1 = 1 -- > r = 0.1111
Score 2 = 2 --> r = 0.2222
Score 3 = 6 --> r = 0.6667
How can I replicate my intent in CASE B, where I have some negative scores? Here, the above-mentioned formula does not reach my goal anymore.
CASE B
Score 1 = 1 -- > r = ?
Score 2 = 2 --> r = ?
Score 3 = 6 --> r = ?
Score 4 = -100 --> r = ?
percentages ratio
asked 5 hours ago
Forinstance
101
New contributor
Forinstance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
You should specify what is the meaning of a negative score. Do you expect that a competitor with negative score has a negative relative importance? It would be helpful if you could provide an example of the situation that you want to model.
– Dmitry
5 hours ago
Thank you Dmitry. Negative numbers come out from the fact that the original scores are standardized with respect to all the market players and not only to the competitors in my subset. Standardization has been achieved subtracting the mean and dividing by the standard deviation. So it means below the average, but not in every case I can access the original average. Not sure if I explained myself clearly.
– Forinstance
5 hours ago
why wouldn't you just shift all the scores by the lowest value? Say, $tilde{r}_i=r_i - min_{j}(r_j)$. For your example this will give: $r_1=101,dots,r_4=0$
– Dmitry
4 hours ago
Because this would give me a problem, I think: I would have 101,102,106 and 0, in case B. Doing the percentage afterwards, I would get: 0.3269, 0.3301, 0.3430 and 0. In orginal scores score 2 was the double of score 1 (2 vs 1), which is however not represeted in these final numbers (0.3269 vs 0.3301). On the other hand, this is represented in case A (0.11 vs 0.22).
– Forinstance
4 hours ago
1
OK, I'll try to come up with some plausible expression later.
– Dmitry
4 hours ago
|
show 1 more comment
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have several competitors in an economic market, each one with a score of a strength indicator. Scores can vary in [-inf,inf]. For a subset of competitors, I need to calculate their relative importance.
With all positive scores (like in CASE A), I've been calculating relative importance using the following formula (like in percentages):
CASE A
Score 1 = 1 -- > r = 0.1111
Score 2 = 2 --> r = 0.2222
Score 3 = 6 --> r = 0.6667
How can I replicate my intent in CASE B, where I have some negative scores? Here, the above-mentioned formula does not reach my goal anymore.
CASE B
Score 1 = 1 -- > r = ?
Score 2 = 2 --> r = ?
Score 3 = 6 --> r = ?
Score 4 = -100 --> r = ?
percentages ratio
asked 5 hours ago
Forinstance
101
New contributor
Forinstance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I have several competitors in an economic market, each one with a score of a strength indicator. Scores can vary in [-inf,inf]. For a subset of competitors, I need to calculate their relative importance.
With all positive scores (like in CASE A), I've been calculating relative importance using the following formula (like in percentages):
CASE A
Score 1 = 1 -- > r = 0.1111
Score 2 = 2 --> r = 0.2222
Score 3 = 6 --> r = 0.6667
How can I replicate my intent in CASE B, where I have some negative scores? Here, the above-mentioned formula does not reach my goal anymore.
CASE B
Score 1 = 1 -- > r = ?
Score 2 = 2 --> r = ?
Score 3 = 6 --> r = ?
Score 4 = -100 --> r = ?
percentages ratio
percentages ratio
asked 5 hours ago
Forinstance
101
New contributor
Forinstance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 hours ago
Forinstance
101
New contributor
Forinstance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 hours ago
Forinstance
101
New contributor
Forinstance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 hours ago
Forinstance
101
asked 5 hours ago
Forinstance
101
101
New contributor
Forinstance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Forinstance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Forinstance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
You should specify what is the meaning of a negative score. Do you expect that a competitor with negative score has a negative relative importance? It would be helpful if you could provide an example of the situation that you want to model.
– Dmitry
5 hours ago
Thank you Dmitry. Negative numbers come out from the fact that the original scores are standardized with respect to all the market players and not only to the competitors in my subset. Standardization has been achieved subtracting the mean and dividing by the standard deviation. So it means below the average, but not in every case I can access the original average. Not sure if I explained myself clearly.
– Forinstance
5 hours ago
why wouldn't you just shift all the scores by the lowest value? Say, $tilde{r}_i=r_i - min_{j}(r_j)$. For your example this will give: $r_1=101,dots,r_4=0$
– Dmitry
4 hours ago
Because this would give me a problem, I think: I would have 101,102,106 and 0, in case B. Doing the percentage afterwards, I would get: 0.3269, 0.3301, 0.3430 and 0. In orginal scores score 2 was the double of score 1 (2 vs 1), which is however not represeted in these final numbers (0.3269 vs 0.3301). On the other hand, this is represented in case A (0.11 vs 0.22).
– Forinstance
4 hours ago
1
OK, I'll try to come up with some plausible expression later.
– Dmitry
4 hours ago
|
show 1 more comment
You should specify what is the meaning of a negative score. Do you expect that a competitor with negative score has a negative relative importance? It would be helpful if you could provide an example of the situation that you want to model.
– Dmitry
5 hours ago
Thank you Dmitry. Negative numbers come out from the fact that the original scores are standardized with respect to all the market players and not only to the competitors in my subset. Standardization has been achieved subtracting the mean and dividing by the standard deviation. So it means below the average, but not in every case I can access the original average. Not sure if I explained myself clearly.
– Forinstance
5 hours ago
why wouldn't you just shift all the scores by the lowest value? Say, $tilde{r}_i=r_i - min_{j}(r_j)$. For your example this will give: $r_1=101,dots,r_4=0$
– Dmitry
4 hours ago
Because this would give me a problem, I think: I would have 101,102,106 and 0, in case B. Doing the percentage afterwards, I would get: 0.3269, 0.3301, 0.3430 and 0. In orginal scores score 2 was the double of score 1 (2 vs 1), which is however not represeted in these final numbers (0.3269 vs 0.3301). On the other hand, this is represented in case A (0.11 vs 0.22).
– Forinstance
4 hours ago
1
OK, I'll try to come up with some plausible expression later.
– Dmitry
4 hours ago
You should specify what is the meaning of a negative score. Do you expect that a competitor with negative score has a negative relative importance? It would be helpful if you could provide an example of the situation that you want to model.
– Dmitry
5 hours ago
You should specify what is the meaning of a negative score. Do you expect that a competitor with negative score has a negative relative importance? It would be helpful if you could provide an example of the situation that you want to model.
– Dmitry
5 hours ago
Thank you Dmitry. Negative numbers come out from the fact that the original scores are standardized with respect to all the market players and not only to the competitors in my subset. Standardization has been achieved subtracting the mean and dividing by the standard deviation. So it means below the average, but not in every case I can access the original average. Not sure if I explained myself clearly.
– Forinstance
5 hours ago
Thank you Dmitry. Negative numbers come out from the fact that the original scores are standardized with respect to all the market players and not only to the competitors in my subset. Standardization has been achieved subtracting the mean and dividing by the standard deviation. So it means below the average, but not in every case I can access the original average. Not sure if I explained myself clearly.
– Forinstance
5 hours ago
why wouldn't you just shift all the scores by the lowest value? Say, $tilde{r}_i=r_i - min_{j}(r_j)$. For your example this will give: $r_1=101,dots,r_4=0$
– Dmitry
4 hours ago
why wouldn't you just shift all the scores by the lowest value? Say, $tilde{r}_i=r_i - min_{j}(r_j)$. For your example this will give: $r_1=101,dots,r_4=0$
– Dmitry
4 hours ago
Because this would give me a problem, I think: I would have 101,102,106 and 0, in case B. Doing the percentage afterwards, I would get: 0.3269, 0.3301, 0.3430 and 0. In orginal scores score 2 was the double of score 1 (2 vs 1), which is however not represeted in these final numbers (0.3269 vs 0.3301). On the other hand, this is represented in case A (0.11 vs 0.22).
– Forinstance
4 hours ago
Because this would give me a problem, I think: I would have 101,102,106 and 0, in case B. Doing the percentage afterwards, I would get: 0.3269, 0.3301, 0.3430 and 0. In orginal scores score 2 was the double of score 1 (2 vs 1), which is however not represeted in these final numbers (0.3269 vs 0.3301). On the other hand, this is represented in case A (0.11 vs 0.22).
– Forinstance
4 hours ago
1
1
OK, I'll try to come up with some plausible expression later.
– Dmitry
4 hours ago
OK, I'll try to come up with some plausible expression later.
– Dmitry
4 hours ago
|
show 1 more comment
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Forinstance is a new contributor. Be nice, and check out our Code of Conduct.
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You should specify what is the meaning of a negative score. Do you expect that a competitor with negative score has a negative relative importance? It would be helpful if you could provide an example of the situation that you want to model.
– Dmitry
5 hours ago
Thank you Dmitry. Negative numbers come out from the fact that the original scores are standardized with respect to all the market players and not only to the competitors in my subset. Standardization has been achieved subtracting the mean and dividing by the standard deviation. So it means below the average, but not in every case I can access the original average. Not sure if I explained myself clearly.
– Forinstance
5 hours ago
why wouldn't you just shift all the scores by the lowest value? Say, $tilde{r}_i=r_i - min_{j}(r_j)$. For your example this will give: $r_1=101,dots,r_4=0$
– Dmitry
4 hours ago
Because this would give me a problem, I think: I would have 101,102,106 and 0, in case B. Doing the percentage afterwards, I would get: 0.3269, 0.3301, 0.3430 and 0. In orginal scores score 2 was the double of score 1 (2 vs 1), which is however not represeted in these final numbers (0.3269 vs 0.3301). On the other hand, this is represented in case A (0.11 vs 0.22).
– Forinstance
4 hours ago
1
OK, I'll try to come up with some plausible expression later.
– Dmitry
4 hours ago