Calculating gain or loss in a partition SQL - sql-server

Question

With SQL partitions min and max values are easy to find, but how is Gain or Loss determined over a partition?
This brings in the time element to compare min and max. If max occurs later in time than min, that would be a "Gain". If min occurs later, that would be a "Loss".
How might the GainorLoss column be calculated?
CREATE TABLE Weights (id int, date date, person varchar(40), Weight int);
INSERT INTO Weights VALUES (1, '2022-09-01', 'Alice', 100);
INSERT INTO Weights VALUES (2, '2022-10-01', 'Alice', 105);
INSERT INTO Weights VALUES (3, '2022-11-01', 'Alice', 110);
INSERT INTO Weights VALUES (4, '2022-12-01', 'Alice', 115);
INSERT INTO Weights VALUES (5, '2022-09-01', 'Peter', 150);
INSERT INTO Weights VALUES (6, '2022-10-01', 'Peter', 145);
INSERT INTO Weights VALUES (7, '2022-11-01', 'Peter', 140);
INSERT INTO Weights VALUES (8, '2022-12-01', 'Peter', 135);
select
person
, date
, weight
, min(Weight) OVER (PARTITION BY person) as minWeight
, max(Weight) OVER (PARTITION BY person) as maxWeight
--if max weight occurs after min weight, then "Gain" ELSE "Loss" AS GainorLoss
from weights
Desired output:
person
date
weight
minWeight
maxWeight
GainorLoss
Alice
2022-09-01
100
100
120
Gain
Alice
2022-10-01
105
100
120
Gain
Alice
2022-11-01
110
100
120
Gain
Alice
2022-12-01
120
100
120
Gain
Peter
2022-09-01
150
135
150
Loss
Peter
2022-10-01
145
135
150
Loss
Peter
2022-11-01
140
135
150
Loss
Peter
2022-12-01
135
135
150
Loss

Answer 1

You can use FIRST_VALUE to get the first or the last value based on an order.
The example below calculates 2 GainOrLess results.
The 2nd is what you described. The 1st is what I think you want.
But with the current sample data they give same result.
select *
, CASE
WHEN LastWeight > FirstWeight THEN 'Gain'
WHEN LastWeight < FirstWeight THEN 'Loss'
ELSE 'Same'
END AS [GainOrLoss1]
, CASE
WHEN MaxWeightDate > MinWeightDate THEN 'Gain'
WHEN MaxWeightDate < MinWeightDate THEN 'Loss'
ELSE 'Same'
END AS [GainOrLoss2]
from
(
select
person
, [date]
, weight
, FIRST_VALUE(Weight) OVER (PARTITION BY person ORDER BY [date], id) as FirstWeight
, FIRST_VALUE(Weight) OVER (PARTITION BY person ORDER BY [date] DESC, id DESC) as LastWeight
, FIRST_VALUE([date]) OVER (PARTITION BY person ORDER BY Weight, id) as MinWeightDate
, FIRST_VALUE([date]) OVER (PARTITION BY person ORDER BY Weight DESC, id DESC) as MaxWeightDate
from weights
) q
ORDER BY person, [date]
person | date | weight | FirstWeight | LastWeight | MinWeightDate | MaxWeightDate | GainOrLoss1 | GainOrLoss2
:----- | :--------- | -----: | ----------: | ---------: | :------------ | :------------ | :---------- | :----------
Alice | 2022-09-01 | 100 | 100 | 115 | 2022-09-01 | 2022-12-01 | Gain | Gain
Alice | 2022-10-01 | 105 | 100 | 115 | 2022-09-01 | 2022-12-01 | Gain | Gain
Alice | 2022-11-01 | 110 | 100 | 115 | 2022-09-01 | 2022-12-01 | Gain | Gain
Alice | 2022-12-01 | 115 | 100 | 115 | 2022-09-01 | 2022-12-01 | Gain | Gain
Peter | 2022-09-01 | 150 | 150 | 135 | 2022-12-01 | 2022-09-01 | Loss | Loss
Peter | 2022-10-01 | 145 | 150 | 135 | 2022-12-01 | 2022-09-01 | Loss | Loss
Peter | 2022-11-01 | 140 | 150 | 135 | 2022-12-01 | 2022-09-01 | Loss | Loss
Peter | 2022-12-01 | 135 | 150 | 135 | 2022-12-01 | 2022-09-01 | Loss | Loss
db<>fiddle here

Answer 2

I think the result would be more accurate if you measure the original weight with the current weight.
Or you can measure the status from the prior weight and the current weight.
It's up to you to choose, or you could just use both methods, they can be combined off course.
And I also added a resulttype for when the weight did not changed, when there is no gain and no loss
This method uses the original weight and the current weight to determine the gain-or-loss status
declare #Weights TABLE (id int, [date] date, person varchar(40), Weight int)
INSERT INTO #Weights values
(1, '2022-09-01', 'Alice', 100), (2, '2022-10-01', 'Alice', 105),
(3, '2022-11-01', 'Alice', 110), (4, '2022-12-01', 'Alice', 115),
(5, '2022-09-01', 'Peter', 150), (6, '2022-10-01', 'Peter', 145),
(7, '2022-11-01', 'Peter', 140), (8, '2022-12-01', 'Peter', 135)
select t.person,
t.[date],
t.weight,
t.minWeight,
t.maxWeight,
t.Original,
case when t.Original > t.weight then 'Loss'
when t.Original < t.weight then 'Gain'
else 'Unchanged'
end as GainOrLoss
from ( select w.person,
w.[date],
w.weight,
min(w.Weight) OVER (PARTITION BY w.person) as minWeight,
max(w.Weight) OVER (PARTITION BY w.person) as maxWeight,
FIRST_VALUE(w.Weight) OVER (PARTITION BY person ORDER BY [date], id) as Original
from #weights w
) t
with this result
-------|----------|--------|-----------|-----------|--------|---------
person |date |weight |minWeight |maxWeight |Original GainOrLoss
-------|----------|--------|-----------|-----------|--------|---------
Alice |2022-09-01| 100 |100 |115 |100 |Unchanged
Alice |2022-10-01| 105 |100 |115 |100 |Gain
Alice |2022-11-01| 110 |100 |115 |100 |Gain
Alice |2022-12-01| 115 |100 |115 |100 |Gain
Peter |2022-09-01| 150 |135 |150 |150 |Unchanged
Peter |2022-10-01| 145 |135 |150 |150 |Loss
Peter |2022-11-01| 140 |135 |150 |150 |Loss
Peter |2022-12-01| 135 |135 |150 |150 |Loss
You can test and change is in this DBFiddle
EDIT
If you want to see the weight changes with regards to the prior weight, you can use the LAG funtion.
In my option this would be the best method to follow up someone's weight change.
This method uses the prior weight and the current weight to determine the gain-or-loss status
select t.person,
t.[date],
t.priorWeight,
t.weight,
case when t.priorWeight > t.weight then 'Loss'
when t.priorWeight < t.weight then 'Gain'
else 'nochange'
end as GainOrLoss,
t.minWeight,
t.maxWeight
from ( select w.person,
w.[date],
w.weight,
min(w.Weight) OVER (PARTITION BY w.person) as minWeight,
max(w.Weight) OVER (PARTITION BY w.person) as maxWeight,
lag(w.Weight) over (partition by person order by [date]) as priorWeight
from #weights w
) t
-------|----------|------------|-------|----------|---------|---------
person |date |priorWeight |weight |GainOrLoss|minWeight|maxWeight
-------|----------|------------|-------|----------|---------|---------
Alice |2022-09-01| |100 |nochange |100 |115
Alice |2022-10-01|100 |105 |Gain |100 |115
Alice |2022-11-01|105 |110 |Gain |100 |115
Alice |2022-12-01|110 |115 |Gain |100 |115
Peter |2022-09-01| |150 |nochange |135 |150
Peter |2022-10-01|150 |145 |Loss |135 |150
Peter |2022-11-01|145 |140 |Loss |135 |150
Peter |2022-12-01|140 |135 |Loss |135 |150
And again a DBFiddle you can use to play with this query
You can combine the 2 methods offcourse