I am relatively new with mysql and php. I have developed a hockey stat db. Until now, I have been doing pretty basic queries and reporting of the stats. I want to do a little more advanced query now.
I have a table that records which players were on the ice (shows as a "fk_pp1_id" - "fk_pp5_id") when a goal is scored. here is the table:

pt_id  | fk_gf_id  | fk_pp1_id  | fk_pp2_id  | fk_pp3_id  | fk_pp4_id  |  fk_pp5_id
1      |     1     |     19     |     20     |     68     |     90     |     97
2      |     2     |     1      |     19     |     20     |     56     |     91
3      |     3     |     1      |     56     |     88     |     91     |     93
4      |     4     |     1      |     19     |     64     |     88     |     NULL
5      |     5     |     19     |     62     |     68     |     88     |     97
6      |     6     |     55     |     19     |     20     |     45     |     62
7      |     7     |     1      |     19     |     20     |     56     |     61
8      |     8     |     65     |     68     |     90     |     93     |     97
9      |     9     |     19     |     20     |     45     |     55     |     62
10     |     10    |     1      |     19     |     20     |     56     |     61
11     |     11    |     1      |     19     |     20     |     56     |     61
12     |     12    |     19     |     20     |     68     |     90     |     97
13     |     13    |     19     |     20     |     68     |     90     |     97
14     |     14    |     19     |     20     |     55     |     62     |     91
15     |     15    |     1      |     56     |     61     |     64     |     88
16     |     16    |     1      |     56     |     61     |     64     |     88
17     |     17    |     1      |     19     |     20     |     56     |     61
18     |     18    |     1      |     19     |     20     |     56     |     61
19     |     19    |     1      |     65     |     68     |     93     |     97

I want to do several queries:

1. Show which of the five players were together on the ice most often when a goal was scored.
2. Select say 2 players and show which other players were on the ice most often with them when a goal was scored.

I was able to write a query which partially accomplishes query #1 above.

SELECT 
fk_pp1_id,
fk_pp2_id,
fk_pp3_id,
fk_pp4_id,
fk_pp5_id,
count(*)
FROM TABLE1
group by 
fk_pp1_id,
fk_pp2_id,
fk_pp3_id,
fk_pp4_id,
fk_pp5_id

Here are the results:

fk_pp1_id    fk_pp2_id     fk_pp3_id       fk_pp4_id       fk_pp5_id       count(*)
1               19            20              56              61              4
1               19            20              56              91              1
1               19            64              88            (null)            1
1               56            61              64              88              2
1               56            88              91              93              1
1               65            68              93              97              1
19               1            20              56              61              1
19              20            45              55              62              1
19              20            55              62              91              1
19              20            68              90              97              3
19              62            68              88              97              1
55              19            20              45              62              1
65              68            90              93              97              1             4

See this sqlfiddle:
http://sqlfiddle.com/#!9/e3f5f/1

This seems to work at first, but I realized this query, as written, is sensitive to the order in which the players are listed. That is to say a row with: 1, 19, 20, 68, 90 will not match 19, 1, 20, 68, 90

So to fix this problem, I feel like I have a couple options:

1. Ensure the data is input into the table in numerical order

2. Re-write the query so the order of the data in the table doesn't matter

3. Make the resulting query a sub-query to another query that first orders the column (left to right) in numerical order.

4. Change the schema to record/store the data in a better way

1, I can do, but would prefer to have the query be fool-proof.
2 or 3 I prefer, but don't know how to do either.
4, I don't know how to do and is least desirable as I already have some complex queries against this table that would need to be totally re-written.

Am i going about this in the wrong way or is there a solution??
Thanks for your help

UPDATE - OK I (hopefully) better normalized the data in the table. Thanks @strawberry. Now my table has a column for the goal_id (foreign key) and a column for the player_id (another foreign key) that was on the ice at the time the goal was scored.

Here is the new fiddle: http://sqlfiddle.com/#!9/39e5a

I can easily get the one player who was on the ice most when goals are scored, but I can't get my mind around how to find the occurrences of a group of players who were on the ice together. For example, how many times were a group of 5 players on the ice together. Then from there, how often a group of 2 players were on the ice together with the 3 other players.

Any other clues???