How to create a equally distributed batting order for little league baseball team

I am trying to create a batting order for my little league team. I have 10 players. I am trying to create a batting order for the ten games where everyone will bat from 1 to 10 in the order. I have one solution where I just move everyone down one spot from the order in the first game, but I am trying to find a way to do this where the kids are not always following the same kids. Mixing it up where they are following different people.

Answer 1

[James Tursa]

Start with a simple pattern that works, and then randperm both the rows and columns. E.g.,

B = zeros(10);
for k=1:10 % start with a simple pattern that works
    B(k,:) = mod(k-1:k+8,10) + 1;
end
B = B(randperm(10),randperm(10)); % permute the rows and columns

Sample run:

>> batting_order
>> B
B =
 4     6     2    10     7     3     8     5     9     1
 3     5     1     9     6     2     7     4     8    10
10     2     8     6     3     9     4     1     5     7
 6     8     4     2     9     5    10     7     1     3
 5     7     3     1     8     4     9     6    10     2
 7     9     5     3    10     6     1     8     2     4
 2     4    10     8     5     1     6     3     7     9
 1     3     9     7     4    10     5     2     6     8
 8    10     6     4     1     7     2     9     3     5
 9     1     7     5     2     8     3    10     4     6

Answer 2

[Sulaymon Eshkabilov]

Use randperm() to generate the orders, e.g.:

ORDER = randperm(10,10)

ORDER = 1×10

3 5 2 6 4 1 8 9 10 7

[Jason Burke]

Thanks, but I do not see how I can use randperm 10 times and get a distribution where each number is in spots 1 to 10 only once.

Answer 3

[Sulaymon Eshkabilov]

Here is how it can be generated for 10 times within a loop:

 for ii=1:10 
     A(ii,:) =randperm(10, 10);
 end

[Jason Burke]

I understand how to run the function 10 times, but I am looking to find a way that each number 1 to 10 lands in each order only once.

I am looking to not get something like below

1, 3, 5, 7, 9, 2, 4, 6, 8, 10

2, 1, 5, 3, 6, 7, 4, 10, 9, 8

I am trying to find a way so each number (1 to 10) lands in each spot (first to tenth) only once.