Simulate outcomes of combinations, with probability of rank among other competitors

Hello,
The title may be a little bit confusing so I'll explain.
I'm running a sports prediction competition, for which I use Excel to calculate the scores.
In each match, there are a few outcomes that can happen. When I enter the results, the scores of the participants update automatically.
After that, the participants will be ranked from highest to lowest score totals up to the current round.
Everything up to this point I have already automated in my Excel sheet after I simply enter the outcomes of matches.
However, I thought it would be cool if I could calculate the probabilities of each player ending up at a certain rank based on all the possible combinations of results that can happen.
The number of combinations is quite large, about 18,5 million combinations, which is a multiplication of 7 different matches' possible outcomes.
Assuming each outcome is equally likely to happen, how can I calculate the probabilities of each participant ending up at a certain position? And is this even possible to run with the amount of combinations that can happen?
I'd like the end result to show a percentage likelihood of each participant of the competition to end up at a certain rank.

Fast answers need visual help. Please read the yellow banner at the top of this page on how to attach a file.

Hello JohnTopley,
I don't need a particularly fast answer with this. Receiving an answer is also not necessary for me.
I don't want to share Excel files here so I'll explain it using cells (note that I'm not an expert of sorts)

There are 7 matches for which participants can enter predictions. The possible results are arranged in cells A1:A13, B1:B13, C1:C13, D1:D13, E1:E13, F1:F10 and G1:G5. When a result is correct, I enter a 1. All other cells remain 0.
I have a column called Leaderboard with the names of the participants, and in the cells next to them are the formulas that calculate the scores they receive based on the 1's I entered. So they are in cells I1:I10 (there are 10 participants right now).
Next to this column of cells - J1:J10 - I use the RANK function which denotes the rank each participant has in the competition. When someone has the third highest score, their rank is 3.
This is what I've got so far.
Through the installation of the Solver, I have learnt to use only binary because then, in extra cells, I can add up the total of cells A1:A13, B1:B13 and so on so that they are a specific number. In this case, for all 7 matches, that sum cell would need to be 1, since there is one result for each matchup. I don't know if I can use the Solver widget for this, but I thought I should mention. These sum cells are in A14, B14 up to G14.
13*13*13*13*13*10*5=18564650, this is the number of combinations of results that can happen on this week's matches. I don't know if this is very large or not large at all.
What I'd like to add is a chart that shows the percentage likelihood of each participant ending up at each rank, from 1st to 10th. When they get first in 1000000 of the 18564650 combinations, that percentage would be approx. 5,4% for 1st. To achieve this, I assume I need to know the following:
- How can I run Excel to simulate all these combinations and their outcomes.
- How can I extract from that data, the percentage of times each participant achieves a certain position on the leaderboard.
For this to work I guess I need to assume that every outcome of every match is equally likely to happen so that I only have to worry about the combinations.

Any help is greatly appreciated. I have no idea of the complexity of this question but it's something I'd like to be able to do properly.

I should probably add that I want Excel to run all the possible combinations by changing one of the cells in each group of possible outcomes from 0 to 1. I know this is something that's possible with the Solver by adding sum cells and adding conditions that each of those cells is 1 (where the Solver considers all possibilities by changing the designated cells in binary fashion to determine the preferred result), but the other parts of this problem make it seem like it can't be done within the Solver alone. Also because the final result I'd like to have - the likelihood of the participants ending up at a certain rank in percentages - is not a result you can select in the Solver.

If you cnnot provide a sample file then you are unlikely to get any answer

Receiving an answer is also not necessary for me

Any help is greatly appreciated.

Hello John,

I will add a file now, but it's a simplified version of the spreadsheet I use because that one contains more data. I'll also simplify the problem, since what I proposed earlier seems unachievable.

In the file, I have seven columns of 0's. These represent the possible outcomes of matches 1 through 7, which are represented in columns A through G. The amount of cells in each column varies per match. The result of the match is denoted by a 1, the other cells remain 0.
On the right side I have five players in column I.. These players get points based on the results of the matches as calculated with the 1's that are added. The score is shown in column J. In column K, it shows the rank of each person based on highest to lowest scores.

I will simplify the task to this:
I would like to (not manually) randomly change one cell in each column from 0 to 1. As explained earlier, this automatically changes the score and rank cells in columns I and J respectively.
This should be an automated process.
This should be repeated, say, 10,000 times.
The amount of times each person gets a certain rank in these 10,000 randomly selected combinations need to be returned as a percentage of times out of all combinations generated. Example: if John gets rank 2 3,000 times, he is 2nd place 30% of the time.
I want this percentage to be calculated for each player and for each rank possible.

Is this something you can do in Excel?

P.S. I tried to add an attachment but I don't know if I did it right. If I didn't, I'll be trying it again.
Also, I didn't put in the effort of adding the formulas from the cells in columns I and J that calculate the scores and ranks since that took quite some time and this is not the actual spreadsheet.

Hello MrShorty,

I have heard of the Monte Carlo simulations. I'm not sure how they apply here, though, because the number of combinations exceeds 18 million.
I decided to share the actual file since it seems otherwise I can't get helped out but removed some information. The formulas are the same.

Left of the leaderboard are a few sections. In the top left, there are 10 sportsmen. One of them is the winner, four of them are semi finalists and two get eliminated. When one of these applies to a player, the value changes from 0 to 1 in the columns C2:C11, D2:D11 and E2:E11.
In the bottom left are the matches of the first week. There are 13 possible results for each of the five matches. The result of a match gets signified by a 1, while the rest remains 0. So in each column, one of the cells from C16:C28 - G16:G28 changes to 1.
Using the Solver widget for other projects I did in the past, I learnt to add a cell that sums up these columns of relevant cells, so that I could add a condition that that cell, say, equals 1.
When I enter a 1 in a cell, the scores of the participants of the prediction competition, which are in the top right, get calculated automatically with the formulas in the cells J2:J12 and K2:K12. In the cells L2:L12, the rank of each participant among the pool of players gets shown.

What I'd like to add to that, is a table where each player's probability of achieving a certain rank gets shown. This would be having the names of the players, each position (1st through 11th) and the percentage of times they achieved that rank.
I would like to do this by running about 10,000 simulations, where in each simulation, exactly one cell for each match gets changed from 0 to 1, while the rest remain 0's. Then, I would like it to note the rank each player received in that simulation, and this 10,000 times. I do not need it to show the amount of points each player got.
At the end, I would like for each player to get a percentage of times it got a certain rank. So if Indy got 1st rank 1,000 times out of 10,000 simulations, they'd get first 10% of the time.

I really hope this is enough explanation for you to be able to help me out. Please don't try to sound too mean; I feel offended by my seeming incapabilities to cooperate with people that know better than me.