Reconstructing a tournament

In a round-robin every player meets every other once. With $n$ players there are $\binom{n}{2}$ games, and if a win scores $1$, a draw $\tfrac{1}{2}$ each, and a loss $0$, the total points handed out equals the number of games. That fixed total is a powerful check: the standings must sum to $\binom{n}{2}$.

Reconstructing results from partial data is logical table reasoning: fill a grid of who beat whom, use each player's score as a row and column sum, and use the fixed total to force the missing entries. Sometimes the data pins down a unique table, sometimes several fit.