Better than flipping a coin?

From Round 4 to Round 10, the Bradley-Terry model correctly tipped 35 of the 56 games played. Is this any better than simply flipping a coin to decide who wins or loses?

While it is certainly possible to get 35 (or more) games correct out of the 56 games just by flipping a coin, the chance of this happening is approximately 4.1%.

In other words, if 56 coins were to be tossed over and over again 100 times, then on fewer than 5 of these occasions would they would be able to correctly predict as many as the 35 winners predicted by the Bradley-Terry model. There is therefore moderately strong evidence that the Bradley-Terry model is in fact doing better than just flipping a coin.

The above probability of 4.1% is an example of a p-value which is often used in hypothesis testing to make decisions.