This will be a little bit handwavy, but here goes.

>! x is 49, ie just less than 50% of the games can be nonsensical.

First we must show Halfbrain's first theorem for x + 1.
>! If more than 50% of the games are nonsensical, then we can partition the points table somewhere such that contestants in the top part have a lower average score than contestants in the bottom part, and that's a contradiction. You can't have a consistent points table where higher contestants are statistically likely to lose to lower contestants.

Next we must show Halfbrain's second theorem for x.  
Step 1:
>! Consider a tournament with a very large number of contestants, all evenly matched. Each wins half their games and loses the other half, so all are on the same score. A late entrant turns up and plays every contestant, winning half and losing half. Now those that won that last game have one more win than those that did not; but each "winner" lost half his games played against someone in the "loser" group. Of all the games, one quarter are played between "winners", one quarter are played between "losers", and half are played between "winners" and "losers". Half of that half will be won by the player from the "loser" group, that is, a quarter will be nonsensical games.

Step 2:
>! We can repeat this by adding another two late contestants. The first one gets the same results as the original late contestant; the second splits both the "winner" and "loser" group in half again. Only half the games remain to be affected (one quarter in each group), and we can only turn a quarter of the affected games into nonsensical games; a total of one eighth.

Step n:
>! We will need $2^{n-1}$ late contestants; one will induce new splits in the existing groups, and the rest will maintain the existing splits. We will make a further $\frac{1}{2^{n+1}}$ of the games nonsensical

Desired target:
>! Repeat as often as you can maintain the group as "large", which will not be all that long. The total number of affected games will be 1/4 + 1/8 + 1/16 + .... which has a limit of 50% that you will never be able to reach. But you can exceed 49%, by which time you will have introduced 127 late contestants and you will have 128 groups.  
>! Note that you don't really have to introduce new contestants, but it makes it easier to picture what's going on.