At 15th level, the Hunter ranger archetype of Ranger can choose the following feature:

Stand Against the Tide. When a hostile creature misses you with a melee attack, you can use your reaction to force that creature to repeat the same attack against another creature (other than itself) of your choice.

Does "repeat the same attack" mean the original attack roll of the "hostile creature" is applied against a new target, or does the hostile creature re-roll the attack?

I'm hoping it just re-applies the same number that was already rolled, because if I'm taking on a throng of orcs, I want to choose carefully when to use this feature. For example, I wouldn't want to use it when the orc's attack roll was a 6, but rather when it was a near miss, like a 16 -- so that it has a better chance of hitting his fellow orc when this feature is applied.

It requires a re-roll

"repeat the same attack" means to use all the same modifiers (i.e. feats like Great Weapon Master) for the attack.

You should want the re-roll. If they have missed you then the roll is likely low. When redirecting the attack to another creature it is fairly likely to also miss them if they have similar AC to you, making this feature not that great. However, if they have to re-roll they have a decent chance of hitting the other creature.

With some math

Say you have an AC of 18 and you are fighting a horde of AC 15 Goblins. Goblins have +4 to hit.

Without reroll

• Goblins rolls >=14 hits you. (35%)


• Goblins rolls <14 misses you. Activate Stand Against the Tide
  
  
  
  
  • Roll >=11 hits other Goblin (15%)
  
  
  • Roll <11 misses entirely (50%)
  
  
  
  

Total chance to hit other goblin = 15%

With reroll

• Goblins rolls >=14 hits you. (35%)


• Goblins rolls <14 misses you. (65%) Activate Stand Against the Tide
  
  
  
  
  • Goblin rerolls
  
  
  • New Roll >=11 hits other Goblin (50%)
  
  
  • Roll <11 misses entirely (50%)
  
  
  
  

Total chance to hit other goblin = 65% * 50% = 32.5%

This makes re-rolling mathematically advantageous. It only gets bigger as the AC of the other creature gets higher. It will never work without a reroll if the creatures AC equals or exceeds your own.

If you know the roll

You will still want the reroll for cases where the other target has an AC close to or exceeding your own. It doesn't significantly change the probabilities though. If you know the roll you can choose to only activate the feature on attacks that it would succeed, but you would need to be attacked at least 3 times a turn for this to have a better chance of hitting than a forced reroll.