I will try my best keep every question/answer as short as possible using links to posts with the complete questions, discussions, and answers.
Q: Is a ref justified by the rulebook to ask the player to tuck their undershirts into their pants or to pull up their undershirts?
A: Yes. Long undershirts give players a bouncy layer and hide hits beneath them. How clothes "fit well" is left to the ref's discretion. If a ref determines that the clothes does not fit well, He may ask the player to correct it.
Rule Citation: 5.06, 22.03 (2)
Q: After being hit in an obvious place, do you have to fire a shot in order to get a penalty?
A: No. Playing on is not limited to the firing of a shot. Remaining in the game with an obvious hit is explicitly stated in the rule book as a type of playing on.
Rule Citation: 19.02, 21.07, 22.03
Q: Can you receive a penalty for asking for a paintcheck on yourself?
A: Yes. Asking for a paintcheck after being hit in an obvious, easily verifiable area (lens, fingers, etc.) is an automatic 1-4-1.
Rule Citation: 21.01(3), 21.01(7), 21.06(3), 22.03 (1), 22.03 (8)
Q: Is an unnoticed hit on the front of a hopper an obvious hit?
A: Yes. Hits that are unobvious are specifically limited to a player's harness and tubes located on player's back. An obvious hit is specifically stated to be a hit that impacts and breaks on observable places on the body or equipment. A hopper, including the very front, is an observable place. The player's knowledge of the hit is not stated in the rule book and is therefore not party to determining the assessment of a penalty. In the event that the player plays on, the penalty is a 1-4-1 to balance the unfair advantage.
Rule Citation: 19.02, 19.03, 19.04, 21.01, 22.03 (1)
Q: While your team is running back the flag, if you pick up your pods and one has a hit on it, are you out?
A: Yes. Although your team may have almost won the game, you are a live player up until you have checked in and the ref removes your armband. If you pick up a hit item, you are now carrying that item. If you are carrying an item with a hit on it, you are now marked with paint and considered eliminated. Since it is not on your back, the hit pod is also an obvious hit. If you drop the item and the ref believes that you are attempting to avoid being called out, that is a deliberate removal of an obvious hit which results in a 3-4-1. This is also true if you are reloading with your gun up and the pod is shot.
Rule Citation: 15.02, 19.02, 19.03, 21.03, 21.03, 22.05 (2)
Q: If one ref performs a paintcheck on a player and misses the hit and calls the player clean but another ref further down the field finds it is that player out?
A: Yes. Out calls superceed clean calls. Therefore if one ref calls a player clean and another ref simultaneously calls him out, that player is eliminated. Further if the hit is in an obvious easily verifiable area, and the player has played on; a 1-4-1 or 2-4-1 penalty is assessed. Also, every ref paintcheck is independent of whatever paintchecks have happened to the player before that. For this reason, if a player feels something and a ref comes to check, that player should direct the ref's attention to the location of the bounce or hit, whatever it may be, to prevent a possible future penalty. Likewise if an exchange happens and a ref calls a player clean, it is the player's responsibility to assist and/or make sure the ref cleans off any invalid hits. Running away from the ref risks possible elimination or penalty from another ref.
Rule Citation: 11.06(3), 19.01(1), 19.01(4), 21.01, 19.02, 19.03, 22.02, 22.03
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