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The monster manual (p. 309) says

Shapechanger. The yuan-ti can use its action to polymorph into a Medium snake, or back into its true form. Its statistics are the same in each form. Any equipment it is wearing or carrying isn't transformed. It doesn't change form if it dies.

What exactly is the word "statistics" referring to? Does it just mean ability scores? Or does it include stuff like max hit points, speed and armor class? In what way (apart from narrative) do the two forms differ, because if it retains all its statistics then mechanically there's no difference, right? Or am I missing something?

Also, I'm assuming "medium snake" refers to the "giant poisonous snake" Stats in the monster manual because it's a medium beast, right? If so, what stats does the Yuan-ti Malison get from the giant poisonous snake if it retains all of its original stats?

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It means "don't use a different stat block".

"Statistics" is a game term defined in MM p 6-11:

A monster’s statistics, sometimes referred to as its stat block, provide the essential information that you need to run the monster.

So in fact the sentence you've highlighted is telling you not to use the stats of another monster like the Giant Poisonous Snake.

The mechanical difference between the forms is already embedded in the Malison stat block

The Malison specifies in its stat block which attacks and abilities are exclusive to its Yuan-ti and Snake forms. e.g. for a type 3 Malison:

Bite (Snake Form Only). Melee Weapon Attack: +5 to hit, reach 5 ft., one creature. Hit: 5 (1d4 + 3) piercing damage plus 7 (2d6) poison damage.

So the "mechanical difference" you're looking for between the two forms is the abilities in the stat block that are exclusive to the Yuan-ti or Snake forms.

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Yuan-Ti Malison keeps his statistics

Shapechange description says:

Your game Statistics are replaced by the Statistics of the chosen creature.

specify in the description of the monster that he has the same stats in every form, serves to indicate that he maintains his original stats.

A monster’s statistics, sometimes referred to as its stat block, provide the essential information that you need to run the monster. (MM, p. 6-11)

The only "Medium Snake" in the manual is the Giant Poisonous Snake, so yes, this is the reference. The Yuan-Ti Malison doesn't get any ability of the Giant Poisonous Snake, in the description he as his own "Bite (Snake Form Only)".

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    \$\begingroup\$ The Malison transforms into a Medium snake and specifies what statistics it has. It's not referring to the Giant Poisonous Snake stat block. \$\endgroup\$ – Vigil May 30 '18 at 10:31

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