One of the holes I've started to notice in my game is my inability to play severly enough against overplays (most often invasions). I have an easy enough time identifying the moves but I often am too soft on the reply, and then my position collapses. Besides just playing and reviewing the games, is there anyway way to study being more severe?

Overplays don't always have to be punished severely.

That said, you could always just try being ridiculous severe whenever a move offends you, in casual experimental games.

It's hard to change your style without trying out new things, after all.

tsumego

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If you were unable to play severely against the move you thought was an overplay, how do you know it was an overplay? If there's no way to play severely against it, then I don't think it's an overplay at all. If you try to play severely against it and your position collapses, then it sounds like a very well-timed invasion rather than an overplay-- maybe you could reply by first strengthening your own position rather than trying to kill the stone.

A diagram would help us understand your question better, but generally speaking, if you can tell the difference between the overplay and the normal move, that would be the first step in devising a plan to profit from it.

If your position collapses after you respond to an overplay, chances are your response was too hard rather than too soft (in other words... an overplay).

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So you've got an eye?
That don't impress me much

When you make a given extension, you must have a counter-plan to deal with invasion that you are happy with. Otherwise perhaps it was your extension that was incorrect (insofaras your own reading verifies it). Relatedly, if you have a good counter-plan feel free to ignore the (often rigidly adhered to) wall height vs distance proverb.

- Otake Hideo, that book that Sodes recommends

If you meant corners:

<proverb about corners being complicated>

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Revisiting Go - Study Journal
My Programming Blog - About the evolution of my go bot.

Attack and defense from the elementary go series. Studying tesuji and shape will build up the tactical knowledge you need to know when and how to play severely.

There is a nice discussion in this thread:
viewtopic.php?f=12&t=1578