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I have seen people theorize on the best way to use challenges. It seems to come down to:

1. Timing - they should be saved for crucial moments, likely later in the game, or to quell momentum

2. Value - big point swings, such as a three point play that puts a star in foul trouble

3. Certainty - Something very obvious that will certainly get overturned and work to your advantage, even if the advantage is small

Where do you stand?

Value IMO

Value and certainty for me - I think you should use it anytime during the game you have a really good chance of reversing a call. Especially if it's a foul on a key player.
I don't think timing matters that much. No need to save it for the end, officials review calls at the end of games.

Hang on to it at all costs
- Danny Ainge

Value. No question. When it swings points that is the quality. Certainly there is a timing element as well but a 3-4 point swing can be the difference in the game. Vital to use it on points.

Certainty. Most coaches overthink this. You should challenge as soon as you are certain you can win it. NBA offenses regularly score over one point per possession, so even a low value challenge is putting points in the board.

Value

Value and certainty. If there is a solid chance that I may reverse a foul on a three point shot and take away a foul from a player who may get into foul trouble I do that. There was an egregious example of bad use of challenge in Portland’s last game vs Nuggets. 3rd quarter, Nurkic gets a foul on Jokic who was shooting a 3. Nurkic jumps to the side and the only contact was Jokic moved his non-shooting hand into Nurkic’s path after the release, so good chance that is over turned because of the unnatural shooting motion. But Stotts didn’t challenge, so Nurkic struggled with foul trouble and Jokic got 3 free throws. Stotts saved the challenge and used it halfway through the 4th on a simple out of bounds call, which is low value (he also didn’t even win the challenge, but it would have been a poor use even if he did).

If there was no clear reason to use the challenge by late in the game, timing comes into play. Might as well take a chance at one if you have enough timeouts.

I think the whole saving it for the end of the game thing is bad strategy over a larger sample size.
Yes it can look genius the one out of 20+ games where it actually works, but it goes unnoticed all the games where it's wasted because there are no meaningful, close calls at the end of the game.
Also, challenging at the end of the games can cost you a timeout which is very valuable the last two minutes, so there is a proportionate risk increase with the potential reward increase.
So I say some combination of value and certainty.

Certainty would make 1,000x more sense if you got awarded a second challenge if successful. If the refs made a mistake, why hold that against a team?

With the rules as they are, value makes the most sense. In theory, each possession is as valuable as any other possession. But in practice, momentum, emotions, etc. all exist.

Eminem wrote:You only get one shot, do not miss your chance to blow
This opportunity comes once in a lifetime

bad timing always seems to come back and bite coaches in the @$$

Value I guess. I wanted to to with certainty on the premise that a guaranteed call now might negate the value of a less certain call later but it still boils down to value. Little value to a certain call when it won't change the outcome.

Anytime your superstar twirls his finger in little circles and stares at you like "I can take your job with one pout."

Saving it makes little sense as you either don't use it plus they look at everything on replay anyways in the last 2 min

Value for sure. Sometimes I noticed with newer coaches, they will do their challenge as soon as their star player starts complaining and waving his finger for the review. When half of the time, the player is just being emotional and it really was a foul. Like Steve Nash's challenge the other day when Blake clearly fouled, it almost seemed like he did that because Blake was freaking out so much. Idk if that's true, but low value challenges make the coach look sort of incompetent.

I would use them to quell momentum like a timeout plus.

Value is a nice ideal but their may boot be a high value moment in the game and I would try to use them cause you lose them regardless

Certainty isn’t absolute because foul call are an interpretation of an event by a ref. If he was blind the first time he saw it in real time. He might be blind the second time he watches it from a recording too.

Both value and certainty. I'm not challenging a call if I'm not certain I'm winning it. I might turn out to be wrong in terms of the refs seeing it my way, but I'm not challenging if I don't feel certain about the call at the time. Value isn't value if you lose the challenge. On the other hand, if all I'm going to get out if is a jump ball at center court, I'm not challenging regardless of how certain I am (unless there's very little time remaining and probably won't have another opportunity to challenge).

If it's a high value challenge -- it puts points on the board for me or takes points away from the opponent AND it saves a foul on a key player -- I'm happy to use it early. On a recent broadcast, Richard Jefferson made a point that I've always believed implicitly, but never heard expressed explicitly: "Guard your first foul like your sixth." Which is also why I hate to see any significant rotation player give a foul in transition on a play that could potentially be defended.

Certainty. Timeouts are valuable.

Im doing the Thibs thing.

If you are on my squad ur playing about 42 minutes a game regardless of anything. get u a big contract and retire early.