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There's a couple of stores around here that do single day tournaments on a monthly basis. Because theres only 3 games, we cant just score on W/L (because there is likely to be multiple 3-0s out of 20-26 people). We also have some very competitive players, and it seems like every tournament gets decided by who gets more of the First Blood/StW/Linebreaker points (we do BAO style missions). I'd love for there to be a better tiebreaker that was more closely tied to win/loss instead of driving to table your opponent every game, or someone missing First Blood on game one ending up 2nd because of that. The tiebreakers DCI uses were brought up, but rejected due to the number of games required for it to work well.

What does everyone else do for tournaments like that?

At our store we do battle to the death with katanas
but nah, But we do painting scores here, it encourages people to paint their armies.

It's not a good idea to do it based on how dominant you are in your games, because two players could easily finish 3-0 but one player gets paired up with someone easy in the first round and the other player may have been paired up with someone of close-to-equal skill.

Having said that, it's really the best way in such a format. Having it be based off of painting, composition, or sportsmanship would only be more of a headache.

But, you could always do a coin toss. Every once in a while I hear in the news that a coin toss decides a mayor, so clearly it would be legitimate for toy soldiers.

Add more granularity and emphasis to your soft scores. If two people go 3-0, and the tie breaker is number of objectives achieved, they will naturally do their best to table every opponent and get all the objectives they can. If the tie breaker is appearance, sports, or overall points then they'll be forced to round themselves out and focus on other aspects of the hobby.

For our one-day events, we tend to either use BP for Generalship, or more simply and arguably much more fairly - award equivalent prize support to any / all undefeated who do not also win Best Overall, and base Best Overall on 50% competitive score (basically, record), and 50% appearance score.

Then people who had tougher or easier games aren't judged better or worse by as irrelevant a metric as margin-of-victory (how tough was their opponent, did they face the right or wrong person on the right or wrong round, etc. etc. etc.), and the person who wins the top prize is always going to be someone who is very well painted ... which encourages better hobbying.