Exactly. And that's the only way you'll win long term. Beating the line isn't even enough, you have to beat it by a big enough margin to include the juice. No other definition is correct and no model can work if this doesn't happen. Sure, you can find value every now and then but the market is very efficient in bigger sports and the closing line will on average be correct if your sample size is big enough.
Those that use a model that finds value in some closing lines (that are able to pick those closing lines that are still "off") are IMHO getting lucky and will not survive if the sample size gets big enough (10k+) when backtested.
Those that use a model that finds value in some closing lines (that are able to pick those closing lines that are still "off") are IMHO getting lucky and will not survive if the sample size gets big enough (10k+) when backtested.