Free Word Order Languages: How Much Freedom?

As many pointed out, 'free word order' is a complete misnomer. I don't know of any language where the label would apply without at least some qualification. As TKR mentioned word order is motivated by information structure and pragmatics but also can display certain tendencies of iconicity and be subject to language default. That's why a language like Russian can be called free-word-order but also SVO at the same time.

There is certainly no way to quantify the free-word-orderedness of languages. Ultimately word order can be twisted in any language in almost any way for a good purpose - for instance poetry. Context and other grammatical elements then function as disambiguators.

The standard explanation for the relatively fixed word order in English is that it is used to encode grammatical information. So in John loves Mary vs. Mary loves John the agent and patient are expressed by position in the sentence whereas in a language like Czech, they would be expressed by a case marker. This is certainly correct in the broad strokes. But even in morphologically rich languages there is a huge amount of homonymy (expecially in the plural) so ultimately, it is the context that differentiates between the agent and patient (there's a Czech sentence that has 126 possible parses because of this). Equally, in English there are all sorts of raising phenomena that make the picture more complicated, as well. Even in English context and semantic defaults can override the word order rules. Whereas in John loves Mary, reversing the word order gives a sentence with a different meaning. When you compare John ate an apple and An apple ate John you see that it's more plausible to imagine both sentences with the same meaning but used in different contexts rather than a scenario where John would have been eaten by an apple.

On the other hand, in a context where order order is supposedly completely free such as coordination, iconicity (i.e. word order mimicking real world features such as sequence of events) can remove a lot of your freedom. So, you're more likely to say 'bread and butter' than 'butter and bread' when you say preceded with 'I ate some' whereas the word order is more free when you precede it with 'I bought'. And there's no freedom at all in 'He opened the window and shouted out obscenities.'

Finally, to illustrate how the word order matters in a 'discourse-configurational' language, let me tell you a little joke that appeared shortly after the velvet revolution. It's about two Moravians (who have a healthy disdain for Czechs). One says to the other. I have good news and bad news. Good news is "Češi udělali revoluci" (Czechs started a revolution) bad news is "revoluci udělali češi" (it's the Czechs who started the revolution). So you can see that although the word order appears to be free at the propositional level, it actually encodes completely different communicative meanings.

Now, when you look at this range of phenomena (and there are more), you can see that it would be impossible to quantify. In any language, the situations where you have a completely free choice in how you order the words are very rare and on the other hand, no language completely bars you from twisting the word order for a particular purpose. You could certainly measure the defaults and prevailing orders but that won't show you freedom but rather a distribution of the different configurations each of which have very limited freedom of order.