Oops. 
I fear I didn't make myself clear enough, which is a mistake of mine because I generally tend to focus on the Greek theater in my interests. I kind of left out which faction I was speaking about, which is why I had mentioned 'I don't know about other theaters', but failed to specify my exacting context.
Well of course, straps were used! Anyone who has seen Iberian greaves [ https://upload.wikimedia.org/wikipedia/commons/0/09/Iberian_greaves_%28MARQ%29.JPG ] [ Celtiberian depiction - https://media.moddb.com/cache/images/groups/1/4/3656/thumb_620x2000/EB-art-celtiberian-heavy-inf.jpg ] , Roman greaves [ https://cyclingarchaeologist.files.wordpress.com/2016/07/image208.jpeg ] , and Gladiator greaves [ https://78.media.tumblr.com/ac2a8350129b7a213d6031dd9f429e6d/tumblr_nw9px72SQ81tgrkdyo1_1280.jpg ] would know as much! (though I think some earlier Roman greaves were done in the Greek way too).
We should acknowledge the fact that (Most, if not all?) greaves in the Greek theater at least, were held on solely by the springy tension of the metal itself. This might have been the case with particular sets elsewhere. In fact, @matmohair, your first picture seems to demonstrate this point. The greave there is not applied and yet is tight enough that it is closed shut without anything tied onto it yet. While the presence of loops in an archaeological find like that indicate additional strapping of 'some' sort were used, well-made greaves that fit the leg snugly generally don't require such. This was the style in the Greek world, while elsewhere sometimes straps of different sorts were used. If it's a rather open greave that of course doesn't really 'wrap around' the shin area, certainly it would require some kind of strap system. Unless you glue it to your shin.
I don't blame most folk for not knowing this, as generally speaking Rome and Romans are far more popular. The mod itself is Rome At War, after all. But, as a matter of fact, Greek greaves from the late Archaic going forward as far as I know, were made to be held on by the spring tension of the bronze, and fit very snugly on the user. This fact is pretty well-established within the community already, to the extent that a Greek impression with the use of buckles on said greaves within the qualifying periods is generally frowned upon as a poorly fit modern substitute. In the Greek world, greaves were very expensive. It is unlikely you would be wearing them if they weren't well-fit to start with. https://www.gutenberg.org/files/52081/52081-h/images/089a-670.png
Some discussion on the matter:
An introduction to Manning Imperial and some of their wares:
And an image based on archaeological finds spanning Greek history. Fairly soon they covered the knee, and before and during the Classical period they became anatomical and no longer had the holes dotting the edging for additional liners, which leads us to believe either some manner of organic material was glued in for comfort and has since rotted away, or that hoplites, as seen in vases, might have worn little more than a leather/felt wrap around the ankle. https://lh3.googleusercontent.com/-4B8BRR41WKU/WLM92zv9y_I/AAAAAAAAQvQ/53g-bdTXdGs/%25255BUNSET%25255D.png
These are apparently the set found at the famous tomb at Vergina, which we attribute to belonging to Phillip II. I believe this is dated to 336 BC, and note that it has neither rings nor holes. https://i.pinimg.com/originals/57/c3/a2/57c3a2843d412b41c70c8f13b42d8152.jpg
I fear I didn't make myself clear enough, which is a mistake of mine because I generally tend to focus on the Greek theater in my interests. I kind of left out which faction I was speaking about, which is why I had mentioned 'I don't know about other theaters', but failed to specify my exacting context. Well of course, straps were used! Anyone who has seen Iberian greaves [ https://upload.wikimedia.org/wikipedia/commons/0/09/Iberian_greaves_%28MARQ%29.JPG ] [ Celtiberian depiction - https://media.moddb.com/cache/images/groups/1/4/3656/thumb_620x2000/EB-art-celtiberian-heavy-inf.jpg ] , Roman greaves [ https://cyclingarchaeologist.files.wordpress.com/2016/07/image208.jpeg ] , and Gladiator greaves [ https://78.media.tumblr.com/ac2a8350129b7a213d6031dd9f429e6d/tumblr_nw9px72SQ81tgrkdyo1_1280.jpg ] would know as much! (though I think some earlier Roman greaves were done in the Greek way too).
We should acknowledge the fact that (Most, if not all?) greaves in the Greek theater at least, were held on solely by the springy tension of the metal itself. This might have been the case with particular sets elsewhere. In fact, @matmohair, your first picture seems to demonstrate this point. The greave there is not applied and yet is tight enough that it is closed shut without anything tied onto it yet. While the presence of loops in an archaeological find like that indicate additional strapping of 'some' sort were used, well-made greaves that fit the leg snugly generally don't require such. This was the style in the Greek world, while elsewhere sometimes straps of different sorts were used. If it's a rather open greave that of course doesn't really 'wrap around' the shin area, certainly it would require some kind of strap system. Unless you glue it to your shin.
I don't blame most folk for not knowing this, as generally speaking Rome and Romans are far more popular. The mod itself is Rome At War, after all. But, as a matter of fact, Greek greaves from the late Archaic going forward as far as I know, were made to be held on by the spring tension of the bronze, and fit very snugly on the user. This fact is pretty well-established within the community already, to the extent that a Greek impression with the use of buckles on said greaves within the qualifying periods is generally frowned upon as a poorly fit modern substitute. In the Greek world, greaves were very expensive. It is unlikely you would be wearing them if they weren't well-fit to start with. https://www.gutenberg.org/files/52081/52081-h/images/089a-670.png
Some discussion on the matter:
https://www.romanarmytalk.com/rat/thread-11236-page-2.html
https://www.romanarmytalk.com/rat/thread-12256.html
https://www.romanarmytalk.com/rat/thread-12256.html
An introduction to Manning Imperial and some of their wares:
'Manning Imperial is a premier manufacturer of historical reproductions. As an international supplier to re-enactors, collectors, museums and the movie industry, we pride ourselves on the high quality and authenticity of all our products. We prefer to use authentic methods of construction wherever possible.
Rather than carrying a large range of products in stock most items are made to order and can therefore be customised to our clients most exacting requirements.'
And a look at some of their models;
Note; copied directly from a museum find. - http://www.manningimperial.com/catalogue/armour/greeves/fluted-bronze-greeves/621
http://www.manningimperial.com/catalogue/armour/greeves/bronze-greeves/625 'Like all of our Greek greeves these are precisely fitted to the individuals leg and the natural spring of the metal holds them in place without the need for straps.'
Rather than carrying a large range of products in stock most items are made to order and can therefore be customised to our clients most exacting requirements.'
And a look at some of their models;
Note; copied directly from a museum find. - http://www.manningimperial.com/catalogue/armour/greeves/fluted-bronze-greeves/621
http://www.manningimperial.com/catalogue/armour/greeves/bronze-greeves/625 'Like all of our Greek greeves these are precisely fitted to the individuals leg and the natural spring of the metal holds them in place without the need for straps.'
And an image based on archaeological finds spanning Greek history. Fairly soon they covered the knee, and before and during the Classical period they became anatomical and no longer had the holes dotting the edging for additional liners, which leads us to believe either some manner of organic material was glued in for comfort and has since rotted away, or that hoplites, as seen in vases, might have worn little more than a leather/felt wrap around the ankle. https://lh3.googleusercontent.com/-4B8BRR41WKU/WLM92zv9y_I/AAAAAAAAQvQ/53g-bdTXdGs/%25255BUNSET%25255D.png
These are apparently the set found at the famous tomb at Vergina, which we attribute to belonging to Phillip II. I believe this is dated to 336 BC, and note that it has neither rings nor holes. https://i.pinimg.com/originals/57/c3/a2/57c3a2843d412b41c70c8f13b42d8152.jpg
