I finished all of the sims with a Paladin Dodge Factor of 3.0 (instead of the live value of 2.259). As usual, the sims are for T17, 18 and 19 heroic and mythic, using the default mastery-heavy gear and the custom mastery/haste balanced sets. In total there are 12 of them.
https://www.dropbox.com/s/war5tvlyyratyn3/divine%20dodge%203.0%20factor.zip?dl=0The mastery-heavy ones are largely the same as they are with the live dodge factor, haste is exceedingly powerful for every sim. I'm leaving them out of this post for brevity, but if you want to see them, feel free to grab the source above and examine to your heart's content. As a stat summary though, the mastery-heavy set is very slightly worse than the balanced set for all of the sims. The biggest difference is T19M, where the the balanced set beats the mastery set by 800 TMI.
Anyway, let's start out with T17.


The heroic set looks really nice, haste is just above mastery. In the mythic set, it actually gets stronger and almost matches stamina. It doesn't beat it though, so we're still good! I think it's interesting that all of the other stats get squished very close together in mythic sim.
T18:


Haste calms down a bit here and matches up with mastery in both sims. Stamina goes from being very strong to on par with the others once we get to mythic gear. I suppose
technically stamina still beats haste in this configuration, so Divine Dodge is still winning.
T19:


Haste is still strong at heroic gear levels, but it falls down to mastery and versatility's level at +1750 rating. I kind of doubt that the boost from T19H to T19M will possibly have that much extra rating on it so I think we can really just stop this graph in the +1000 range, where haste is in-line with stamina. In mythic gear, stamina itself becomes one of the worst stats quite early on so all bets are off. Haste is on top (aside from bonus armor of course) but everything is relatively close in value here. Interestingly, mastery looks like it loses some ground to versatility.
Stat comparison:
T17H Mastery (Live): 21628 dps, 32207 dtps, 22468 hps (10081 aps), 109.9k TMI
T17H Balanced (DD=2.259): 20877 dps, 30584 dtps, 21670 hps (9818 aps), 108.5k TMI
T17H Balanced (DD=3.0): 20886 dps, 30665 dtps, 21695 hps (9847 aps), 108.6k TMI
T17M Mastery (Live): 25097 dps, 28279 dtps, 25589 hps (11376 aps), 97.8k TMI
T17M Balanced (DD=2.259): 24123 dps, 26539 dtps, 24577 hps (11026 aps), 96.1k TMI
T17M Balanced (DD=3.0): 24128 dps, 26658 dtps, 24545 hps (10987 aps), 96.2k TMI
T18H Mastery (Live): 31254 dps, 50014 dtps, 36348 hps (16686 aps), 127.6k TMI
T18H Balanced (DD=2.259): 30011 dps, 46203 dtps, 34886 hps (16250 aps), 124.9k TMI
T18H Balanced (DD=3.0): 30016 dps, 46467 dtps, 34912 hps (16263 aps), 125.1k TMI
T18M Mastery (Live): 36807 dps, 42490 dtps, 41732 hps (19000 aps), 109.4k TMI
T18M Balanced (DD=2.259): 35348 dps, 38533 dtps, 40060 hps (18386 aps), 106.2k TMI
T18M Balanced (DD=3.0): 35365 dps, 38816 dtps, 40165 hps (18490 aps), 106.5k TMI
T19H Mastery (Live): 48236 dps, 72155 dtps, 58451 hps (27966 aps), 143.2k TMI
T19H Balanced (DD=2.259): 46055 dps, 64002 dtps, 56253 hps (27002 aps), 137.4k TMI
T19H Balanced (DD=3.0): 46079 dps, 64715 dtps, 56300 hps (27034 aps), 138.0k TMI
T19M Mastery (Live): 58214 dps, 58519 dtps, 68320 hps (31997 aps), 117.9k TMI
T19M Balanced (DD=2.259): 55459 dps, 50209 dtps, 65230 hps (30642 aps), 111.6k TMI
T19M Balanced (DD=3.0): 55497 dps, 50940 dtps, 65395 hps (30752 aps), 112.3k TMI
It's obvious from these stats that tuning the Dodge Factor has an impact on DTPS and TMI while leaving DPS and HPS alone (within error bars anyway). Setting it higher decreases our survivability, setting it lower increases it. Since it has absolutely no impact on any other part of the game, as Theck pointed out, it's a perfect tuning knob to make haste desirable without making us overpowered. In all of the sims so far, haste has been on top while our TMI has been very close to the live sim's values. I'm interested to see what we'd have to set the Dodge Factor at in order to match live's TMI, and take a look at how haste ranks in that situation. Right now, though, it's looking like Divine Dodge (with the proper dodge factor tuning) is an excellent candidate for saving haste.
I'm running another round of sims with the Dodge Factor set to 5.0, all 12 should be done within the hour. I'll try to post them with some analysis before my raid starts tonight.