An interesting fact about Jutland is that it if the British had better communications and intelligence and better decision making under Jellicoes part, they really could have delt truly severe damage to the German fleet. So what if the British were able to catch the Germans before they reached the horn? Could this prevent the German U boat campaign, thus leading to less damaged British supplies? Could this make Germany surrender earlier? Could Britain even try to invade Wilhelmshaven to put more pressure on Germany proper?
The only problem there is getting crews for them, and materials. Whilst the HSF literally cannot be wiped out, lets assume it gets badly roughed up with the following losses
4 x Koening Class Dreadnoughts
1 x Kaiser Class Dreadnought
1 x Ostrifrieland Class Dreadnoughts
1 x Nassau Class Dreadnought
3 x Deutschland Class Pre-Dreadnoughts
And of the 1st Scouting Group, the only survivor is Derfflinger, the rest (Moltke, Lutzow, Von Der Tan, Seydlitz) are all sunk as well as heavy losses among cruisers and assorted losses amongst German DD's and other ships being shot up or damaged.
To replace these, the Germans are going to have the resources available to build 2 Bayerns and 1 x Lutzow, if they put more resources into other ships, then it comes at the cost of artillery, machine guns, rifles and bullets. Fleet morale would be badly shaken and in a strategic sense, the High Seas Fleet has just had its eyes plucked out with the loss of 1st Scouting Group and various Cruisers being sunk. They've lost their scouting ability, and have no real way of replacing the lost ships in any appreciable number compared to what the UK's shipyards are going to be pumping out.
The High Seas Fleet simply won't be able to challenge the RN again, the RN could lay up some of its older Dreadnoughts or Battlecruisers, freeing up the crews for escorts, its a big morale boost for the Allies and the UK will throw Knighthoods and more at Jellico and god forbid, Beatty. It will be a morale hit for the Germans, any hope they have right away of breaking or loosening the blockade is gone. Fisher might get sexually aroused at the thought of his Baltic Plan getting dusted off, but as folks pointed out, the only way to do that is to go through Danish territorial waters and the Danes won't do that because they'll get invaded by the Germans, or join the Central Powers (Not that it helps much mind).
Thank you for this breakdown of what the Germans would might reasonably be left with. Complete agreement on the fleet morale being very low, I think that would probably preclude any aggressive actions for the rest of the war. However, I can't resist predicting a completely unrealistic progression of events:
June 1: Remains of HSF struggle into its bases.
June 2 - June 30: Newspapers try to describe the whole affair in terms of a Wagnerian sacrifice; naval command heads roll, the Kaiser is distraught;
July: Dreadnoughts are repaired, surviving pre-dreadnaught crews are transferred to fill out casualties;
August 29: Hindenburg is appointed Chief of General Staff, with Ludendorff in tow;
August 30: Ludendorff has a near panic attack over the possibility that the British will get into the Baltic, convinced the Kaiser than the only way to save Germany is to occupy Denmark;
September (first half): Denmark is occupied, its agricultural resources are exploited, the belts are mined and u-boats and coastal artillery deployed there;
September (second half): realizing that the HSF will never be able to challenge the RN, but eager to restore some reputation, the surviving heavy units are thrown against the Russian Baltic Fleet. Russian Baltic fleet fights and dies courageously, several dreadnoughts are lost to coastal artillery and mines, but the HSF breaches the Russian central mine belt, smashes Kronstadt and puts Petrograd under its guns. Alexandra and Rasputin convince Nicholas to sue for peace. The HSF is too battered to be of any use by now.
October: Separate peace with Russia - Germany gets Poland and Russia promises to provide the Ukrainian harvest as reparations. Since revolution is (for a time anyway) averted and the Russian state remains in control, there is no need for Germany and Austria-Hungary to use occupation troops to enforce the harvest collections, as in OTL. Without Russia to help it, Romania surrenders as in OTL. Between Russian and Romanian grain and Danish pork, the turnip winter is averted.
1917:
February 1: Germany does not re-start submarine warfare. No idiotic telegrams are sent to anyone. Wilson is not able to drag America into the war.
May 1: faced with bankruptcy and an impeding Central Powers offensive reinforced by troops transferred from the east, the Entente sues for peace.
Kaiserreich triumphant, and all because the British won at Jutland.