I know I am a little late to the gag (it first aired in October 2014), but I am sure I would have taken (or is that had will have taken?) a great interest in the linguistics of it because I was actually studying verb tenses for a Tricky Bits e-mail at that time. As I said in that e-mail, this stuff can be incredibly, mind-numbingly complex, yet as native English speakers, we use verb tenses in our day-to-day conversations without much thought.
So is there an underlying basis for all these haves, hads, and hases? Let's see:
“This is Hot Tub Time Machine all over again. Look. If future Biff goes back to 2015 right after he gives young Biff the almanac, he could get back to the 2015 with Marty and Doc in it because it wasn’t until his 21st birthday that 1955 Biff placed his first bet.”
When Sheldon conjectures, Leonard changes it to had will have placed: "It wasn’t until his 21st birthday that Biff had will have placed his first bet." Sheldon concurs with Leonard’s new tense.
So what are they doing here? They are creating a new alternate-future tense by combining two of our current tenses. Will have placed is the future perfect, which can denote a future action that will be completed prior to a specific future time. This gives them a 1955 perspective: He will have placed his first bet prior to arriving back in 2015.
This is standard English until they add a had in front. Had adds the past perfect and is meant to modify the future perfect will have placed. In this sense, I think it adds an imaginative conditional that normally refers to past time: If he had (will have) placed it, he could get back to the 2015 with Marty and Doc in it. Adding a past perfect atop the future perfect doesn't seem to really clarify what is happening in this imaginary timeline, but alas, our quandary continues with Sheldon:
“Unlike Hot Tub Time Machine, this couldn’t be more simple. (sic) When Biff gets the almanac in 1955, the alternate future he creates isn’t the one in which Marty and Doc Brown ever used the time machine to travel to 2015; therefore, in the new timeline, Marty and Doc never brought the time machine …”
This time, when Leonard conjectures out of spite, Sheldon changes it to never had have had brought.
This amalgamation of three tenses clears the threshold of ridiculous: Had brought is the past perfect, or the action completed in the past prior to some other event. (Also note, this changes firmly their perspective. They are no longer in 1955 looking into the future but in 2015 looking backwards, at least grammatically.
If Marty and Doc had never brought the time machine to 2015, Biff would not be able to go back.
Have adds the present perfect and, as I see it, a conditional element to this otherwise standard-timeline present perfect tense. Up to here, they've switched perspectives, but are staying close to their first formation.
If Marty and Doc have (had never) brought the time machine to 2015, Biff would not be able to go back.
But Sheldon doesn't stop there, and I can only see another had adding a further conditional to this make-believe conditional past perfect construction, bringing into account the alternate timeline.
If he had [have] (had never) brought it, he could get back to the 2015 with Marty and Doc in it.
The switch to present perfect in the middle there doesn't sit with me. It appears to me that a had had had never brought makes more sense (which shows you how crazy all this is!)
Where do they go wrong? Neil Whitman noted some of their missteps. Here are a couple:
1) “The main way Sheldon and Leonard twist the verb-tense syntax is to allow auxiliary have to take complements that it doesn’t take in monolinear-time Standard English. First, they put it with the modal will, when modal auxiliaries are always the first in a series of auxiliary verbs.”
In other words, the modal will should always go first, so it should be will had have placed.
2) "Ordinarily, this kind of situation would call for the so-called 'future in the past': Biff would place his bet sometime later."