ok..as usual what i say is more or less a guess.
An increased gap would probably increase the burn rate slightly, but i am more or less sure that it would help alot if the mixture is lean.

You've answered your own question.  Increased gap means increased voltage for spark/arc breakdown.  Eventually you can get enough voltage to cause insulation failure in the HV train.

Spark gap and voltage requirements are determined mostly by compression, air/fuel mixture, and fuel type. An increased gap requires increased voltage and amperage in order to maintain spark density. Decreasing the gap can make it vulnerable to incomplete burn or misfire. Once you have "enough" gap and voltage, it won't do any good to add more.

I just want to add that increased gap tolerates leaner mixture without misfire.

Like in all things engineering wise, there are compromises to be made.  I think it helps to think of the ignition as having available energy in wattage or volts X amps X real time in milliseconds.  The spark duration in Milliseconds is apart of the equations and the less volts you need the more amps and duration of spark and vise versa.  Voltage is needed to overcome the gap so if you have a larger gap it takes more voltage, however, there is less available amps & spark duration i.e. the compromise.  Remembering that Amperage not volts is what does the true work.

So when you open the gap up, you lower the amps and spark duration.  The entire compromise is like a game of percentages.  The wider the gap in the spark plug, the more likely there will be some hydrocarbon/02 mixture floating by to be ionized by the spark and the longer the spark duration the more opportunity to find some to ionize.  The leaner the mixture the more voltage it take, and lean mixture tend to have more voids or pockets of either 02 or/HC, but not necessarily together, thus lean misfire.  

It’s all about the compromises that have to be made.  If the mixture is too lean you need huge ignition requirements both in energy, secondary insulation and probably the most important cost.  The bang for the buck is what’s it’s all about.  I saw 20 to 24 to 1 air/fuel mixture being reliable used in a stand engine by using extremely wide spark plug gaps of over .200 with over 7 millisecond spark duration but the combination of high cost and short spark plug life didn’t justify the results.   And just because you can ignite a very lean mixture it doesn’t mean that the results are necessarily what you want as well, because as in this case, the power got to be so low that there was no way to justify the results either.
al1

I spent a day just varying the gap and observing the results. I adjusted the timing to optimum after each gapping as well. I got the best performance with a gap just smaller than that which caused a misfire. I also noticed that the smaller gap caused pinging more readily. As mentioned, real-life compromises dictate the best overall gap.

Agree with what is said above. However, as i interpret the original question (ie not considering energy req.); bigger is better.

Just a thought I wanted to throw in is all the ignition systems I am familiar with limit the amperage in the secondary to avoid a potentially lethal situation.----Phil

reducing the size of the electrode will allow you to increase the gap without as much loss. such is the reason for platinum and iridium plugs. guess you might think of thise little electron flowing along with all the other basic electrical calculations.

Some years ago I undertook an extensive study of various spark plug designs and types. This was carried out on a single cylinder version of a modern contemporary 24 valve 3.0 litre high performance V6 engine design.
The types of plugs that were tested were
a)    a conventional “J-gap” type (1.4mm gap)
b)     J gap with fine centre electrode (1.4mm gap)
c)    surface gap with four ground electrodes higher than the centre electrode(1.3mm gap)
d)    surface gap with four ground electrodes lower than the centre electrode(1.4mm gap)
e)    ring gap design with find centre electrode(1.2mm gap)
AFR sweeps, EGR and spark timing sweeps were carried out, COV of IMEP stability limits were investigated (lean limits, EGR dilution tolerance). For the results the surface of the plugs was examined using a microscope and scanning electron microscope. The full results of the tests are too extensive to go into.
In addition the electrode orientation was investigated.
Plug design in “b” was found to offer the most stable and repeatable combustion even up until AFRs as lean as 21.5. This was closely followed by the plug design of  “d”.
A similar trend was shown for EGR tolerance, where “b” could tolerate 23 % and “d” almost as much but with a poor COV of IMEP of 6-7%.
HC emissions were monitored also and showed concurrence with the plug types that misfired earlier in the test.
In terms of orientation, the plugs were tested at 60 degree rotational increments with everything else kept constant. It was found that spark plug orientation affects engine operation smoothness in the AFR range of operation of 14.6:1 (stoich) up to 17.6:1. COV of IMEP of cylinder pressure fluctuation increased when the ground electrode faced the primary intake port. Examination of the spark plug surfaces suggested that the sparks between the centre and ground electrode billow out in the direction away from the primary intake port to the spark plug in the main flow direction.
Overall the fine centre electrode J –gap plug could run in extended lean operation compared to the surface gap and ring gap designs. The surface gap type plugs have additional energy loss to the insulator. Voltage requirements decreased for reversed polarity operation at part load but increased at wide open throttle. This indicated that the ground electrodes were hotter than the centre electrodes under light loads and vice versa at WOT.