The Bates 2016/2014 issue with simplifying estimates of climate sensitivity by reduction to tropical regions has some profound impacts. If you have followed my rants, the tropical oceans and oceans in general are my main focus. The tropical oceans are like the fire box of the heat engine and the poles are a large part of the heat sink. Space is of course the ultimate heat sink, but since there is a large amount of energy advection toward the poles, average global surface temperature depends on how well or efficiently energy moves horizontally as vertically. Since the atmosphere will adjust to about the exact same outward energy flow over time as required to meet the energy in equals energy out requirement with some small "imbalance" that might persist for centuries, the oceans which provide that energy and are capable of storing energy related to the "imbalance" so if you "get" the oceans you will have "gotten" most of the problem. The correlation of the oceans with sensitivity and "imbalance" just provides an estimate of how much can be "got".
Interpolation methods used for SST and OLR will tend to enhance the "global" correlation so there is some additional uncertainty, but for government work, SST and OLR are pretty much the best of your choices.
"Believers" are adamant about using "all" the land surface temperature data, including infilling with synthetic data, if you are going to get a "reasonable" estimate of climate sensitivity with "reasonable" meaning high and highly uncertain. Basic thermodynamics though allows the use of several references, each with some flaws, but none "useless". If you can only get the answer you are looking for with one particular reference, you are not doing a very good job of checking your work. Perpetual motion discovery is generally a product of not checking your work very well. Believers demanding that certain data be included and only certain frames of reference be used is a bit like what you would expect from magicians and con artists.
In the first chart I used 1880 to 1899 as the "preindustrial" baseline thanks to Gavin Schmidt. There is about 4.5 billions years worth of "preindustrial" and since the data accuracy suffers with time, the uncertainty in Gavin's choice of "preindustrial" is on the order of half a degree which is about 50% of the warming.
The whole object of using "teleconnections" is to find the best correlation with "global" and to use relative correlations to estimate uncertainty. This is what Bates 2016 has done. He limited his analysis to the region with the "best" data that represents the most energy and based his uncertainty range on the estimated correlation of his region of choice with "global". Lots of caveats, but Bates has fewer than Mann and the greater than 3C sensitivity proponents.
So the debate will continue, but when "believers" resort to antagonistic tactics to discredit quite reasonable analysis they should expect "hoax" claims since they are really using con artist tactics whether they know it or not.
Even the weak 23% correlation between tropical SST and the global surface temperature is "significant" when the number of points used is large. With a bit of smoothing to reduce noise though you can get an eyeball correlation and thanks to Gavin's baseline you can see that the northern hemisphere extra tropical region is the odd region out. If you recall, Mann's "global" reconstruction was really a northern hemisphere ~20N to 90N reconstruction with a few southern hemisphere locations kind of tossed in after the fact. That 20N-90N area is about 33% of the globe and happens to be about the noisiest 33% thanks to lower specific heat capacity. Understandably people are concerned with climate change in the northern extra tropical region to the point they are biased to that region, but an energy balance model just happens to focus on energy not real estate bias.
If you are a fan of pseudo-cycles you probably notice that the 20N-90N regional temperature looks a lot like the Atlantic Multi-decadal Oscillation (AMO). There is likely some CO2 related amplification of the pseudo-cycle along with land mass amplification due to lower specific heat capacity, but that pesky 0.5 C degree wandering would make it hard to determine what is caused by what. For the other 67% of the global, land and ocean included, the Bates 20S-20N tropics serves as a reasonable "proxy", "index" or "teleconnection" depending on your choice of terms.