Since the 11 December 2020 release we provide a tool (aP_operational_resolution) to compute a so-called "operational resolution". From the Release Notes:
The operational resolution of a dataset is therefore the isotropic resolution at which a 100% complete dataset would contain the same number of unique observations. Its main "raison d'etre" is to reduce three anisotropic diffraction limits of a dataset (as determined e.g by STARANISO) to a single number that could be used to (1) give an approximate indication of the level of detail one can expect to see in a map based on that dataset, and (2) allow the ranking of multiple datasets, e.g. from a screening campaign, on the basis of that criterion.
Consider an anisotropic dataset that is such that its STARANISO cut-off surface is a perfect ellipsoid and its ellipsoidal completeness is 100%. Its operational resolution will then be almost exactly the geometric mean of the three diffraction limits along the principal axes of the ellipsoid. This will be lower than the highest diffraction limit because of the spherical incompleteness of the ellipsoid at that highest limit, thus avoiding the misrepresentation of resolution by that highest limit alone. Of course any deviation from a perfect ellipsoidal shape for the STARANISO cut-off surface and any departure from 100% ellipsoidal completeness will cause this simple relationship to hold only approximately.
Any further cause of spherical incompleteness at that highest limit, beyond anisotropy (e.g. cusps, gaps between detector modules, insufficient angular widths of rotation ranges), will further decrease the number of observations, and hence the operational resolution. This justifies the term "operational": the number of available observations is the same as for a complete isotropic dataset at that resolution, and therefore will provide the same ratio of observations to parameters at the refinement stage.
Interestingly, when the worldview of diffraction data was still purely isotropic, no urgent need had been expressed to downgrade resolution by taking account of incompleteness. It was anisotropy, and the very systematic way in which it degraded spherical completeness, that made that need too urgent to be ignored.
Let's take 5E73 as an example. We can run different pipelines to get the following type of analysis for a traditional "Table-1" (using MRFANA and ignoring anomalous statistics):
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# Pipeline-1/REDACTED.mtz
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Overall InnerShell OuterShell
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Low resolution limit 41.540 41.540 1.485
High resolution limit 1.480 6.859 1.480
Rmerge (all I+ & I-) 0.090 0.021 -2.370
Rmeas (all I+ & I-) 0.099 0.023 -2.588
Rpim (all I+ & I-) 0.039 0.009 -1.027
Total number of observations 471373 5711 4536
Total number unique 75531 883 728
Mean(I)/sd(I) 7.1 24.7 -0.7
Completeness 97.0 99.5 95.0
Multiplicity 6.2 6.5 6.2
CC(1/2) 0.999 1.000 0.196
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# Pipeline-2/REDACTED.mtz
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Overall InnerShell OuterShell
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Low resolution limit 37.002 37.002 1.455
High resolution limit 1.450 6.717 1.450
Rmerge (all I+ & I-) 0.096 0.029 2.218
Rmeas (all I+ & I-) 0.105 0.032 2.509
Rpim (all I+ & I-) 0.042 0.013 1.143
Total number of observations 245932 3074 1828
Total number unique 41352 481 412
Mean(I)/sd(I) 6.5 104.2 0.0
Completeness 99.8 100.0 97.6
Multiplicity 5.9 6.4 4.4
CC(1/2) 0.997 0.991 0.234
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# Pipeline-3/REDACTED.mtz
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Overall InnerShell OuterShell
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Low resolution limit 33.759 33.759 1.435
High resolution limit 1.431 6.623 1.431
Rmerge (all I+ & I-) 0.129 0.048 7.280
Rmeas (all I+ & I-) 0.142 0.053 8.273
Rpim (all I+ & I-) 0.058 0.021 3.825
Total number of observations 245873 3181 1433
Total number unique 42939 494 345
Mean(I)/sd(I) 4.5 13.4 0.0
Completeness 99.3 100.0 78.8
Multiplicity 5.7 6.4 4.2
CC(1/2) 0.992 0.987 0.488
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# Pipeline-4/staraniso_alldata-unique.table1
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Diffraction limits & principal axes of ellipsoid fitted to diffraction cut-off surface:
1.916 1.0000 0.0000 0.0000 _a_*
1.601 0.0000 1.0000 0.0000 _b_*
1.380 0.0000 0.0000 1.0000 _c_*
Overall InnerShell OuterShell
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Low resolution limit 33.759 33.759 1.569
High resolution limit 1.401 4.651 1.401
Rmerge (all I+ & I-) 0.048 0.024 0.717
Rmeas (all I+ & I-) 0.052 0.026 0.794
Rpim (all I+ & I-) 0.021 0.010 0.335
Total number of observations 170352 8532 7589
Total number unique 27456 1372 1374
Mean(I)/sd(I) 17.2 47.2 1.9
Completeness (spherical) 59.7 99.8 10.5
Completeness (ellipsoidal) 91.3 99.8 70.4
Multiplicity 6.2 6.2 5.5
CC(1/2) 0.999 0.999 0.820
Based on those overviews, one could already compare the different processing runs, but it becomes difficult since multiple metrics are potentially looked at and compared. Furthermore, the different pipelines might present their results in very different ways or even compute the nominally identical metric in a different way (assuming Friedel's Law being true or false for example). Not all synchrotron systems normalise those quality metrics (using e.g. a program like MRFANA to have identical binning and computations).
So what do we get if we take the scaled and merged files produced by each pipeline and analyse the operational resolution using the "aP_operational_resolution" tool? This would be the file a user would pick up and move towards the next steps (structure solution using molecular replacement or experimental phasing, ligand detection or refinement).
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# Pipeline-1/REDACTED.mtz
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Unit cell ....................................... 57.690 83.080 96.400 90.000 90.000 90.000
Space group ..................................... P 21 21 21 (19)
Recorded diffraction limits ..................... 41.5400 - 1.4800 A
NOTE : analysing (operational) diffraction/resolution
limits based on intensities (IMEAN,SIGIMEAN)
NOTE : diffraction limits for columns IMEAN,SIGIMEAN =
41.54 - 1.480 A
Per-reflection cut-off Operational Resolution
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I/sigma(I) >= 5.0 : 2.2736 A for 21955 reflections
I/sigma(I) >= 3.0 : 2.1170 A for 27077 reflections
I/sigma(I) >= 2.0 : 2.0145 A for 31342 reflections
I/sigma(I) >= 1.0 : 1.8777 A for 38589 reflections
I/sigma(I) >= 0.0 : 1.7046 A for 51308 reflections
all : 1.4955 A for 75599 reflections
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# Pipeline-2/REDACTED.mtz
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Unit cell ....................................... 83.119 96.444 57.701 90.000 90.000 90.000
Space group ..................................... C2221 (20)
Recorded diffraction limits ..................... 37.0017 - 1.4500 A
NOTE : analysing (operational) diffraction/resolution
limits based on intensities (IMEAN,SIGIMEAN)
NOTE : diffraction limits for columns IMEAN,SIGIMEAN =
37.00 - 1.450 A
Per-reflection cut-off Operational Resolution
-----------------------------------------------------------------
I/sigma(I) >= 5.0 : 2.5831 A for 7602 reflections
I/sigma(I) >= 3.0 : 2.3713 A for 9726 reflections
I/sigma(I) >= 2.0 : 2.2342 A for 11591 reflections
I/sigma(I) >= 1.0 : 2.0497 A for 14896 reflections
I/sigma(I) >= 0.0 : 1.5490 A for 34117 reflections
all : 1.4508 A for 41367 reflections
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# Pipeline-3/REDACTED.mtz
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Unit cell ....................................... 83.217 96.509 57.751 90.000 90.000 90.000
Space group ..................................... C 2 2 21 (20)
Recorded diffraction limits ..................... 33.7591 - 1.4305 A
NOTE : analysing (operational) diffraction/resolution
limits based on intensities (IMEAN,SIGIMEAN)
NOTE : diffraction limits for columns IMEAN,SIGIMEAN =
33.76 - 1.431 A
Per-reflection cut-off Operational Resolution
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I/sigma(I) >= 5.0 : 2.0545 A for 14863 reflections
I/sigma(I) >= 3.0 : 1.9153 A for 18282 reflections
I/sigma(I) >= 2.0 : 1.8292 A for 20905 reflections
I/sigma(I) >= 1.0 : 1.7067 A for 25663 reflections
I/sigma(I) >= 0.0 : 1.5322 A for 35285 reflections
all : 1.4335 A for 42958 reflections
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# Pipeline-4/staraniso_alldata-unique.mtz
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Unit cell ....................................... 83.222 96.509 57.746 90.000 90.000 90.000
Space group ..................................... C 2 2 21 (20)
Recorded diffraction limits ..................... 63.0252 - 1.4010 A
NOTE : analysing (operational) diffraction/resolution
limits based on intensities (IMEAN,SIGIMEAN)
NOTE : diffraction limits for columns IMEAN,SIGIMEAN =
33.76 - 1.401 A
Per-reflection cut-off Operational Resolution
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I/sigma(I) >= 5.0 : 2.0010 A for 16031 reflections
I/sigma(I) >= 3.0 : 1.9105 A for 18415 reflections
I/sigma(I) >= 2.0 : 1.8538 A for 20145 reflections
I/sigma(I) >= 1.0 : 1.7849 A for 22483 reflections
I/sigma(I) >= 0.0 : 1.7214 A for 25003 reflections
all : 1.6688 A for 27456 reflections
Now we have a common value (Per-reflection cut-off of I/sigma(I) >= 2.0) for each of the 4 pipelines:
Pipeline-1 : 2.0145 A for 31342 reflections <<< P212121 ! Pipeline-2 : 2.2342 A for 11591 reflections Pipeline-3 : 1.8292 A for 20905 reflections Pipeline-4 : 1.8538 A for 20145 reflections
This becomes much easier to compare now.