Throw Bonuses - Nice! Great! Excellent! and all that.

Analysis
The Throw Bonus

Based on our analysis, we found that the average multiplier for throw bonuses are as follows:

Throw TypeMultiplier
Nice1.15
Great1.5
Excellent1.85

Since ring size and throw bonus are correlated, we are unable to fully untangle whether the multipliers are constant for each type of throw or if the value vary based as a function of ring size (2 - Color Target Ring / White Ring) with our current dataset. They're identical on the average.

What we are confident of is that when the ball hits outside of the ring, the multiplier is always equal to 1.

The graph below shows how much your catch rate improves with an average throw bonus:

Throw Bonus

Click here to learn more about how we generated this graph.

Analysis
Should I aim for the smallest ring if I don't think I can get the ball in the ring?

From our research, the answer to this question is no. You only get a throw multiplier if you successfully land a nice, great or excellent throw. We expect our conclusion for the Throw bonus to be somewhat controversial because of contradicting research from trainer RhyniD.  

However, at a closer examination of Trainer RhyniD's raw data, we found that the GUCT and Throw bonus are compatible with the data RhyniD collected, despite reaching opposing conclusions. The reason being, in reaching his conclusion, RhyniD did not account for the curve ball bonus, which as we showed yesterday is quite significant.

In a follow up analysis of RhyniD's data, Trainer Binzouin is surprisingly prescient with his analysis, creating this graph:

Binzouin Graph

 

The Improvement Factor in this graph has direct parallel with Multiplier in the GUCT formula. If Binzouin kept at it a bit further, it's likely he could eventually derived the GUCT on his own! 

Between 0.7 to 1.0 Rhynid Radius, we see the trend line flatlined at about 1.7 "improvement factor", which coincidentally, is also what we found the Curve bonus to be. On closer examination of Trainer jdero's throw technique, we found RhyniD's dataset consists almost entirely curveballs.  This is reflected in Binzouin's graph.

Between 0 to 0.7 Rhynid Radius, which are the limits of Throw bonus thresholds, the improvement factor trends as we expect by multiplying Curve and Throw Bonuses.

In other words, the cause of the statistical discrepancy between game's stated catch rate and the empircal data RhyniD found, which he attributed to reticle size, was instead the curve ball bonus. When taking curve ball into account, we found GUCT to be a good match with the underlying data RhyniD collected.

Confirmation Tests

As a final confirmation of the GUCT multipliers, we ran binomial tests of the unbinned data. All of the pre-0.41 update factors were included: ball, curve, berry and throw bonus. We first calculated the GUCT catch rate for all throw attempts using the established multipliers.

Then, we ran two tailed binomial tests to see if the probabilities from the sample are statistically different from the calculated catch rates. We repeated these tests after restricting our data to only cases where berries were used and then only cases where berries were not used. The results of these tests are summarized in the table below. Given that less than 5% of tests rejected the hypothesis that calculated catch rate is accurate, we are quite confident in our calculated values for the multipliers.

ConditionRejected TestsFail to RejectTotal
All Multipliers1715881605
No Berry1010801090
Berry5616621
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