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I have the impression that the term pinball loss refers to the same as quantile loss (a.k.a. tick function); e.g. see the thread "How to calculate pinball loss for quantiles and for point forecasts?". Trying to visualize a pinball, I think the angle at which the ball hits a perfectly straight/flat wall and the angle at which it rebounds from it are the same (at least locally; on a skewed plane, straight lines become curved due to gravity). Meanwhile, quantile loss is characterized by different angles (as in the picture below) for all quantiles except the median. On the other hand, the image of the ball hitting a pin instead of the wall is not a very helpful analogy to the picture of the quantile loss function either.

Does that mean pinball loss is a misleading substitute for quantile loss?

enter image description here

P.S. Another funny thing is that the pictures illustrating quantile loss usually have a $90°$ angle between the incoming and the outcoming lines, which is again misleading. It is not a huge problem, though, as the loss function can often be scaled by a constant without major effects on the analysis, allowing to achieve the desired angle.

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"Pinball loss" and "quantile loss" are synonyms. As are "linlin", "hinge", "tick" or "newsvendor loss". I took these from Gneiting (2011, "Quantiles as optimal point forecasts", International Journal of Forecasting). See also any website on quantile modeling, e.g., here (look, it has the same picture as your question!) or here.

I don't quite see this nomenclature as misleading. After all, we don't call it a "reflection loss", in which we would indeed expect the angles with the horizontal axis to be equal. In a pinball machine, toggling the flippers is supposed to change the angle at which the ball leaves from the angle at which it arrives.

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  • $\begingroup$ Hmm, that makes sense if we think about rebounding from a flipper rather than a wall or a pin and measure the angle w.r.t. the "horizontal" base of the machine (if it has a horizontal base to begin with) or the "vertical" side walls (if they indeed are "vertical) rather than the flipper itself. Once you know what you are looking for, the name can be justified (just barely), but for a newbie this sounds pretty misleading... Thanks for your answer! $\endgroup$ Jun 9, 2020 at 15:00
  • $\begingroup$ I always thought the term 'pinball loss' was attributed to it because it looks like two pinball flippers, not that they represent the ball's trajectory. $\endgroup$ Apr 24, 2021 at 13:57

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