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Jakub Wasilewski

I think the bubble size on the original chart is proportional to the number of players who did surpass their "breakout". So the 22 bubble is "5 out of 10" and sits at 50%, while the 25 bubble is something like "5 out of 25" and sits around 20%.

Andrew Gelman

I find the original chart to be incredibly confusing. I'm reading "Percent who had a better two-year span" over and over again, it's all a blur to me. For me (but maybe not for the average audience), I'd rather just see a bunch of line plots, showing the trajectory of WAR for each player. I feel like I'm staring at the bubble plot trying to deduce what the underlying trajectories were, but then why not just show the trajectories? In this case, I wonder if it's missing the point to be tinkering with the graph that was displayed.


Jakub: your interpretation makes more sense but then the legend is very unclear!

Andrew: You're absolutely right. That's why I pushed a chart re-do to the bottom of the page :) I wonder why he didn't just analyze the WAR trajectories as you said. If he did that, he will notice things like survivorship bias, and tenure bias. My understanding though is that this type of thinking is at the core of sabermetrics, just treat everything as probability estimates at some level of aggregation.


I Strongly AGREE With this statement:
This bubble chart is no different from others: it is impossible to judge the relative sizes of bubbles. Even though the legend provides us two reference points (a nice enough idea on its own), it is still impossible to know, for example, what proportion of players did better later in life when they first peaked at age 24. The bubble for age 23 looks like it's exactly five players but I still cannot figure out how many players the adjacent bubble represents.

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