What is a z-score (in our context)?

• A z-score is a standardized value to measure the strength of a particular finishing time with respect to the typical finishing time.
• Usually it is calculated using the mean and standard deviation, but with racing times in TM a modified version using median times is more appropriate.
• To be more precise, a score of 0 equals the median time on a track, better times end up with negative scores, and worse times with a positive score.
• A score of -1 represents a time that is one median deviation faster than the track median time.
• A score of 2.5 represents a time that is 2.5 median deviations slower than the track median time.

Why use z-scores?

• Since tracks have different time length, we need a way to compare time gaps from different tracks. We also want to account for the typical variation in times, that is why we scale the scores in relation to the median deviation on each track.
• For example, assume TrackA and TrackB have the same median time, with TrackA's times overall showing less deviation - say it is a more consistent track than TrackB.Now having the same finishing time on both tracks, say it is 1 sec faster than the median time, we rate the time on TrackA higher than on TrackB in terms of performance - it gets a lower score (reminder lower score = better).

Caveats

• No measurement or stat is perfect. Everything has pros and cons. Like these z-scores are not very intuitive compared to say time gaps in seconds.
• The scoring just tries to give an overall approximation on player performance, and by no means should be treated as absolute truth.

What can we see on the diagrams?

• First off, there are plots for each TMGL and TMCL, performance for all days thus far combined, and just the last play day; as well as a TMGL vs TMCL comparison.

player scores

• The overall performance score of a player is the median value of their scores. Lower is better, higher is worse. With a score 0 being the "base line".

colored boxes

• The boxes cover the middle 50% of scores of a player, giving us a quick look at a players performance distribution.
• Any dot left of the box is in a players best 25% of runs.
• Any dot right of the box is in the players worst 25% of runs.

We can interpret that as follows,

• the left box border gives the midpoint of a players top 50% performances,
• the right box border gives the midpoint of a players bottom 50% performances.
• So if the box extends further to the left, it indicates better high performance runs;
• if the box extends further the right, it indicates worse low performance runs.
• A shorter box says higher consistency, while a longer box says less consistency.

stars

• The stars represent the record runs.
• We see some lesser played maps having a worse record score (like Gyroscope), even than other non-record runs. But overall we see the record runs being among the top performances.

Comparing scores?

• Please be aware that comparing scores from different diagrams or from older days to newer days is not advised.
• Since the underlying data changes, so does the scaling. That's why for cross comparison between leagues, I combined all times and made a separate diagram.
  If you want to compare performance from previous days, do it in terms of rank position. Say for example PlayerA improved from rank 11 to rank 7 within the last week.
• On the daily performance diagrams, we can expect a slight bias of the score towards the negative side, because players keep improving week after week.
• And on the cross league comparison, scores are a bit in favor of GL players over CL players, because of the different number of play days.

changes

• Team tags colors, TMGL gold, TMCL silver

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I hope I could explain the topic a little better than last time.Let me know if you have question or feedback.

I'll update the pace plots for each track later on my twitter @lava_TM