Joe, John, and I have been bowling in the Bernaski League for three seasons now. When we started, we stunk. Now, we have a mild B.O. [El Jefe is in his first season and still stinks.] In other words, we are far from being good bowlers, but it’s pretty clear that we have gotten better. We all have our ups and downs, but when viewed from the long term perspective, we have improved. I will look at the long term numbers in another post, but herein I want to focus on the last thirteen weeks, the time period for which we have detailed data.
It is an interesting problem to try to detect improvement in bowling skill over the short term because individually and as a team, our game and series scores fluctuate wildly. The simplest way to try to gauge improvement would be to look for a relationship between time and pin totals for the team. If we are improving, there should be a clear relationship between these two variables. In reality, however, it is not so clear.
The ideal case might involve a team whose average increased a steady one or two pins per week. In that case, we would see a graph that looks like the one above and to the left (click on it to make it bigger). In the real world, however, while the average may slowly creep up like this, there is a huge amount of fluctuation around that average from week to week as shown in the middle graph above (based on fictitious data). In the second case, the improvement signal is swamped by a huge amount of noise, and to even see it would require looking at scores over a long period of time. The graph above and right is identical to the one in the middle except I have expanded it to include 34 weeks of data instead of 13. Notice how the signal becomes immediately apparent when viewed from the long term perspective.
I believe that the latter two graphs are a good description of our bowling improvement. We fluctuate wildly around our average, but our average keeps growing steadily. Here is the evidence for this contention. I looked at the team average for our core bowlers week by week. I left out both of our subs (sorry Becker and Gingy) who have done wonders for us of late. This is shown in the graph below and left. Notice that it looks like we are treading water, that no improvement is evident. In fact, if you fit a regression to this scatter, it would suggest that we are getting worse by approximately 0.14 pins per week as a team. My contention is that if we had data for the entire season, the graph would look a lot like the one above and to the right. In fact, it’s not difficult to demonstrate that this is the case.
The graph above and right shows our team handicap over this same time period. The handicap is calculated using data from the entire season, and over the 13 weeks for which we have data, we have taken 11 pins off of our team handicap (from 287 to 276), an approximate improvement of one pin per week for the whole team. In contrast to week-to-week team averages, the change in handicap tells us how well we have been bowling recently compared to all prior weeks in the season, and it shows clearly that were are improving… one pin at a time.
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