Purpose

This app can be used to compare track athletes (only distance events right now). Users can view all athletes from a conference sorted by events of their choosing. Users can also select an athlete and conference to see which athletes from the chosen conference are most similar to the selected athlete.

To run program

• Run "python3 app.py localhost 5001" in the command line then go to "localhost:5001" in a browser.

To add new conference

• Navigate to the tfrrs page of the conference you want to add
• The url of the page should look like "https://www.tfrrs.org/leagues/1408.html", (1408 is a placeholder in this case, the actual value will be the conference id of your conference)
• Run "python3 scraper.py 1408 m" to add the men's side of the conference and "python3 scraper.py 1408 f" for the women's.

Similarity Methodology

On the athlete comparison page, there is a "similarity" column. Here is an explanation of how that is calculated.

• We want to measure similarity of two athletes $x$ and $y$, which we will call $S(x, y)$.
• A simpler problem is measuring the similarity in event $v$ of their prs $x_v$ and $y_v$, $s(x_v, y_v)$.
  • We can start off with $s(x_v, y_v) = exp(-|x_v-y_v|)$.
  • To standardize across events, we define $s(x_v, y_v) = exp(-\frac{|x_v-y_v|}{\sigma_v})$.
  • Handily, this stays between $0$ and $1$, with $1$ meaning perfect similarity.
• Next, we define the set of all events $x$ and $y$ have both run as $V_{xy}$.
• Averaging all of the $s(x_v, y_v)$ in $V_{xy}$ gives us $S(x, y) = \frac{1}{|V_{xy}|}\sum\limits_{v \in V_{xy}} s(x_v, y_v)$.
• This is a good start, but we would like to judge athletes on their best events.
  • We want $w_v(x, V)$ to be the weight we give event $v$ in some events $V$ run by athlete $x$.
  • Let $z_v(x)$ be the z-score of $x_v$, i.e. $\frac{x_v-\mu_v}{\sigma_v}$
  • Let $z_{min}(x,V)$ be athlete $x$'s lowest z-score of any event in $V$.
  • Then we can define $w_v(x, V) = exp(z_{min}(x, V)-z_v(x))$
  • This weight stays between 0 and 1, with athlete $x$'s best event receiving a score of $1$.
• We can use these weights to redefine $S(x,y) = \frac{\sum\limits_{v \in V_{xy}} s(x_v, y_v)w_v(x, V_{xy})w_v(y, V_{xy})}{\sum\limits_{v \in V_{xy}} w_v(x, V_{xy})w_v(y, V_{xy})}$
• This is better, but similarity metrics will still be too high in some cases like this one:
  • Alice is a 10k runner and Bob is a sprinter and their only shared event is the 800.
  • They have slow but identical times that are worse than their prs in their specialty events.
  • In this case, $S(Alice, Bob)$ will be $s(Alice_{800}, Bob_{800}) = 1$, which is too high.
  • We want high similarities to imply that athletes specialize in the same events.
• Luckily, we can fix this by tweaking the weights used in the numerator of our function.
• We can define $V_x$ as the set of all events run by $x$.
• $w_v(x, V_x)$ then gives an event weight that takes into account everything $x$ has run.
• Incorporating this into our function gives us $S(x,y) = \frac{\sum\limits_{v \in V_{xy}} s(x_v, y_v)w_v(x, V_x)w_v(y, V_y)}{\sum\limits_{v \in V_{xy}} w_v(x, V_{xy})w_v(y, V_{xy})}$.