The draw for the 2017 Wimbledon men’s tournament is complete and with it comes the questions of which player has a good or bad draw. My favorite this time around is ESPN’s “Federer, top seeds face tough Wimbledon draw”. The opening line is “The “Big 4″ got a tough draw at Wimbledon.” Wow, the entire big 4 all got tough draws. But is that correct? This conversation happens entirely qualitatively with no quantification analysis utilized. Since Riles Clubhouse publishes our probabilities when the draw (Wimbledon Predictions) is announced, it was natural to approach the draw analysis with the same quantification.

Draws for grand slams have specific rules. The #1 and #2 seeded players are placed on opposite ends of the bracket whiles the #3 and #4 seeds are then drawn into either half of the bracket. Then the seeds for #5 through #8 are placed individually drawn into each one of the top 4 seeds quarter. Next, seeds #9 to #12 are individually drawn in the same section as seeds #5 to #8 (as potential 4^{th} round opponent). Likewise, seeds #13 to #16 are drawn into the same section as seeds #1 to #4. Next, seeds #17 to #24 are individually drawn into the section of seeds #9 to #16 as their potential 3^{rd} round opponent. Again, seeds #25 to #32 are drawn into the same section of seeds #1 to #8 as their 3^{rd} round potential opponent. Finally, the remaining 96 players are randomly drawn into the remaining available spaces.

This process creates a massive number of possible draw permutations. To model this large number of variations, a Monte Carlo simulation is employed in which we run hundreds of potential draw outcomes and use of Riles Clubhouse methodology to estimate each player’s probability of reaching each round in the tournament. The actual draw is then compared to the hundreds of draw simulations to determine if a player has an advantageous or poor draw.

For example, Andy Murray’s round by round probability is shown below. The orange line is the actual draw probability while the dark gray line is the average simulated draw probability. The dash lines represent +/- 2 standard deviations away from the average. If the orange line is above the solid gray line, then that player has an advantageous draw. Likewise, if the orange line is below the dark gray line, the player has a poor draw.

Also, from the analysis we can calculate the percentile that the actual draw is compared to the simulations. An average draw would be 50% percentile, a poor draw below that, and a good draw above 50%. Using Andy Murray as the example again, his draw percentile is 91% meaning that he has a great draw. Below is a comparison of the draw percentiles for each of the seeded players.

The seed with the best draw is Andy Murray at 91% percentile. This means that his current draw is better than 91% of the draw possibilities. Looking at his draw in more detail, we can see that specifically his draw has its biggest bump from Round of 32 to Round of 16.

The player with the worst draw is Tomas Berdych at 2% percentile. His opening opponent of Jeremy Chardy is no picnic followed by Ryan Harrison or Borna Coric, followed likely by Richard Gasquet and then Dominic Thiem.

Once the opening serve is underway, this analysis of the draws becomes filed away. But the impact of the draw will define this year’s tournament. Look for potential deep runs for Gilles Muller, and Ivo Karlovic while we could see Tomas Berych and Rafael Nadal struggle earlier than their seed suggests.