With the Ryder Cup finishing today (thanks to all the rain delaying the traditional Sunday finish) there will be no doubt be a slight increase in internet traffic with anxious fans wanting to keep up to date with the latest results. For any non-golfers out there, the Ryder Cup is a team event contested once every two years between 12 golfers from Europe and 12 golfers from the USA. Over the course of the tournament, there are 28 points to be won and currently, as of Sunday night, Europe are leading 9½ to 6½. The final 12 singles matches are to be played today and with each match worth a point, Europe require only 5 more points to win the Cup. Colin ‘Monty’ Montgomerie, the European Captain, will no doubt have had a sleepless night, wondering whether he has picked the best order for his players to tee off this morning. We’ve used his favourite technique, Monte Carlo simulation to help answer two simple questions:
- What is the probability of a European victory?
- Who is likely to sink the winning put?
To answer these questions we’ve created a simple Monte Carlo model (or more truthfully re-run a model from 2008). 1. What is the probability of a European Victory? With a 3 point lead, Europe are in a strong position but as each singles match has three possible results, there are 312 = 531,441 different outcomes and it’s hard to quantify the actual probability of success. Fortunately, Monte Carlo simulation is ideally suited to this type of problem when a high level of complexity and short timescales mean an analytical solution is not possible. Our model simulates today’s play hole by hole and a sample simulation is shown below. For details of the methodology, please see our previous article: Faldo’s Folly or Monty’s Carlo. In summary we’ve used historical data to calculate the chance of each hole being won, lost or drawn and made slight adjustments (e.g. 5% or 10%) to these win probabilities based on the relative form of each pairing from the first 3 days of the Ryder Cup.
In the simulation above, the early matches are shared, only for Europe to win the Cup in the last match just as the US sensed an upset. Running 5,000 simulations the model shows Europe winning 4,063 times. Consequently, we deduce Europe should win roughly 8 times out of 10 (a probability of 81%). 2. Who is likely to sink the winning putt We can also keep track of which player hits the critical putt (or chip, or…) that wins the Ryder Cup:
The graph above shows the probability of each match containing the winning stroke. It is unlikely that Luke Donald in Match 3 will deliver a European victory (given that Europe needs 5 points) but it could happen if Matches 4 and 5 finish quickly. We also see a slight dip in Match 8 – this equates to Francesco Molinari (who has only won 25% of his points so far) struggling against Tiger Woods (who has 2 wins from 3). But the biggest blue bar is saved for Match 10 which would mean Peter Hanson scoring a memorable victory over Phil Mikelson. Anyway, back to work, and stop watching the live updates…