Algorithm for Playoff Scenarios?

• brocks
In summary, the final playoff event before the Tour Championship starts tomorrow for professional golf. Players earn points throughout the regular season and the top 125 are eligible for the first playoff event. The points earned in the playoff events are higher than in the regular season and are added to the players' totals. The top 100 players after the first event, top 70 after the second event, and top 30 after the third event proceed to the Tour Championship. It is possible to predict how far a player can fall in the standings by inputting the points chart and current totals, assuming optimal play from the competition. This can be solved mathematically using an excel sheet or the simplex algorithm.

brocks

If you follow professional golf, you know that the final playoff event before the Tour Championship starts tomorrow.

During the regular season, in addition to tons of money, the players earn points according to how they finish in each event. The points charts are here:
http://www.pgatour.com/fedexcup/fedexcup-overview.html

The 125 players with the most points are eligible to compete in the first playoff event. The top ten players (with their points shown) at the beginning of the playoffs this year were:

Tiger Woods 3059
Matt Kuchar 2293
Brandt Snedeker 2218
Phil Mickelson 2166
Bill Haas 1505
Billy Horschel 1487
Justin Rose 1447
Jordan Spieth 1436
Henrik Stenson 1426

In the playoff events, the points for a given placing are higher than in the regular season (see the charts in the link above). Playoff points earned in the first playoff event are added to what the players earned during the regular season, and the 100 players with the highest totals proceed to the second event. The top 70 players after that event proceed to the third playoff event, and the top 30 after that proceed to the Tour Championship.

My question is, is there an algorithm (other than brute force) that can tell you how high a player is guaranteed to finish at each stage?

For example, Tiger Woods started the playoffs in first place, with over 3000 points. He's earned another 1000 points in the first two playoff events, but suppose he had played terribly and earned zero points in the first two events. His 3000 points would still be in fifth place now, so he would easily be eligible for this week's playoff event, and probably wouldn't need any more points to get into the Tour Championship next week.

In the real world, the best players tend to finish high every week, so most of the points go to a small number of players, so Tiger won't fall very far, even with bad play. But in a worst case scenario, each player below Tiger could earn just enough points to pass him, and he would fall much farther down the standings than in the real world.

I'm looking for a way to input the points chart and the current totals, and output the farthest a player can fall in the next one, two, or three events, assuming optimal play from the competition.

If anyone can point me to a website that discusses this kind of problem, I'd be very grateful.

This sounds as if an excel sheet would be the appropriate tool to solve it. It all depends on the data you have given, i.e. how the points are gained or lost. To solve it mathematically, it looks as if it is a linear optimization problem, solvable by e.g. the simplex algorithm.

What is an algorithm for playoff scenarios?

An algorithm for playoff scenarios is a set of steps or instructions that can be followed to determine the possible outcomes of a sports playoff. It takes into account the rules and regulations of the sport, the current standings of teams, and any tie-breaking procedures to determine the potential matchups and outcomes of the playoffs.

Why is an algorithm for playoff scenarios important?

An algorithm for playoff scenarios is important because it provides a systematic and unbiased way to determine the potential outcomes of a playoff. It takes into account all relevant factors and eliminates any potential biases or human errors in the decision-making process.

How is an algorithm for playoff scenarios developed?

An algorithm for playoff scenarios is developed by analyzing the rules and regulations of the sport, studying past playoff scenarios and outcomes, and considering any tie-breaking procedures that may be in place. It may also involve using mathematical models and simulations to determine the most likely outcomes.

Can an algorithm for playoff scenarios accurately predict the outcomes?

An algorithm for playoff scenarios can accurately predict the potential outcomes, but it cannot predict the actual results of the playoffs. There are many variables and factors that can affect the actual outcomes, such as injuries, team dynamics, and unexpected events.

How often is an algorithm for playoff scenarios used in sports?

An algorithm for playoff scenarios is commonly used in sports, especially in professional leagues where the stakes are high and the outcomes can have a significant impact. It is also used in fantasy sports and by sports analysts and commentators to make predictions and analyze potential playoff matchups.

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