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## Main Question or Discussion Point

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

Keegan Bradley 1416

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.

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

Keegan Bradley 1416

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.