Michael,
On every page of this thread, Tiger Woods is mentioned as most likely the only player in the history of the game who’s average was good enough to win at a measurable rate.
You yourself even stated it in Reply #46:
In any case, I think peak Tiger could show up and play at his average and still win. He wasn't guaranteed to win (he was pretty much guaranteed to win when he did outperform himself - think 2000 US Open and Open), but he could win. Just about anyone else needs things to fall their way to win in a given week.
Continuing to bring up Tiger as an example of average strategy and attempting to extrapolate his once in forever level of performance to the rest of the PGA Tour demonstrates a gross misunderstanding of the basis for this discussion.
That same misunderstanding appears to have been applied to the coin flip example. The example YOU established in Reply #76. I just simply ran the test. If you don’t like the results, that's on you.
Since you no longer like the coin flip test, let’s dive deeper using ACTUAL scoring data:
Through Colonial last year, 21 events and 105,065 combined holes played, the unadjusted scoring average on the PGA tour was 71.15. Par for the combined calendar of courses over that period was 71.52. The average scoring range on the tour at that time was from 69.24 to 73.62.
The breakdown of individual scoring over those 105,065 holes was as follows:
- -2 (0.62%)
- -1 (21.53%)
- E (62.82%)
- +1 (13.83%)
- +2*(1.19%) *Double Bogey or Greater
Using these probabilities we can create a weighted simulation to test what would happen if a group of randomly generated players played against the low scoring average. This time, rather than using a 50% field average, the percentage was increased to 75%, leaving only 36 of 144 players trying to ride out a hot streak to the win. As the best scoring average was 2.28 strokes under par, the threshold to ensure a win would be set at -9.12. So the test group would have to have a player shoot -10 or better to ensure a win.
After 1,000 simulated tournaments, The test group won 999 tournaments and the average benchmark won 1 tournament.
That’s it, just 1.
A 0.1% win rate.
It even surprised me that it was that low!
Comparing the simulated wins to the actual wins from the source data, the range of winning scores and win average match up to each other. It is clear that the simulation created an accurate portrayal of real world events.
| Simulated Wins (1000) | Actual Wins (25) |
Lowest Winning Score | -25 | -25 |
Average Winning Score | -16.26 | -16.05 |
Median Winning Score | -16 | -17 |
Highest Winning Score | -9 | -6* |
Wins Below Threshold | 1 | 1 |
*2021 PGA ChampionshipIf you care to take a look at the simulation results, or to run your own simulation, you can do so here:
GCA: PGA Tour Winning Simulator (Weighted Scoring) Since you insist on bringing up Tiger Woods, let's look at what an average 2000 Tiger Woods would do in this scenario. With an unadjusted scoring average of 68.17 for the year, Tiger’s average four day score would be -13.4. Running another 1,000 tournament simulation, Average Tiger Woods would win 13.8% of the time. Out of his 9 wins in 2000, only one of them was anywhere near or below this threshold, the US Open. Looking into the other 8 wins that year, his average play would have only won 3 of them. Even Tiger needed to chase his tail to win at the rates he did.
First of all, it's not birdie or bogey vs par. It's something like this:
Aggressive: birdie 22%, par 58%, bogey 20%
Optimal: birdie 19%, par 70%, bogey 11%
Now run each of those for 72 players each and 72 holes each and then tell me who wins most of the time.
Where did your numbers come from?
The Aggressive group’s probabilities are very close to PGA Tour averages that I posted above. The PGA Tour averages should have been used as a control group for your test, not as an experimental group. Especially when you consider the average PGA Tour player has nearly the same birdie probability with a significantly less bogey probability. Clearly you assume a greater risk has to be taken on to earn birdies than is actually true.
How can you justify the change in Aggressive (average) strategy to “Optimal” strategy? Only a 3% reduction in birdie probability to a 12% increase in par probability, and a 9% decrease in bogey probability! So a minimal difference in birdie potential, but a much lower risk of making a bogey! How are you correlating that? Do you actually have data to support those probabilities?