Probability, Golf, Wagers

CONGRATULATIONS to Charl Schwartzel on winning the Masters yesterday!!!! It was highly entertaining and extremely contentious championship to the end. Of course any golf major that Tiger Woods does NOT win is a GOOD golf major. Tiger threw a scare into the field with a 31 on the front nine but eventually finished fourth, four shots back of the winner.

What do I have against Tiger Woods???? Nothing really. Nothing personal anyway. Except that I grew up as a Nicklaus fan, and this tiger does NOT change his stripes.

Ever since Tiger won his first major (the 1997 Masters) it has become accepted as DOGMA that Tiger will eventually break Nicklaus’s record of 18 professional major victories. It has been accepted as a “foregone conclusion.”Sort of like it was a “foregone conclusion” that Big Brown would win the 2008 Belmont Stakes and Triple Crown (as erroneously predicted by his trainer, who shall remain nameless).

Tiger has won 14 major professional golf championships, still short of Nicklaus’s 18. All this reminds me of a story about a small wager I made back in 2006. I recall this story for your possible edification.

It was the summer of 2006. I was taking a smoke break at work, outside the offices of TJC. I was joined by a coworker by the name of Matt. As usual, we proceeded to shoot the sports BS. Not sure how we got there, but he inquired what kind of odds I would give him on Tiger winning the next three golf majors (2006 PGA, 2007 Masters, and 2007 US Open).

I did some preliminary calculations in my head. Tiger at that point had won 11 of the 39 majors in which he had played. Therefore, I estimated that the odds of him winning any given major were abut 5-2 (2.5-1; 28 losses versus 11 wins; technically 2.55-1). So I mentally calculated 2.5 x 2.5 x 2.5 = 15.625, cut that in half, and generously offered Matt 8-1 on his stated proposition. I thought at that time that the correct odds were between 15-1 and 16-1.

So I offered 8-1. That is the ultimate purpose of wagering. Get the odds on YOUR side. Place the opponent on the SHORT side of the correct odds. Matt held out for 10-1. We compromised on 9-1, my $90 against his $10.

I got to thinking about the mathematics of it all later though and realized that I had actually screwed Matt a lot worse than I originally thought. The actual odds should have been more like 40-1 or 50-1. The mathematics are complicated (at least to most people). I will delve into them as a sidebar at the conclusion of this post.

Of course I was tempted to point out to Matt how cleverly I had screwed him. Except he got in the first word. He proceeded to tell me how he had consulted a college “professor” of “statistics” who had assured him (Matt) that he had a “good” bet. I tried to explain to Matt that yes, 9-1 was a good bet if the odds of Tiger winning a single tournament (major or otherwise) were even (50% probability of winning; 7-1 were the correct odds if the probability of winning a single event were 50%). But if the odds of Tiger winning a single tournament (major or otherwise) were less than 30%, then the odds of Tiger winning any three tournaments consecutively were astronomically higher.

I tried to point out that even at the height of his best form, Tiger was never even money to win a given tournament. He was usually 2-1, 5-2, 3-1, somewhere around that (right in line with his overall results of 11 of 39 in the majors).

Needless to say, Matt was impervious to my explanations. He thought he had a “good” bet. A “professor” of “statistics” had told him so. So I studiously avoided Matt for awhile. It was either that or tell him what a XXXXXXXXing IDIOT he really was. I chose discretion.

Unfortunately for me Tiger won the 2006 PGA at Medinah by many strokes. I FUMED. I FUMED and studiously avoided Matt for the next eight months.

It is a peculiarity of the golf calendar that the four majors are played in April, June, July, and August. It is eight months between the last major of one year and the first major of the next year.

Fortunately for me, Tiger did NOT win the Masters in April of 2007. Zach Johnson did. That was the FROZEN Masters. Tiger did make a good run at it. His second shot in the water on Sunday at 15 did him in.

And I have to give Matt credit. I did not have to TRACK him down to collect my $10. He showed up at my cubicle Monday morning and congratulated me and concluded the wager in a satisfactory manner (with $10 passing into my hand). I ceased avoiding him after that.

Just for the record, Tiger did not win the 2007 US Open either. Angel Cabrera did. Tiger finished one shot behind Cabrera. I have to give Tiger credit. If he does not win, he is usually right there in contention. I sincerely hope that Tiger finishes SECOND in at least 18 more majors.

And the moral, of this story is???? I could say that understanding probability and mathematics might just help you to wager more successfully (in a general sense, not strictly with relation to horse racing).

But the real moral of this story is about breaking records. The “foregone conclusion” does not seem quit so “foregone” anymore. What are the actual odds now that Tiger will break Nicklaus’s record of 18 professional major victories????

My answer would be: not nearly as “foregone” a “conclusion” as it appeared to be back in June of 2008, when Tiger won his 14th major (the US Open at Torrey Pines). Tiger is 35 now. The “young guns” are not afraid of him at all. The probability of him breaking that record diminishes now with each major tournament that he does NOT win.

——————————————————————————————-

SIDEBAR–THE ACTUAL NUMBERS

If the probability of one player winning any one event is 50%, then the probability of the same player winning three consecutive events is 12.5% (50% x 50% x 50% = 12.5%). One half times one half times one half equals one eighth. Eight possibilities. In one of those eight possibilities the player wins all three events. In the other seven possibilities the player does NOT win all three events. Correct odds are 7-1.

If the probability of one player winning any one event is 33.33% (one out of three), then the probability of the same player winning three consecutive events is 3.7%. One third times one third times one third equals one 27th. 27 possibilities. In one of those 27 possibilities the player wins all three events. In the other 26 possibilities the player does NOT win all three events. Correct odds are 26-1.

If the probability of one player winning any one event is 25% (one out of four), then the probability of the same player winning three consecutive events is 1.5625%. One quarter times one quarter times one quarter equals one 64th. 64 possibilities. In one of those 64 possibilities the player wins all three events. In the other 63 possibilities the player does NOT win all three events. Correct odds are 63-1.

You can verify these numbers by thinking of them as a three-race win parlay in terms of horse racing. A $2 three-race win parlay in which all three winners are even money pays $16 (7-1). A $2 three-race win parlay in which all three winners are 2-1 pays $54 (26-1). A $2 three-race win parlay in which all three winners are 3-1 pays $128 (63-1).

So given that Tiger was somewhere between 2-1 and 3-1 to win any given golf major, the odds of him winning three consecutive golf majors were somewhere between 26-1 and 63-1. If you use 11 of 39 as a past performance indicating future probability, the actual numbers were 11 x 11 x 11 (121) divided by 39 x 39 x 39 (59,319). So 59,319 total possibilities, 121 of them successful, 59,198 not successful. So the correct odds should have been about 49-1 (59,198 divided by 121).

You could make the argument that Tigers was so dominant back then that his actual odds of winning a single major were less than 2-1. The bookies disagreed. I do not recall the bookies ever offering odds as low as even money on Tiger winning a particular major. As I said before, he was usually favored at 2-1, 5-2, 3-1, somewhere in that vicinity.

Anyway, going strictly by the numbers, I should have given Matt something like 40-1 or 50-1 on the proposition instead of the 9-1 I actually did. Do I feel any remorse about that???? NADA. After all, a college “professor” of “statistics” had told him he had a “good” bet. Who was I to disillusion him????? I took his $10 instead. Perhaps that taught him a lesson. I kinda doubt it though.

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8 Responses to Probability, Golf, Wagers

  1. Pingback: Probability, Golf, Wagers | Boojum's Bonanza | http://Golf-USA.Co.Cc

  2. Pingback: Probability, Golf, Wagers | Boojum's Bonanza | http://Golf-USA.Co.Cc

  3. Pingback: Probability, Golf, Wagers | Boojum's Bonanza | GolfWarning

  4. Warren Wynshaw says:

    What are your odds calculation that Tiger will (or will not) beat Jack Nicklaus’ record of major wins?

  5. Pingback: Estimating Odds | Boojum's Bonanza

  6. Philip says:

    Managed to do the odds on Tiger beating Nicklaus’ record? got a mte who is begging me for odds as he thinks tiger is definitely going to win four more majors.. in fact, starting with this weekend.

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