Are Luck and Favorable Variation the Same Thing?

Recently, I attended a conference at which there were several talks analyzing aspects of competitive games. In one of them, the speaker contended that the qualifying mechanisms for the PGA Tour were not very good -- particularly Q-school. His basic argument was, due to natural variations in golfers' scores, the limited number of rounds in Q-school, and the ratio of qualifiers to participants, there was a decent probability that some relatively weak golfers would make the Q-school cut at the expense of more deserving golfers. (He backed this up with a statistical analysis using empirical data.) I don't remember the exact figure, but I think he estimated about a 20% probability that Phil Mickelson would fail to make the final Q-school cut, which is quite high considering he's probably one of the top ten golfers in the entire world, let alone those trying to qualify for the PGA Tour.

In explaining his work, the speaker kept using some form of the word "luck", as in, "given a large number of golfers it's almost inevitable that some of them are going to get lucky and beat people who are better than them." About halfway through the talk somebody in the audience stopped him and said, "I don't buy your premise that this is luck. I've played a lot of golf and watched a lot of golf. You don't luck your way through multiple rounds, you have to outplay people, so I'm not buying it." A somewhat contentious, back-and-forth ensued, before the speaker conceded the point and said, "fine, we have a disagreement on the definition of luck, so I'll just use the term 'favorable variation', from now on." This seemed to placate the man in the audience.

It made me think. Are luck and favorable variation the same thing? As an example, consider poker, a game in which luck and skill are both large factors. There are two basic ways a poker player can beat a superior opponent. The first is they get really lucky, in the conventional sense of the word. Their opponent completely outplays them, but through total chance, they hit their cards and win (think flushes and full houses on the river). This is obviously not sustainable (see the law of large numbers or this Mark Knopfler title). The second way is that the inferior opponent experiences favorable variation. They outplay their opponent on that particular occasion. Maybe they notice an aberrant betting tendency by their opponent and exploit it, or maybe they are just "in the zone", and they make all the right reads, while their opponent makes the wrong reads. This is not sustainable either, because their opponent is better and eventually will adapt, and the tides will turn, but is this luck? On the one hand, you might say "no", it's skill, the usually inferior player just played better. There is nothing lucky about it. On the other hand, you might say "yes". It is a deviation from the expectation that favored the inferior player, and in this sense it's indistinguishable from the first scenario.Whatever the answer, it's an interesting question.

He's just upset

A quote from Maurice Jones-Drew running back for the Jacksonville Jaguars expressing his discontent about not getting the ball enough and the offense in general during a loss to the Seattle Seahawks

I'm very frustrated. We're not consistent with anything. We had, what, 13 running plays last week? We weren't behind the whole game.

True, it was 0-0 for first drives of the game. The Seahawks scored on their second drive and went on to win 41-0.

Week 4: TMQ Tidbit

Tidbit from this week's TMQ.

At the endgame, Green Bay faced a tactical dilemma TMQ thinks most coaches play wrongly. Down 30-20, facing a fourth-and-6 on the Minnesota 14 with one minute remaining, Green Bay kicked a field goal, then tried an onside kick. NFL coaches in this situation almost always take the field goal, then the onside kick. You need a touchdown and a field goal. If you take the field goal and then recover the onside kick, you are at least 50 yards from a touchdown. Before the field goal, Green Bay was only 14 yards from a touchdown. The Packers' chance of converting a fourth-and-6 and getting the touchdown from close range was greater than their chance of kicking a field goal and then scoring a touchdown from long range. Score the touchdown first, and if you recover the onside kick you're only 20 yards from the field goal attempt. TMQ thinks coaches almost always take the field goal in this situation because what they're really doing is playing to make the final score closer.

The bold font was added by me, because it's typical TMQ. Where does this statement come from? Is this just his guess? Does he actually have an estimate for the probability of winning in each scenario? The statement might very well be true, but it's by no means obvious. Sure, the Packers are closer than they would be after an on-side kick recovery, but it's 4th down. After the recovery it would be 1st down. This is a crucial point that he neglects to take into account. Let's say it was 4th and goal from the 14, instead of 4th and 6. Would TMQ still advocate going for it, under the same rationale: the Packers are only 14 yards away from the endzone, as opposed to the 50+ they would be after an on-side kick recovery? What about if it was 4th and 20 from the 25?

Also, I don't agree with his thought in the last sentence. I don't think that NFL coaches are playing to make the final score closer. I think NFL coaches are trying to win, but as I've mentioned before, I think they often equate putting off a loss with going for a win. If the Packers go for it, there is a decent chance they fail, and it's basically game over. If they kick there is a very good chance they make it, and they still have a slim hope of winning. Kicking might be the wrong move, but it's the move that has the highest probability of extending the game. And in scenarios like the one at hand, the move that has the highest probability of extending the game seems to be the one many NFL coaches prefer.