In sporting events, periodically a player or a coach tells the media that they are better than their record indicates. When they do this, a talking head on one of the sports programs tells the audience that this is just not true. A team is only as good or as bad as their record indicates.
This is drivel. Unquestionably incorrect. And yet it is repeated often enough that many people believe it. It’s easier to quote the catchy phrase “you’re only as good as your record” than to actually analyze a situation.
The correct play is the one that gives you the best chance for success if you played from a particular position hundreds of times. This may be called “expected points.” Your record is sometimes dominated by whether a particular play worked “this time.” This may be called “actual points.”
When you are trying to decide what to do, the best play is to try to maximize expected points. These don’t turn into actual points until after the play is run.
Every play at sports has a probability of success. Five years ago in the NFL playoffs, Tony Romo of the Dallas Cowboys uncharacteristically botched the hold on an easy field goal as time expired — so the Cowboys lost to the Seattle Seahawks 21-20. A field goal (which would have yielded 3 points and won the game for Dallas) from that distance is completed perhaps 98% of the time. That particular time fell into the other 2%. Dallas played well enough to win the game. But they lost on a fluke.
In the 2011 season, the Denver Broncos and their much-talked-about quarterback Tim Tebow, won several games in the fourth quarter or overtime that needed highly-improbable sequences of good fortune. Simply put, in 2011, the Broncos were not as good as their record.
In the early part of games, if a team has a fourth-and-goal from the 1 yard line, it’s usually the correct play to go for the touchdown — for two main reasons. First of all, they are likely to make it. And second, if they fail, their opponents have to go 99 yards to score. Still, a lot of coaches take the “guaranteed” three points from this position and go for the field goal.
Each year, some teams have a much tougher set of opponents than other teams. If your team faces a team on the one week when its star player is out, that’s pretty lucky for one team and unlucky for the other. A team with a 10-6 record may or may not be better than a team with a 7-9 record — despite what the pundits say.
The same is true at gambling. A smart way to bet is to try to maximize expected value. This will almost never turn out to be the same as actual value because you don’t know what actual value is going to be until it is too late to change it.
As an example, consider drawings. In May, Shirley’s name was called at a South Point drawing and we ended up with $28,000 (actual value) towards a new car. Our total equity showing up every day for the South Point drawings that month might have been $2,000 (expected value) for the two of us.
A few months later there was a similar set of daily drawings at the South Point — worth slightly less. The two of us together probably had an expected value of $1,500. The actual value turned out to be $0. I didn’t prepare any differently for the one we won versus the one we didn’t. I did my “due diligence” both times and we scored one time and not the other. And beforehand we had no idea if we’d score at all and if so, in which drawing.
I’ve entered drawings at other casinos where I was sure I had the most tickets and my name wasn’t drawn. Even if you enter a lot of drawings, your results won’t average out because drawings are different sizes. As an extreme, let’s assume you enter three drawings where first prizes are $50,000 or more, and 25 drawings where first prizes are $2,000 or less. It’s hard to define what “average” would mean.
At some casinos, I played a slightly negative game while earning tickets for the drawing — expecting (hoping) that the results of the drawing would more than make up for the losses on the play. I know the actual value of my winnings. And I know the actual amounts of my wins and losses from the play. I don’t know the expected value on the drawings. To figure that out I’d need to know how many other tickets were in the drawings. And that information is usually not available.
Strong players sometimes have losing years — and lucky players sometimes have winning years. In my case I’ve had one losing year since I started in 1994 — and I have a good “excuse” why that one losing year happened. Having a losing year now and then isn’t unusual.
If you have a losing year every year, pretty soon your excuses run hollow. If you’re making good choices and playing well, you’re going to come out ahead most of the time.
Without giving exact numbers, my annual scores over the last four years have been: big win, moderate loss, really big win, small win. The people who believe “you are what your record says you are” would say that I played good in 2008, best in 2010, poorly in 2009, and barely acceptable in 2011. I think that’s nonsense. I believe I played well all four years.
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