My pick here and in five of my seven pools, the Cowboys, lost last week, and I'm disappointed about it. As much as I can cite the math and the reality that few of us were going to win our pools anyway, like many, I enjoy the action each week. Don't get me wrong - survivor is a miserable, unjust, stress-inducing form of torture, but the hope, the dream of getting a massive payout for a scant investment is like a drug. And while I stand by the notion that in order to optimize your chances of actually winning your pool, you need to take risks in proportion to their prospective payouts, for many, that hope is the reason they do this every year, and so how far they get matters a lot to them. Put differently, no one's happy when the keg runs out at the party - even if in the end drinking more beers probably wasn't going to get you laid anyway.
At the same time, I did note that the Packers had an 87 percent chance to win, and the Cowboys were merely at 80. If you strictly believe you should pick the team with the best chance to win this week, then last week's column should have influenced you to go with Green Bay. Again, I think that was the wrong play - at least according to the Yahoo! numbers and the Vegas ones - even though it ultimately panned out.
And as I wrote in East Coast Offense this week, considering only the odds of surviving this week and neglecting the payout commits you to some obviously terrible decisions. The question I asked was if 999 of your 1,000-person pool had the Packers, and you had just two choices, the Packers or the Bills, which team would you take? Even if we give the Bills just a five percent chance to win that game, you'd have a 1 in 20 chance to win your pool then and there. But if you went with the Packers, you'd have a 1 in 1000 chance to win. If you seriously would take the Packers, then you're either in denial about the true likelihood of your winning, or you're far more interested in enjoying the ride than giving yourself the optimal chance to win. To understand the magnitude of that error, consider this: the Patriots are -900 to win Sunday's game. That means you can risk $900 on the Patriots to win $100. Any sports book will take that bet. If you saw that 999 people were on the Pats this week in your 1,000-person pool, you could take the Bills and bet $90 K on the Pats. If the Bills win, you win your $100 K pool and lose $90 K to the book. IF the Pats win, you're out of your pool, but you won your bet. Either way you win $10,000. Or you could throw away $10,000 guaranteed in exchange for taking the Pats and hoping to turn your $100 entry fee into a winner over the course of the year.
That one has to consider both the payout and the likelihood of the win to optimize the chances for winning the pool is a fact no matter how many people are in it, the week of the year or your distaste for losing early. Unless your pool has a reward for making it to Week 6, or Week 8 or Week 10, when you go down makes no financial difference. It's win or bust, and in cases like that, it's often the optimal strategy to risk losing sooner rather than to take the longer, but less promising path. It's like going on 4th and 1 from your own 35 with three timeouts and three minutes left, losing 35-30. Sure, punting and hoping for the three-and-out keeps you alive longer, but the percentage play is to risk the game then and there to get the first down. It's also like being dealt 14 in Blackjack against the dealer's 10. You have to hit even though you could bust. If you stay, you get to hang around and see what the dealer has, but the math is the math. Sometimes, you'll bust, and the guy who stays will win, but that doesn't make it the right play.
Accordingly, I'm going to rank the teams both by likelihood of winning and the percentage of people taking them in Yahoo! pools. Again, if you simply prefer to take the team with the best winning percentage, then ignore the order I put them in and just pay attention to their likelihood of winning. It's your money, so you can hit or stay no matter what the dealer is showing.
Surviving Week 3
In my opinion, there are three big favorites (according to Vegas) that deserve consideration: the Patriots, the Ravens and the Vikings. According to Yahoo! 54 perecnt are on the Pats, 22 percent on the Ravens and 7 percent on the Vikings.
Vegas has the Pats at -900/+650 (let's average the two and say the real line is 775), the Ravens at -550/+425 (487.5) and the Vikings at -600/+450 (525). The odds translate to 775/875 for the Pats, 487.5/587.5 for the Ravens and 525/625 for the Vikings. That comes out to 89 percent for the Pats, 83 percent for the Ravens and 84 percent for the Vikings.
But the Vegas odds are just the current market value which while an essential starting point to the discussion is not necessarily perfect. Personally, I think the Lions are more dangerous than the Browns, and I trust the Ravens more than the Vikings. So I'll change it to Pats 88 percent, Ravens 84 percent and Vikings 78 percent. Using those numbers, which is the optimal play?
|Scenario 1||Scenario 2||Scenario 3||Scenario 4|
|Outcome||NE W, BAL W, MIN W||NE W, BAL W, MIN L||NE W, BAL L, MIN L||NE W, BAL L, MIN W|
|Odds||(.88*.84*.78) 58%||(.88*.84*.22) 16%||(.88*.16*.22) 3%||(.88*.16*.78) 11%|
|Scenario Equity||1/94 (of 10K) = $106||1/87 = $115||1/65 = $154||1/72 = $139|
|Expected Equity||$106*.58 = $61||$115*.16 = $18||$154*.03 = $5||$139*.11 = $15|
|Scenario 5||Scenario 6||Scenario 7||Scenario 8|
|Outcome||NE L, BAL W, MIN W||NE L, BAL W, MIN L||NE L, BAL L, MIN L||NE L, BAL L, MIN W|
|Odds||(.12*.84*.78) 8%||(.12*.84*.22) 2%||(.12*.16*.22) .5%||(.12*.16*.78) 1.5%|
|Scenario Equity||1/40 = $250||1/33 = $303||1/11 = $909||1/18 = $556|
|Expected Equity||$250*.08 = $20||$303*.02 = $6||$909 * 0 = 0||$556 * 1.5 = $8|
Because this has eight scenarios instead of 4 (due to three viable teams), I made it based on $100 per person in a 100 person pool. Also, because 53 of 100 took the Pats, 22 took the Ravens and 7 took the Vikings, that only adds up to 83, so there are 17 other entries which picked different teams. I assumed 11 of the 17 lesser choices (roughly two-thirds) would get through, i.e, these numbers assume six other people lose.
In scenarios 1-4, New England wins, and in 5-8 they lose. So if you take the Pats, you add up the expected equity of 1-4, and get $61 + $18 + $5 + $15 = $99. Essentially, given this spread of people picking the Pats and the percentages, the Pats cost you $1 in expected equity. The Ravens win under scenarios 1, 2, 5 and 6. They are: $61, $18, $20 and $6 for a total of $105. The Vikings win under scenarios 1, 4, 5 and 8. They are: $61, $15, $20 and $8 for a total of $104.
So given these numbers, the picks are 1. Ravens, 2. Minnesota, 3. Pats.
Here's a more qualitative breakdown of the games (Yahoo percentage picked in parenthesis).
1. Baltimore Ravens (22%) The Ravens seem to struggle for some reason against the Bengals, but their defense is still very stout, and the offense is likely to get going now that they're back home and not facing two of the league's better defenses. The Browns ability to run block and pass protect makes them a little bit dangerous, but unless Baltimore turns it over a bunch of times, they should be able to pull away. I give the Ravens an 84 percent chance to win this game.
2. Minnesota Vikings (7%)
The Vikings are Vegas' pick, given the Yahoo! pick distribution, i.e., had I plugged in the straight Vegas odds (which has the them at 84 percent). But as much as it's tempting to expect the Vikings to regress upward toward last year's mean, and the Lions to regress downward to the doormats they were, I have to wonder whether substantive and irreversible changes haven't taken place for both teams. Even a QB in his prime would be hard-pressed to repeat Favre's 2009, and for a guy coming off ankle surgery, turning 41 in a month and missing his top receiver (and with Percy Harvin dinged up, too), it's almost impossible. The Lions are in their second season under Jim Schwartz, have a healthy Calvin Johnson, an explosive tailback in Jahvid Best and made some defensive upgrades, particularly on the line. The bottom line, Minnesota could still roll, but I have them only at 78 percent.
3. New England Patriots (54%)
The Pats are the biggest favorites this week against a hapless Bills team, but Buffalo is strong against the pass, and New England has virtually no running game. The upgrade to Ryan Fitzpatrick who might be able to find Lee Evans down the field is a plus, but it'll still be a tall order for them to get on track in New England. I give the Pats an 88 percent chance to win this game.
4. Indianapolis Colts (1%)
Going on the road is never easy, especially when it entails playing at altitude, but the Colts looked about as sharp as a team can look last week, and it's hard to see how Denver will keep pace. I give the Colts a 68 percent chance to win this game.
5. San Diego Chargers (1%)
The Chargers got back on track against Jacksonville last week and should be able to handle a Seahawks team that seems to be in transition. The one caveat here is that Qwest Field is not typically an easy place to play given the crowd noise, something that seemed to have an effect on the Chargers in Kansas City. I give the Chargers a 67 percent chance to win this game.
Notable omissions: none