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Maximizing weekly AND season-end winnings

 Confidence pool, Office pool strategy, Weekly Payout  Comments Off on Maximizing weekly AND season-end winnings
Aug 062014
 

(Updated Sept. 2)

A reader requests the optimal strategy for maximizing his pool winnings. He writes:

I’m in a small pool that pays both weekly and at the conclusion of the season. To maximize my payoff, I need to win weeks and finish on top. 60% of the funds are paid weekly, the rest after week 17. I need enough variability to win weeks, but not too much, first place pays 20% of the pot.  

Five obstacles argue against tuning your strategy too precisely: risk, noise, user error, modeling other entries in your pool, and the bias/variance tradeoff.

Risk
The accuracy of picking favorites to win outright varies over time. Typically it ranges between 60% and 70%. Some years it is as low as 57% or as high as 75% over the course of a season. We can go three years without getting a single week when all the favorites win. So even using the highest expected point model, such as WinThatPool’s, is no guarantee you will win your pool by season-end, although in most small pools (say, fewer than 20 entries) it should always rank near the top. In pools with 50 to 100 entries, depending on the others’ skill and on the year you should finish in or near the top five, but coming out #1  is not guaranteed.

Noise
An NFL season entails only 256 games spread among 17 weeks. That is a small sample size, with lots of room for bad streaks for the best model and good streaks by useless models. Better to join a pool whose season stretches into the playoffs.

User error
Have you ever entered the wrong side of a game you picked correctly just because Yahoo! or ESPN or poolhost displayed the game wrong, or at least differently from how you expected? It only takes one of those slip-ups to put you permanently behind. I have seen other pool members forget to pick the winner of the Monday night game in time and miss out on winning that week. It happens.

Modeling other entries in your pool
There is a right way to do this, and it is beyond most entrants’ capabilities. It is quite complex, and it entails simulation. In 2009 WinThatPool used to recommend confidence pool picks to optimize winning that week’s pool. Such recommendations depend heavily on the size of the pool, that is, the number of other entries. If demanded by enough readers, WinThatPool might add that feature back.

Bias/variance tradeoff
WinThatPool’s recommendations are effectively unbiased, which is ideal for maximizing points over the course of a season. Lots of entries pick the right favorites but their confidence ranks are biased. Unbiased confidence ranks are what you want for a season-long prize. Compare WinThatPool’s picks to, say, Brian Burke’s win probabilities on AdvancedFootballAnalytics(AFA). Which teams will win is seldom in disagreement between our picks, but in the past Burke’s probabilities have been biased – that is his 80% and 90% picks have not won 80% and 90% of the time. If you applied his picks in a confidence pool, you probably finished out of the running for a season-long pot.

Weekly strategy: Deviate on one heavy favorite
The corollary is WinThatPool’s recommendations are a starting point (hence the slogan, “your starting point for winning office pools”). If you really want to risk your season-long ranking by going against the model, select one of the highest confidence games that week and pick the underdog without changing the confidence points. For week 1 in 2014, that might mean picking Buffalo over @Chicago, and leaving it at 14 points. Your expected point total is worse than picking @Chicago, but if the upset occurs so few of your pool-mates will pick Buffalo that you’re in a good position for the Week 1 pot. Another possibility is to use a different, biased set of confidence ranks. For example, you could simply apply AFA’s picks, but so many people read those picks in the NYTimes chances are you won’t be the only one doing so.

By the way, I am not complaining about AFA or its model. AFA (formerly known as Advanced NFL Stats)  is an innovative sports analytics blog. Brian Burke has influenced how the game is played – how many sports sites can say that? Burke was an early critic of received wisdom that too often resulted in overly conservative play. I credit him with evolving how fans, commentators, and even coaches think about football strategy and tactics, and specifically for catalyzing the growing tendency for NFL coaches to go for it on fourth down.

Update – I would add that AFA’s in-game modeling is revolutionary, and one of the primary reasons so many pay attention to AFA. 

Best strategy? Start with the season-end strategy and switch if necessary
If after several weeks you fall too far behind you can always switch from the season strategy to the weekly strategy, but you probably cannot do the opposite unless you win Week 1. Figure out in advance what your expected winnings are for the weekly pot and the season pot by assuming a 1/n chance, where n is the number of entries. Compare your expected winnings for 17 chances at the weekly prize with one at the season prize. Pick either strategy and pursue that. If you start out with the season-end strategy, you will probably contend for the season pot, and maybe through a combination of other users’ errors and noisy luck, you might also win a week.

 Posted by on August 6, 2014 at 1:38 pm

Pomeroy Ratings Worked as Designed in Rounds 1, 2

 March Madness, Pomeroy, Weekly Payout  Comments Off on Pomeroy Ratings Worked as Designed in Rounds 1, 2
Mar 222010
 

Prior to the tournament tip-off, the Pomeroy ratings predicted just under 24 favorites (not necessarily higher seeds, favorites) to survive the first round and 9 of them to survive through the second round.  The actual results:  24 survived Round 1, another 8 survived Round 2.

 Posted by on March 22, 2010 at 5:04 pm

Why the Demographics of Your Pool Matter

 neglected teams, Office pool, Office pool strategy, Weekly Payout, WPM  Comments Off on Why the Demographics of Your Pool Matter
Nov 112009
 

The only way the demographics of your pool would not matter would be if all other participants picked teams at random. If that were the case, you could just pick all the favorites all the time. You’d win all the season-ending payouts and more weekly payouts than anyone else.

But they don’t pick at random, do they? They mostly pick favorites, sprinkling in a few upsets here and there. That creates an opportunity for you, at least in terms of winning more weekly payouts than anyone else.

By picking mostly favorites most of the time, the other participants are behaving rationally as individuals but irrationally as a group. Take a look at some of the weaker favorites — those whose Win Probabilities are less than 70% — and you’ll notice that frequently the percentage of participants who picked them was still quite high, maybe over 90%. If the Win Probabilities are accurate, those favorites might lose between one third and half the time but when they do almost nobody in your pool will reap the benefit. So why don’t you reap the benefit?

The trick is threefold: 1) Forecast the number of participants in your pool who will pick each team, 2) identify underbet teams relative to their win probabilities, and 3) simulate game/pool outcomes thousands of times to determine the optimal number of underbet teams to pick in your pool. Those form the basis of Weekly Payout Maximizer recommendations.

The right number changes from week to week, according to the win probabilities and fan pick forecasts. For Regular scoring pools it’s also different from the right number for Confidence pools.

 Posted by on November 11, 2009 at 10:05 am

NFL Contrarian: Weekly Payout Maximizing Picks for Week 9

 neglected teams, NFL, Office pool, Office pool strategy, Weekly Payout, Win probability, WPM  Comments Off on NFL Contrarian: Weekly Payout Maximizing Picks for Week 9
Nov 082009
 

For Confidence Pool participants with fewer than 22 participants, Tennessee is likely to be underbet relative to its WinProbability. You’re more likely to win this week’s payout with the picks below. If you’re participating in a pool with several fans of Tennessee, since Tennessee might not be underbet in your pool, you’ll find alternative picks are below.

Points Pick WinProb
13 Tennessee 39%
12 New Orleans 79%
11 Atlanta 76%
10 New England 75%
9 Seattle 75%
8 Green Bay 75%
7 Indianapolis 72%
6 Jacksonville 67%
5 New York G 62%
4 Pittsburgh 58%
3 Baltimore 58%
2 Chicago 58%
1 Philadelphia 58%

For pools with Tennessee fan bias and fewer than 22 participants:
Points Pick WinProb
13 Kansas City 33%
12 New Orleans 79%
11 Atlanta 76%
10 New England 75%
9 Seattle 75%
8 Green Bay 75%
7 Indianapolis 72%
6 New York G 62%
5 San Francisco 61%
4 Pittsburgh 58%
3 Baltimore 58%
2 Chicago 58%
1 Philadelphia 58%

For pools with 22 or more participants, you’re advised to pick 2 underbet teams.

Points Pick WinProb
13 Tennessee 39%
12 Kansas City 33%
11 New Orleans 79%
10 Atlanta 76%
9 New England 75%
8 Seattle 75%
7 Green Bay 75%
6 Indianapolis 72%
5 New York G 62%
4 Pittsburgh 58%
3 Baltimore 58%
2 Chicago 58%
1 Philadelphia 58%

For pools with 22 or more participants and several fans of Tennessee, use these picks:

Points Pick WinProb
13 Kansas City 33%
12 Dallas 42%
11 New Orleans 79%
10 Atlanta 76%
9 New England 75%
8 Seattle 75%
7 Green Bay 75%
6 Indianapolis 72%
5 New York G 62%
4 San Francisco 61%
3 Pittsburgh 58%
2 Baltimore 58%
1 Chicago 58%

For pools with 22 or more participants and several fans of Kansas City, use these picks:

Points Pick WinProb
13 Tennessee 39%
12 Dallas 42%
11 New Orleans 79%
10 Atlanta 76%
9 New England 75%
8 Seattle 75%
7 Green Bay 75%
6 Indianapolis 72%
5 Jacksonville 67%
4 New York G 62%
3 Pittsburgh 58%
2 Baltimore 58%
1 Chicago 58%

 Posted by on November 8, 2009 at 6:37 am

Football Pool Participants Misunderstand Randomness: Pick a few underdogs they overlook

 Confidence pool, neglected teams, Office pool, Office pool strategy, Weekly Payout  Comments Off on Football Pool Participants Misunderstand Randomness: Pick a few underdogs they overlook
Oct 312009
 

Knowing Win Probabilities is necessary to have a shot at winning your office pool, but it’s not sufficient. It’s not sufficient because Win Probabilities are an open secret: your friends in your pool know them, too. And they’re everywhere, and the best ones are free. Even if they weren’t everywhere, you could estimate your own to a very high degree of accuracy by looking at Vegas money lines. You don’t even have to visit betting websites to see Vegas lines; they’re available in USA Today in plenty of time for you to make your picks.

This is why I make my Win Probabilities available for free as a convenience to my visitors. Mine are based on a generic formula derived from Vegas lines. Other estimates of Win Probabilities, Power Indexes, or rankings abound — one of the longest lived and best known is Jeff Sagarin’s Predicted Points model on USA Today. Brian Burke’s WinChance estimates are made available on the New York Times website after a few weeks into the season, and his record is enviable. I wouldn’t discourage anyone from using them; both are very impressive. But over time, I expect sports bettors and books learn which models work the best and their lines gravitate toward the best models anyway.

The fact that your friends know about Win Probabilities, point spreads, or power rankings means that everyone in your pool will pick mostly favorites, most of the time, and if it’s a confidence pool they’ll rank the teams in descending order by Win Probability. Therefore, most of their pick sheets will look remarkably similar. You need to stand apart.

Predicting upsets is a futile exercise in guessing random outcomes. You can either waste your energy trying to predict upsets, or you can focus instead on which upsets, if they occur due to randomness, will help your picks stand apart. So you need to consider the joint distribution of game outcomes and participant picks. By selectively choosing an upset or two, you can let randomness do your work and when those upsets occur, you will stand apart in your weekly pool results.

 Posted by on October 31, 2009 at 11:50 am

Helpful Information Hidden in Plain Sight: Other Participants’ Picks

 neglected teams, Office pool, Office pool strategy, Weekly Payout, Win probability, WPM  Comments Off on Helpful Information Hidden in Plain Sight: Other Participants’ Picks
Oct 312009
 

If you play office pools using some of the largest online pool websites — ESPN, Yahoo, UPICKEM, etc. — you can see the percentages of other users’ picks for every team. If you take a look at them, you’ll notice they’re remarkably similar. But how do you use this information? Here’s how: it is a decent initial approximation for the percentages of picks in your own local pool.

Let’s say 10% of all users on ESPN picked Cleveland, and you play in a pool with 15 participants. Using the ESPN distribution estimate, that means you can expect 1.5 of your participants picks Cleveland.

But it can’t be 1.5. It could be 1 or 2. It could also be 0, 3, 4, or 5, or more if you’re playing in a pool of Cleveland fans. Given the ESPN probability p, where p=10%, the formula for estimating the probability in an N-participant pool that a certain number i picked a team is:

Combin(N,i)*p^i*(1-p)^(Ni)

Enter that formula in Excel, substitute the is and you can see the probabilities that the number of your friends who picked Cleveland are:

0 21%
1 34%
2 27%
3 13%
4 4%
5 1%

If you’re not considering this for every game every week, you’re short-changing your office pool picks.

 Posted by on October 31, 2009 at 11:25 am

NFL Contrarian: Weekly Payout Maximizing Picks for Week 8

 Confidence pool, neglected teams, Office pool strategy, Weekly Payout  Comments Off on NFL Contrarian: Weekly Payout Maximizing Picks for Week 8
Oct 312009
 

For Confidence Pool participants with fewer than 30 participants, Buffalo is likely to be underbet relative to its WinProbability. You’re more likely to win this week’s payout with these picks: (Buffalo fans, your picks are below)

Points Pick WinProb
13 Buffalo 41%
12 San Diego 87%
11 Chicago 82%
10 Indianapolis 80%
9 Arizona 76%
8 New Orleans 74%
7 Dallas 73%
6 Detroit 61%
5 New York J 60%
4 Baltimore 58%
3 Tennessee 58%
2 Green Bay 58%
1 New York G 52%

For Buffalo fans, if your pool is teeming with other Buffalo fans then Buffalo probably won’t be underbet. Use this pick set instead.

Points Pick WinProb
13 Philadelphia 48%
12 San Diego 87%
11 Chicago 82%
10 Indianapolis 80%
9 Arizona 76%
8 New Orleans 74%
7 Dallas 73%
6 Detroit 61%
5 New York J 60%
4 Houston 59%
3 Baltimore 58%
2 Tennessee 58%
1 Green Bay 58%

If your pool is larger than 30 participants, you’ll need two underbet underdogs. Your choices are below:

For non-Buffalo, non-Philly fans:
Points Pick WinProb
13 Buffalo 41%
12 Philadelphia 48%
11 San Diego 87%
10 Chicago 82%
9 Indianapolis 80%
8 Arizona 76%
7 New Orleans 74%
6 Dallas 73%
5 Detroit 61%
4 New York J 60%
3 Baltimore 58%
2 Tennessee 58%
1 Green Bay 58%

For Buffalo fans:
Points Pick WinProb
13 Philadelphia 48%
12 St. Louis 39%
11 San Diego 87%
10 Chicago 82%
9 Indianapolis 80%
8 Arizona 76%
7 New Orleans 74%
6 Dallas 73%
5 New York J 60%
4 Houston 59%
3 Baltimore 58%
2 Tennessee 58%
1 Green Bay 58%

For Philly fans:
Points Pick WinProb
13 Buffalo 41%
12 St. Louis 39%
11 San Diego 87%
10 Chicago 82%
9 Indianapolis 80%
8 Arizona 76%
7 New Orleans 74%
6 Dallas 73%
5 New York J 60%
4 Baltimore 58%
3 Tennessee 58%
2 Green Bay 58%
1 New York G 52%

 Posted by on October 31, 2009 at 10:50 am

The Football Pool Strategy Paradox

 neglected teams, Office pool strategy, Weekly Payout  Comments Off on The Football Pool Strategy Paradox
Oct 262009
 

Football pools are not contests of football knowledge or predictive ability:  they’re contests of strategy and discipline.

    Strategy paradox:  Never pick upsets for a season prize; always pick upsets for weekly prizes

For a season payout pool you stand a better chance of winning the prize if you pick all the favorites each week, regardless of whether you believe they’ll actually win.  You don’t realize how overconfident you are in your own beliefs, but if you ignore them and follow the discipline you’ll be in the running entering the final week(s) of the season.

For a weekly payout pool you’ll win more often if every week you selectively pick an upset or two, even if you’re certain those underdogs won’t win.  “Selectively” does not refer to using a better upset prediction model, it refers to picking teams your friends are not picking.

    Discipline:  On weeks when it doesn’t win the weekly payout strategy can make you look like you know nothing about football

Let’s say you’re in a 17 person pool with a weekly payout.  An average participant should expect to win one payout in a 17 week season.  By using the weekly strategy, you could win 2 or 3 times in a season, but you might come in dead last a dozen times too. Even though there’s no cost to losing badly versus losing well, not winning several weeks in a row can undermine your confidence in the strategy

 Posted by on October 26, 2009 at 1:30 pm
Oct 242009
 

If you’re playing in a pool with Weekly Payouts, you have an opportunity to profit by your friends’ tendency to overpick favorites.

Thousands of simulations using this week’s Win Probabilities and likely user pick distributions reveal the following are the picksheets most likely to win you this week’s payout. “Most likekly” doesn’t refer simply to the underdogs most likekly to win, but to the underdogs most likely to win and not have been picked by others in your pool. The number of upsets is conditional on the number of participants in your pool, which is why there are multiple pick sheets below.

Confidence Scoring
60 or fewer participants
WPM Pick WinProb

13 KANSAS CITY 35%
12 NEW ENGLAND 89%
11 INDIANAPOLIS 86%
10 PHILADELPHIA 71%
9 GREEN BAY 71%
8 NEW YORK G 71%
7 CAROLINA 71%
6 NEW ORLEANS 70%
5 NEW YORK J 68%
4 PITTSBURGH 65%
3 DALLAS 63%
2 HOUSTON 60%
1 CINCINNATI 53%
Expected 62.5

Confidence Scoring
61 or more participants
WPM Pick WinProb
13 KANSAS CITY 35%
12 CLEVELAND 29%
11 NEW ENGLAND 89%
10 INDIANAPOLIS 86%
9 PHILADELPHIA 71%
8 NEW YORK G 71%
7 CAROLINA 71%
6 TEN 70%
5 NEW YORK J 68%
4 PITTSBURGH 65%
3 DALLAS 63%
2 SEA 60%
1 MIA 53%
Expected 57.1

If your pool uses Regular scoring (each correct prediction has the same weight as each other), the same picks and numbers of upsets apply, according to the number of participants in your pool.

 Posted by on October 24, 2009 at 7:38 am