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Whether to pick upsets in your bracket depends on the pool’s scoring method

 2015, basketball, March Madness, Office pool, Office pool strategy, Tournament  Comments Off on Whether to pick upsets in your bracket depends on the pool’s scoring method
Mar 132015

The traditional NCAA bracket entry is scored in progressive powers of two, such that each round offers 32 points. First round games are worth 1 point, second round 2, etc., and the final game is worth 32.

The leverage of the championship game – worth 32 points out of a possible 192 – is why so many entries pick the overall favorite. This year that favorite will be Kentucky. I predict your pool, if it uses traditional scoring, will have over 40% of the entries picking Kentucky as the champ.

The problem with picking the overall favorite yourself is it is what is known as a “crowded trade.” You already know nearly half the other entries are picking Kentucky. So whether you win the pool, with Kentucky as your champ, is a different matter from whether Kentucky wins the tournament. If Kentucky wins, your pool’s champ will probably be determined by a handful of early round games.

The corollary to this is that if you’re confident in your picking ability, you SHOULD pick Kentucky, because you expect other entries to have worse records than yours in the earlier rounds.

I prefer to look for low hanging fruit in terms of strong teams being underpicked by fans in pools. I predict schools like Virginia, Arizona, Wisconsin, and Villanova will all be underrepresented in pool entries to win it all relative to their probability of winning the whole tournament. Imagine you’re the only one in your pool who picks Wisconsin – that’s a wide margin of error for any earlier round games that you missed. Compare that to if you pick Kentucky – your early round picks had better be nearly perfect.

Scoring method matters. Some pools score rounds in a linearly increasing sequence (1, 2, 3, 4, 5, 6); in this case the final game counts for a mere 6 out of 120 points. Some pools now use Fibonacci (1, 2, 3, 5, 8, 13); here the final is worth only 13 out of 137. In both cases, getting the champ wrong hurts you less than it does in a traditional power-two pool, so you can afford to take more chances.

 Posted by on March 13, 2015 at 4:05 pm

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.

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.

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

Confidence pool end game: Don’t outsmart yourself

 Confidence pool, NFL, Office pool strategy, Win probability  Comments Off on Confidence pool end game: Don’t outsmart yourself
Jan 202014

While adhering to the recommended picks on WinThatPool! should always put you among the leaders by season-end, due to the imprecision of Win Probabilities whether you are in 1st or 5th entering SB week will largely depend on chance.

Approaching Super Bowl XLVIII I find myself in the same position I was in a year ago: 2nd place in a pool of some 90 participants. Here’s a doctored screenshot of my pool’s standings last year, just prior to the SB. (The screenshot is doctored to obscure the other team names, and I changed my team name to WinThatPool to avoid readers’ confusion).Standings_pre_SB

I was 1 point in front of the person in 3rd, 7 points behind the leader. The person in 4th place was 5 points behind the one in 3rd (and out of the money) and the guy in 5th place was 7 behind the guy in 3rd.

Last year I wound up winning the pool, but that was more due to luck than to well-conceived game theory. Let me elaborate.

Last year, San Francisco had a 61% Win Probability over Baltimore. The prizes for 1st, 2nd, and 3rd last year were: 500, 300, 200. I was looking at 300 if the standings held through the SB. Both the guy in 1st and the guy in 3rd place had consistently bet the favorite all season long, so it was predictable that both would bet San Francisco.

I started anticipating what the guys in 4th place would do. If I were in 4th and looking at finishing out of the money, I’d pick the underdog. That way, if the favorite won (and all participants in 1st, 2nd and 3rd had picked the favorite) I wasn’t going to finish in the money anyway. But if they all picked SF, I was close enough to vault into 1st if Baltimore were to win. The same rationale applied to the guy in 5th place. That they both would pick Baltimore seemed self evident.

What this meant was: assuming both guys in 4th and 5th picked Baltimore (applying the above rationale), if I also picked Baltimore the worst that could happen to me if SF won was to fall to 3rd place. Seemed almost like a hedge position: if Baltimore wins, I win, if SF wins, I get 3rd place. The key assumption was that the guys in 4th and 5th considered their options the way I had. So I picked Baltimore.

When game time came around, both the guy in 4th and the guy in 5th had picked SF! I had outsmarted myself. If SF would have won, I would have finished in 5th place, out of the money. So I got lucky that the underdog eventually won. Sometimes it’s better to be lucky than good.

Strategy for SB XLVIII
This year the Win Probability is close enough to even that I won’t assume anything about what the guy in 1st will pick, never mind the guys in 4th or 5th. I’m going with Denver, cold temps or not.

In the coming week I will analyze the Fan Pick distributions to arrive at strategies depending on assumptions about the guy(s) in front of you.

 Posted by on January 20, 2014 at 6:10 pm

Conference championship confidence pool analysis and tactical suggestions

 2013, 2014, Confidence pool, NFL, Office pool strategy, Win probability  Comments Off on Conference championship confidence pool analysis and tactical suggestions
Jan 152014

Editor’s note: this table and analysis were updated 1/17/14, 9:00p PST. Some fan picks have moved significantly since the initial post.

The table below lists the allotment of fan picks based on the “pick distribution” for Confidence pools available presently on Yahoo.

Confidence Points
%Fans 16 8
20% DEN SF
9% SF NE
2% NE SF

Confidence pool analysis and tactical suggestions:
There is considerable disagreement across fan picks, which makes for some decent potential for tactical maneuvering. If you’re within 8 points of someone ahead of you, even without any tactics by you at all there is a modest chance you could catch them just by entering the highest expected point total slate (16 DEN, 8 SEA). Among slates with 16 points on Denver, 44% of them pick SF instead of SEA. Among slates with 16 on SEA, they’re highly skewed toward DEN.

At this point, if you’re behind by over 16 points, I suggest the second least popular slate, 16 on NE and 8 on SF. The chance of both teams winning is about 1/6. Chances are you’ll be the only one in your pool with that slate, and in the event both teams win you’ll move up anywhere from 8 to 24 points on everyone else.

 Posted by on January 15, 2014 at 1:47 pm

NFL Divisional Playoff round analysis of fan picks

 2014, Confidence pool, NFL, Office pool strategy, playoffs  Comments Off on NFL Divisional Playoff round analysis of fan picks
Jan 102014
%Fans Team 16 12 8 4 Avg. Conf.
88% SEA 36.7% 20.8% 18.6% 11.4% 11.8
13% NO 0.1% 2.1% 4.2% 6.1% 6.8
76% NE 6.6% 34.2% 17.4% 17.7% 9.6
24% IND 0.2% 3.6% 7.8% 12.4% 6.6
41% CAR 1.1% 6.7% 10.3% 22.7% 6.6
59% SF 2.6% 14.2% 16.5% 26.0% 7.6
91% DEN 52.4% 17.7% 20.9% 0.0% 13.4
9% SD 0.2% 0.6% 4.4% 3.7% 6.8

Strategy considerations:

Here’s the boring strategy: the pick set with the highest expected point total (DEN 16, SEA 12, NE 8, SF 4) also has the highest average rank. The next two strategies with the highest average rank are (SEA 16, DEN 12, NE 8, SF 4) and (NE 16, DEN 12, SEA 8, and SF 4).

If you’re behind by a lot, you’re running out of chances, but going with the favorites won’t cut it. Again SD looks tempting; SD has about a 1 in 4 Win Probability, but fewer than 10% of fans are picking SD. All other things being equal, ranking SD with 16 or 12 should give you that many more points than whomever you’re chasing, but if SD loses you’re nearly done. If you’re not so desperate, just give DEN only 4 points, which the table suggests almost nobody is doing. That way you still get something if DEN wins, but if they lose you haven’t spent 16 points on them.

 Posted by on January 10, 2014 at 3:50 pm

2013 NFL Confidence Pool Picks and Win Probabilities: Week 14

 2013, Confidence pool, NFL, Office pool, Office pool strategy, Win probability  Comments Off on 2013 NFL Confidence Pool Picks and Win Probabilities: Week 14
Dec 032013
Game Victor Win Probability Confidence
Houston@Jacksonville Houston 59.0% 6
Indianapolis@Cincinnati @Cincinnati 66.5% 11
Atlanta@Green Bay @Green Bay 70.1% 13
Cleveland@New England @New England 72.5% 15
Oakland@New York (NYJ) @New York (NYJ) 57.7% 3
Detroit@Philadelphia @Philadelphia 57.9% 4
Miami@Pittsburgh @Pittsburgh 59.4% 7
Buffalo@Tampa Bay @Tampa Bay 58.0% 5
Kansas City@Washington Kansas City 61.5% 9
Minnesota@Baltimore @Baltimore 71.0% 14
Tennessee@Denver @Denver 82.5% 16
St. Louis@Arizona @Arizona 67.9% 12
New York (NYG)@San Diego @San Diego 59.7% 8
Seattle@San Francisco @San Francisco 57.4% 2
Carolina@New Orleans @New Orleans 61.9% 10
Dallas@Chicago Dallas 55.0% 1
Possible points: 136    
Expected: 91.4    
Likely range: 61 to 119    

The table lists WinThatPool’s recommended Confidence pool picks for this week. If you want to maximize your chance of winning a year-end payout, use these picks. (If you want to maximize your chance of winning a weekly prize, you should deviate from one or more of these picks.)

Below the top table is a summary of the possible points available this week, the expected points from these Confidence weights, and the likely range (90% confidence interval) of possible points.

Win Probabilities could have changed since being posted.
Note the date/time stamp of this post.

 Posted by on December 3, 2013 at 9:30 am

Why “Your Starting Point” for Winning Office Pools? Because strategies vary.

 Confidence pool, NFL, Office pool strategy, Win probability  Comments Off on Why “Your Starting Point” for Winning Office Pools? Because strategies vary.
Sep 122013

Sometimes visitors ask why the modest slogan, “your starting point?” Why not something more boastful, more hyperbolic? The answer: Strategies vary, but they all start here.

The reason is, unless you are in a very small (a dozen or fewer) participants, following the NFL confidence pool picks from WinThatPool will probably not be enough to win a pool. But it is an excellent place to start, and an apt benchmark against which to measure any other methodology. Consider the different optimal strategies for a year-end prize and for a weekly prize.

Year-end Prize Strategy
WinThatPool’s picks are meant to maximize your expected number of points over the course of a season. You will notice that many other participants in your pool use confidence ranks quite similar to these. So don’t be surprised if each week one or more people in your pool use confidence ranks identical to these. By year-end, differences will be down to a few random outcomes, and possibly a mis-entered pick or two. So consider these ranks your starting point, and deviate from one or more of these picks a few times during the season, no more. The easiest thing to do is follow these ranks to a T for the first dozen weeks or so. If you are not in the lead, use the Weekly Prize Strategy described below during the last week or two.

Weekly Prize Strategy
All things being equal, every entry’s chance of winning a prize is 1/n, where n is the number of entries. For example, in a pool with 85 entries, each entry should win once every 85 times, or once in five NFL seasons. While WinThatPool’s ranks are dominant over the course of an entire season, in any single week they will almost never win a prize (their chance of winning is much lower than 1/n; in an 85 player pool you might wait a decade or longer before you win a weekly prize). Instead, start with WinThatPool’s picks and then take a bold deviation – pick the underdog in one of the top three games (rank 16, 15, or 14 in a 16 game week) and leave the confidence rank unchanged. By doing so, you will have almost no chance to win the cumulative prize at season-end, but your chance of winning a weekly prize will be much better than 1/n.

 Posted by on September 12, 2013 at 10:24 am

Anchoring Bias Evident in Popular Online Confidence Pools

 Confidence pool, NCAA football, Office pool strategy  Comments Off on Anchoring Bias Evident in Popular Online Confidence Pools
Dec 212009

Fan Pick Distributions:  Consistent Across Sites
Several websites sponsor college bowl confidence pool contests on all 34 bowl games.  The two most popular probably are those on ESPN and Yahoo.  It is interesting to compare how the contestants in the two sites’ confidence pool contests allocated their picks.

The first observation is how similar the percentages of contestant picks are. They’re so close they resemble polling results taken a few days apart. The correlation coefficient of the two distributions is 0.99.  Here’s a plot of the two series:

Fan Confidence Distributions:  Clear Example of Anchoring Bias
The second thing that’s obvious is how different the contestants’ average confidence weights are for each pick.  In this 34 bowl game contest, contestants are supposed to predict the game winners and rank their predicted winners according to how confident they are each team will win, assigning numbers from 34 (highest confidence) down to 1 (lowest confidence).  Given the similarity of the percentages of fans that picked each team, it is reasonable to expect their average confidence on each team might be similar as well.  But as you skim down the columns labeled “Conf.,” you’ll notice on Yahoo the later games get more confidence weight, while on ESPN the later games get less weight.  That’s no mere illusion:  the correlation coefficient of Confidence weights between Yahoo and ESPN is -.62.  What’s going on here?  How could contestants with nearly identical views on who will win have such different degrees of confidence about their expectations?

A simple answer lies in the two columns labeled “Default.”  While some online confidence pools require the user to enter or pull-down a confidence weight, both Yahoo’s and ESPN’s entry pages begin with pre-assigned confidence weights.  It’s up to the user to deviate from these default assigments.  In Yahoo’s contest, the assignments are in ascending order, while in ESPN’s they’re in descending order.  Clearly the contestants on both sites were anchored by the starting confidence weights.  Multiple regression analysis reveals that in both contests over 50% of the variation in Average Confidence Weight is explained by the Default weighting.
 Posted by on December 21, 2009 at 1:21 pm