# Welcome to PoologicTM

This site is dedicated to helping you win your college basketball tournament office pool.

\$250,000. That is my minimum estimate for profits made by the users of this site, assuming they played the recommended multiple-entry strategy. Please donate some of your winnings to the Jimmy V Foundation for Cancer Research. (Poologic is not affiliated with the V Foundation.)

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## What are the winning strategies?

The core strategy is the the point maximization strategy.

The multiple entry strategy and the contrarian strategy are variations on the point maximization strategy that involve entering variants of the expected-point-maximizing pool sheet.

## What is the point maximization strategy?

Use the Poologic Calculator to determine the pool sheet that maximizes the expected number of points for some pool scoring systems.

Point maximization involves picking the sheet that will provide the highest expected number of points. For a pool with standard scoring , you can get a close approximation to the expected-point-maximizing pool sheet by picking the higher seeds up to the last four teams and then picking the favorites among these four. You can use the AP poll or the USA Today/ESPN poll to rank the four number one seeds. The Poologic Calculator uses the Sagarin ratings and the point spreads to determine the favorite in each game, so it will produce a slightly different (and perhaps slightly better) expected-point-maximizing pool sheet for standard scoring rules.

If the pool scoring system provides incentives for picking upsets, then point maximization can become very complex. See Breiter and Carlin [1] for more information on how to handle some types of scoring systems with incentives for upsets. The Poologic Calculator implements the Breiter-Carlin method.

Point maximization works well in pools with upset incentives. In standard scoring pools, it performs badly because it provides an insufficient advantage to overcome the fact that the champ it recommends will be overbet.

## What is the multiple entry strategy?

The multiple entry strategy is highly recommended.

In a standard scoring pool, the basic idea is to enter multiple sheets, where each sheet has a different pick for champion. Each sheet is a variant of the expected-point-maximizing pool sheet with the champion constrained to be a particular team. If possible, use the ROI Calculator to determine the best champs to pick in a multiple entry strategy. But if estimating the values needed for the ROI calculator is too daunting, then the best rule of thumbs are: (1) avoid the team(s) that are #1 in the AP or ESPN polls, (2) Avoid the office favorites, (3) Pick one-seeds or two-seeds for champ, but in pools with less than 30 entries, you may want to stick to one-seeds.

In a pool with upset incentives, betting different champs may not be the best multiple-entry strategy. It may be better to bet an entry from each of the probability models available from the Poologic Calculator. My empirical study lends support to this approach.

## What is the contrarian strategy?

You don't need to concern yourself with the contrarian strategy if you are willing to employ the multiple entry strategy. The contrarian strategy is for folks that want to enter just one pool sheet. The contrarian issue is largely a moot point if you are willing to enter multiple sheets.

The idea is to avoid picking the office favorite(s) for champion and instead pick a team that is a less popular than office favorite(s). This strategy works because you may get little or no competition when you go against the office favorite(s) [2]. Let's say that the team that you choose as the champion has a 15% chance of winning the championship. If you are the only person to pick that team as the champion, then you have about a 15% chance of winning a pool with top-heavy scoring.

For instance, let's assume that your pool is in Kentucky and Kentucky is number one in the nation. You look at objective probabilities and see that Kentucky has a 20% chance of winning the championship. The next best team is UNC with an 18%. You would bet the expected-point-maximizing pool sheet with with UNC constrained to be the champ.

## Which is best, contrarian or point maximization?

If two teams are about equally likely to win the national championship and one of them is the local favorite, then you should go against the local favorite.

The matter gets complicated when the local favorite has the highest objective probability of winning the championship by a large margin. A definitive answer is not available at this time for this situation. (The following mathematical section was written before the ROI Calculator was available. The ROI Calculator implements all this math, so you may prefer to just use it rather than slog through the math.) As a rule of thumb in a pool with top-heavy scoring, the contrarian strategy should be used when:

C < ((F+K)*Pc/Pf)-K

Where:

• C is your estimate of the number of pool sheets that will be entered for the contrarian pick (not counting your sheets).
• F is your estimate of the number of pools sheets that will be entered for the office favorite (not counting your sheets).
• Pc is the probability that the contrarian pick will win the championship.
• Pf is the probability that the office favorite will win the championship.
• K is a factor that represents the advantage of the point maximization strategy in your pool. I think that a typical value for K would be about 6 based on some simulations that I have run that assume that other office mates are using conventional wisdom and that the points awarded for each correct pick were 1,2,4,8,16,32 for rounds 1 to 6 respectively. The value of K depends on how your opponents play the pool and how the rounds are scored. If others were using an approach closer to the point maximization strategy, then K would be lower. If the sheet scoring is less top-heavy (with smaller multipliers for the later rounds) then K will be slightly larger. If 20 points instead of 32 are awarded for the championship round and points awarded for rounds 2 to 5 are scaled accordingly, then K will be about 10% larger.

For instance, Duke had a .4 probability of winning in 1999 and UCONN had a .2 chance. So, UCONN was a good contrarian pick if:

C < ((F+6)*.2/.4)-6 = .5F - 3

So, if you estimate that at least 15 pool sheets will be entered for Duke by your opponents, then .5*15 - 3 = 4.5, so UCONN is a good pick as long as 4 or fewer pool sheets are entered for UCONN by your opponents. Note that this does not mean that entering a sheet for Duke is a bad idea. The straight point maximization strategy will still probably give you a positive return on your investment. This analysis just means that a contrarian sheet picking UCONN is the best single sheet to enter when a sufficiently low number of other pools sheets are entered for UCONN.

By the way, this approach in modeled on the idea that entering a single sheet using the point maximization strategy is equivalent to entering K sheets using conventional wisdom or some other inferior strategy. This model seems to be a useful approximation.

But, this proposed approach has not had any independent review, so beware. I may change my advice on this matter based on future analysis.

## What if others use the same strategies?

If one or more others play a similar strategy, this can reduce the advantage of the point maximization strategy. You should monitor the pool sheet summaries that your pool manager distributes to look for evidence that others are using similar strategies. In general, you need to learn as much as you can about the tendencies of your opponents in the pool. In a pool with top-heavy scoring, if none of your opponents are advancing the four number one seeds or odds-on favorites to the semi-final round, then you have little to worry about.

If two are more of your opponents start entering exactly the same point maximization pool sheet as you enter, then it's time for new strategies. You can vary the point maximization pool sheet selecting one nearly even match-up in the first round and calling a minor upset. But ties are very unlikely unless the strategies described in this web page become the strategies used by a significant fraction of all those who play the pool. We are a long way from that now.

## How does the pool manager's sheet scoring rules effect my strategy?

You will need to understand the scoring procedure for your pool. Unless you are the pool manager, the sheet scoring procedure will not be under your control.

Top-heavy scoring is typical. In top-heavy scoring, the pool is almost never decided until after the championship games because picking the champion is weighted heavily in the scoring system. This means that picking the champion is important because the winner of the pool will usually correctly pick the champion.

Standard scoring is a simple scoring system where the points awarded for picking the winner of a game are based on the round of the game and no other factors. For standard scoring, you can approximately maximize your expected point total by simply picking the lower seed to win each game. One common standard scoring system awards up to 32 points for each round evenly divided among the games of the round.

Some pool scoring systems provide an incentive for correctly guessing upsets. This can make it very complicated to determine the best strategy for maximizing your expected score, but the Poologic Calculator handles the common types of upset incentives. .

Sometimes, the pool manager permits the purchase of insurance that allows a player to advance his favorite team without incurring a penalty for picking the underdog. If the insured team loses, then the victor in subsequent rounds automatically replaces it. If insurance is available and the purchasing of insurance is common in your pool, then this can reduce or eliminate the advantages of the contrarian strategy.

## How should I determine outcome probabilities for each game?

Ken Massey's Page provides a convenient source of outcome probabilities calculated in an objective manner. From the Massey Page, Click on "NCAA Tounament Analysis" and then click on "Probability of winning the tournament". This shows the teams in the order of their probability of winning the tournament. The "Champ" column shows the probability that each team will win the championship. These are the probabilities needed to make precise decisions in the multiple entry strategy and the contrarian strategy.

Breiter and Carlin [1] describe another method for generating probabilities that uses point spreads for the first round and pre-tournament Sagarin ratings for subsequent rounds. The Poologic Calculator and the ROI Calculator use the Breiter-Carlin method to calculate probabilities. You can get the ROI Calculator to show these probabilities by setting the total entries to 1 and leaving all the team-specific entries at 0.

## What is the conventional wisdom on how to play the pool?

There seems to be a belief that one should enter a pool sheet that has a pattern of upsets similar to the pattern of upsets that occur during a typical tournament year. I have seen advice to this effect on some other web sites. See for yourself on my pool strategy links page.

It is easy to see the flaw in conventional wisdom. Suppose you had to guess the outcome of fliping a biased coin three times, where the coin had a 60% chance of landing head. If you applied conventional wisdom to this contest, then you would predict a mixed outcome of some heads and some tails, since this is the most likely pattern in the outcome. Predicting some tails is just like predicting some upsets to get a typical pattern of upsets on your entry sheet. But, if you predict all heads, then you maximize your performance - you would be right on 60% of the flips.

## What are all these models?

I refer you to the models information page.

## I won! How can I thank you?

Just donate some of your winnings to the Jimmy V Foundation. Mark the gift "In Honor of" Poologic. You do not need to provide a snail-mail address for the honoree. The V Foundation will inform me of the total amount of all gifts without revealing any of the personal information of the givers.

## References:

[1] "How to Play Office Pools If You Must" by David Breiter and Bradley Carlin (Chance Vol. 10, No 1, 1997, pp. 5-11)

[2] "March Madness? Strategic behavior in NCAA basketball tournament betting pools" by Andrew Metrick (Journal of Economic Behavior & Organisation Vol. 30, 1996, pp. 159-172)