Pick’em Advice: How Pool Size Impacts Pick Strategy In Football Office Pools

Pick’em Advice: How Pool Size Impacts Pick Strategy In Football Office Pools

September 4, 2019 – by Tom Federico

Baker Mayfield and his linemen know that size matters when it comes to your pool picks (Photo by Daniel Dunn/Icon Sportswire)

Winning an NFL pick’em contest requires a higher level of thinking than simply identifying the most likely teams to win.

As you make your picks each week, a host of other strategy factors should influence your game by game decisions. Those factors include your pool’s rules and prize structure, the expected pick popularity of every team, your current position in the standings, and the number of entries in your pool. (Read our pick’em strategy guide for more.)

In this post, we examine the potential impact of pool size on pick strategy for NFL and college football pick’em pools. We’ll use a simplified example to show how the number of entries in your pool can influence the picks that give you the best chance to win.

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The Four Stooges NFL Pick’em Pool

With Week 1 of the 2019 NFL season coming up, Larry, Moe, Curly, and Shemp (aka the Four Stooges) have decided to compete in an NFL pick’em pool. Here’s how it works:

Each player gets one entryBuy-in is $100 per entryThe winner takes home the entire $400 prize potIf multiple players tie for first, they draw straws to determine the winner

The rules are simply to pick straight up NFL game winners, with one point awarded per correct pick. But the pool only lasts one week, and only includes the following three games:

Cincinnati at SeattlePittsburgh at New EnglandLA Rams at Carolina

Game Win Odds

The Four Stooges all have their own opinions on these games, but based on betting market odds and our Week 1 predictions, the objective win probabilities looked roughly like this at publication time:

Game	Favorite	Win Odds	Underdog	Win Odds
1	Seattle	80%	Cincinnati	20%
2	New England	70%	Pittsburgh	30%
3	LA Rams	60%	Carolina	40%

The Four Stooges’ Picks

When the pick deadline arrived, here’s what all the picks looked like (win odds in parentheses, upset picks in bold):

Game	Larry	Moe	Curly	Shemp
1	Seattle (80%)	Seattle (80%)	Seattle (80%)	Cincinnati (20%)
2	New England (70%)	New England (70%)	Pittsburgh (30%)	Pittsburgh (30%)
3	LA Rams (60%)	Carolina (40%)	LA Rams (60%)	Carolina (40%)

Player Pick Summary

Reviewing these picks, here’s what you should notice:

Larry is the conservative one, picking all three favorites.Moe and Curly each threw in one upset pick, but neither had the cojones to pick against Seattle.Shemp, who had been drinking heavily after Larry twisted his earlobe, picked all three underdogs.

So who made the best picks?

The Expected Pool Winner Is…

Do the math, and Larry made the best picks.

By playing it safe in such a tiny pool, he let his opponents shoot themselves in the foot by picking too aggressively, giving himself a 42% chance to win in the process (compared to baseline win odds of 1-in-4, or 25%).

As a result, his expected payout is $168 (the $400 pot times a 42% chance to win) for an expected return of 68% on his $100 buy-in fee. Warren Buffett would be jealous.

The Other Guys

Moe has a 38% chance to finish with the highest score, but only a 28% chance to win the pool once you account for tiebreakers (which we’re assuming are a random draw of straws in this example).

Curly has a 28% chance to finish with the highest score, and a 19% chance to win after accounting for tiebreakers.

And reckless Shemp has a 21% chance to finish with the highest score, but only a 10% chance to win, after accounting for the tiebreaker.

At those pool win odds, Moe still has a positive expected return-on-investment (ROI) on his pool entry fees of 13%, but Curly and Shemp are expected to lose money.

The Takeaway: Small-Pool Strategy

Let’s trace this overly simplified lesson back to game theory.

In a tiny pick’em pool, in which you only need to beat a small number of opponents, taking even moderate risks with upset picks can be too aggressive of a strategy, and will likely decrease your odds to win the pool.

Picking all favorites or “chalk” may look wimpy and draw the mockery of your pool opponents, but in some cases it absolutely makes the most sense.

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Pool Twist #1: Moe The Copycat

In the example above, Larry is in the driver’s seat with his all-favorites picks, but a big reason why is because he was the only player in the pool to pick all the favorites.

What if Moe hadn’t picked Carolina to upset the LA Rams, and had instead picked all the favorites too?

In that case, the best outcome Larry could hope for would be to tie Moe for highest score in the pool, and then to win the 50/50 straw draw to take home the pot. That change in dynamic decreases Larry’s expected pool profits.

In this new scenario, Larry and Moe would both have a 32% chance to win the pool, and an expected ROI of 29% each. Curly and Shemp both would be slightly better off than before, but still expected to lose money.

So Larry’s prospects decrease if another player ends up making the same picks as him, but picking all favorites still gives him the best expected return of anyone in the pool (tied with Moe).

Pool Twist #2: Add 396 Friends

Something fascinating and fun happens when you significantly expand the pool’s size, though.

Let’s imagine a pool not with four entries, but with 400 entries: the Four Stooges and 396 of their closest lovable numbskull friends. Winner take all, same games to pick.

In a pool that big, an expected pick distribution might look something like this:

200 players pick like Larry (all 3 favorites)100 players pick like Moe (2 favorites, 1 minor upset)90 players pick like Curly (2 favorites, 1 moderate upset)10 players pick like Shemp (all 3 underdogs)

So who made the best picks for the 400-entry pool?

The Highest Expected Pool Profit Goes To…

The Shemps, by a significant margin.

In bigger pools, public bias toward favorites often presents great opportunities to increase your expected pool profits by aggressively picking unpopular (and typically fairly risky) teams.

You just need to stand firm in your conviction that you’ve made the higher expected value gambit, and ignore the inevitable ridicule of your opponents who mock your crazy looking picks.

(If there’s one thing we’ve learned over years of helping subscribers win football pools, it’s that making the best picks often requires thick skin. Your opponents will mock you if you pick all the favorites, and they’ll mock you again if you make crazy looking picks — even if you’re playing optimally in both cases.)

Why It Often Pays To Be Aggressive In Bigger NFL Pools

By picking all underdogs, the Shemps still only have a 21% chance to end up with the highest score in the 400-person pool. That’s the lowest of any of the Stooges.

But here’s the kicker: when the Shemps’ picks have the highest score in the pool, each Shemp has somewhere between a 1-in-10 chance (if all 3 underdogs win, and only the Shemps are tied for first) and a 1-in-200 chance (if the biggest favorite wins, but the other two underdogs pull off the upsets, leaving them tied with all the Moes and Curlies) of winning the straw draw and taking home the pot.

The key here is mainly the scenario where each Shemp has a 1-in-10 chance to win the tiebreaker. No other Stooge has anything similar. The closest is the 1-in-90 chance that the Curlies have to win the tiebreaker when only the moderate favorite pulls the upset.

After doing all the math, it turns out that each Shemp has a 0.37% chance to win the pool and take home the $40,000 pot.

Combine the possible outcomes and probabilities (a 0.37% chance to win $40,000, a 99.63% chance to lose the $100 entry fee), and in the long run, on average, each Shemp is expected to get $48 back from each yearly $100 entry into the pool. That’s an expected average return of almost 50%.

When Boom or Bust Beats Playing It Safe

By picking all favorites in a much bigger pool, the Larrys will still get the highest score much more often than the Shemps do. After all, favorites do win more often.

But when the Larrys’ picks win the pool, each Larry still has to win a straw draw against a whopping 199 other Larrys in order to take home the pot. In short, the Larrys failed to differentiate their entries, and that’s a crushing blow to expected profits. On balance, they come out much further behind. The Curlys are expected to lose money too.

In a bigger pool with a small number of games involved, playing it safe often gives players a false sense of hope. Most of the time, a conservative player will get a higher score than a riskier player, and the conservative player will more often end up finishing decently in the final standings. But even finishing in the top 10% of a 400-person contest (say, in 30th or 40th place) usually wins you nothing.

You need to win the damn thing (or finish in the top few places, typically) to take home a prize. In big pools, making a greater number of unpopular, often riskier picks usually accomplishes that goal more often — even if that strategy tends to bomb in the years it doesn’t win.

Conclusion

Of course, your pool is almost certainly much more complex that the Four Stooges pool. You’ll be picking a lot more games over the course of the season, and if your pool has both weekly and end-of-season prizes, you will need to decide which type of prize you most want to chase.

And depending on your pool’s exact format and prize structure, and what week of the season it is, pool size may or may not be a driving factor in your optimal pick strategy.

Still, the general strategy concept we’ve explained in this post will almost always apply to some degree. The greater the number of entries in your pool, the less likely the safest, most conservative pick strategy is to pay dividends.

If you’re in an NFL pick’em contest, make sure you check out our Football Pick’em Picks. We also provide NFL Survivor Picks and NFL Betting Picks.

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