Monmouth University Researchers Look at Poker Player Ranking Based on WSOP Data

The researchers looked at whether a player's position early in a tournament can help predict how far they will advance and how much they will earn. It also examines whether the widely used Independent Chip Model (ICM) accurately reflects the value of players' chips as a tournament reaches its final stages.

“There’s widespread belief in poker that if you have a chip and a chair, you have a chance,” Scott told Gambling.com.

Each player was given 30,000 chips to start, but by the end of the first two days, their stacks would vary dramatically. 

Scott, Sher and Paz found that it was better to compare player chip counts with the average stack in each tournament instead of focusing on a fixed number of chips across events.

For the Day 1 analysis, players were grouped into four quarters based on their chip-stack ranking, with a separate group for the top 10%. It was then possible for the researchers to compare the average chip stacks and finishing prize money in each group.

Another part of the analysis was to divide players into three categories: those who finished out of the money, those who cashed before the final table, and those who reached the final nine. 

This was an important step because it allowed the researchers to study whether having a larger-than-average stack in the early round links to reaching the later stages of a tournament.

The second part of the study examined the Independent Chip Model (ICM), which uses players' chip stacks and a tournament's payout structure to estimate how much each remaining player's chips are worth in expected prize money. Unlike a cash game, where a chip has a fixed value, tournament chips have a changing value because finishing positions pay different amounts.

• The researchers compared ICM predictions with the real winnings of players who reached the final day across the 25 tournaments. 
• Players were divided into groups based on their chip value heading into the final day: the top 25%, middle 50%, and bottom 25%.

Scott, Sher and Paz then used regression analysis to compare actual winnings with predictions from the ICM. 

The analysis also included a control for previous tournament appearances, since 21 players in the sample reached the final day more than once. To avoid having a disproportionate influence on the results from larger tournaments, the research team adjusted one analysis for tournament prize amounts.

This approach allowed the researchers to test both sides of the study, looking at whether accumulating chips early was connected to better tournament results, and whether the standard model used to value those chips accurately showed what happened once players reached the final stages.

Scott, Sher and Paz found in their research that players with larger chip stacks early in WSOP Circuit tournaments were substantially more likely to reach the final stages and earn more money. It also found that while the Independent Chip Model broadly lined up with the tournament results, it often underestimates the winnings of players with the largest stacks and overestimates players with medium-sized stacks.

The difference was already clear as early as Day 1. Players who eventually made the final table had an average stack 50.8% above the tournament average, while those who cashed without reaching the final table had stacks just 2.4% above average. Players who finished out of the money had stacks 43.9% below average at the end of Day 1.

The academics also found a clear relationship between Day 1 ranking and eventual earnings. Players in the bottom 25% by chip stack had an average of 61,509 chips and ultimately received an average of $3,315. Players in the top 25% averaged 306,679 chips and $14,864 in winnings. 

The top 10% averaged 384,651 chips and $16,880 in prize money. Scott states, 

“These results suggest that a high-risk/reward approach is advantageous in tournament play, especially early in a tournament.”

This relationship was also obvious for players reaching the final table. They would be in the 70th percentile of chip stack value after Day 1, on average. 

There were 225 players who made the final table across the research tournaments, and only 48 (21.33%) were in the bottom half of the field after Day 1. 

Because these are averages, the research team points out that sometimes players in lower Day 1 positions would reach the final table.

The Independent Chip Model (ICM) is a solid tool for estimating how much money a poker tournament player will win, but the study finds it isn't perfect. It underestimates real payouts, with every $1 the model predicts a player will win, they actually took home around $1.14. 

Across nearly 300 final-day players, this $0.14 gap was too consistent to be a fluke, suggesting the ICM formula has a systematic flaw. Stack sizes can confuse the ICM, leading to incorrect predictions, especially for big and short stacks.

The gap in the model’s accuracy became clearer when the research separated players by stack size. Players in the bottom 25% of stacks on the final day earned an average of 100.33% of the ICM prediction, so their results were very close to the model’s estimate. 

Players in the top 25% earned 107.62% of their ICM predictions, while those in the middle 50% earned only 94.20% of their expected winnings.

In other words, players with the largest stacks would outperform the ICM estimates, while medium stacks would underperform. 

Scott, Sher and Paz point to possible explanations such as players with larger stacks having more strategic options in poker gameplay. However, the researchers admit their data cannot confirm why this gap happens.

The findings give poker players another way to think about their position during a tournament. It seems that building an early chip stack can directly impact where a player eventually finishes and how much they earn. It’s also interesting that the research suggests the players should use ICM predictions with caution, especially for large and medium stacks.

If a player reaches the late stages of a tournament with a large stack, the research could provide a more useful gauge of their outcomes than ICM calculations. Players with medium stacks may need to understand that the predicted earnings may differ from the final result. 

This is where the authors are cautious, saying that the ICM still has practical value for players, especially when it comes to performance and for negotiating deals to divide remaining prize money.

ICM is commonly used to calculate how prize money should be divided according to the chip stacks of remaining players. The study finds there are differences between the ICM prediction and actual winnings that are systematic. While the research is not advocating for discarding the Independent Chip Model, it does suggest it should be used for mathematical expectations and not a guarantee of stack earnings.

Poker tournament operators could also see benefits from the research. The study deals made through ICM predictions can shorten tournaments while allowing players to secure some of their potential winnings, reducing costs associated with hosting an event. 

If operators have more understanding of the difference between ICM estimates and real outcomes, they could give players more accurate information.

The findings add some data-driven weight to something players already suspect: that having more chips early matters during a poker tournament. 

While the results do not mean a short-stacked player cannot recover, they show that such comebacks are relatively uncommon.

Poker is only one of many gaming and probability-related studies conducted by Robert Scott and Mikhail Sher. The duo is completing a book titled “Beat the Sportsbook: The Theory and Practice of Successful Sports Betting,” which examines how sports bettors can improve their chances of winning by overcoming biases like overconfidence and reliance on knowledge of the team, curbing emotional betting, having a better understanding of the value offered by the odds, and implementing more trading-like conventions in the sports betting decision-making process.

Scott and Sher are now in the final stages of writing a book, “Beat the Sportsbook: The Theory and Practice of Sports Betting,” which is expected to be published in 2027. Scott points out that the book will cover the basics of sports betting but will also highlight how probability and variance influence outcomes. 

It also offers insights into how several sportsbooks operate and how bettors can use that knowledge to their advantage. 

However, he was very clear about sports betting being up to chance, and that neither the research nor the book guarantees success in betting, which should be done responsibly and always be seen as entertainment and never a sure way to earn money.