Drinking my morning coffee and digging through my Twitter feed in search of a story, I came across an article by Mickey Doft over at PokerNews, in which he asks the question, “Does Bagging the Chip Lead on Day 1 of the WSOP Main Event Translate Into Success?” It’s an interesting question, but I found his analysis a little bit disappointing, for a few reasons.

Some of my complaints are admittedly nitpicky: for instance, I’m not sure why he chose to look at Day 1A, 1B, 1C and (when it existed) 1D separately, since the flight should make little difference. Or, if it does matter due to differences in field composition between the flights, then the effect should be independent of that produced by a chip lead. Splitting them up that way just confuses the issue, in my opinion, but there are more important problems with the article.

Doft doesn’t put his results in any sort of statistical context. He notes that in the years since 2007, three Day 1 chip leaders – Jacobson, Cada and Lamb – have made final table appearances, and that Jacobson and Cada both won their respective events… but he makes no mention of what the odds were like of this happening.

Finally, by focusing only on the actual chip leaders, rather than everyone with a deep stack, he cuts down his sample size unnecessarily; the chip leaders aren’t typically that far ahead of other top-10 stacks, so any deep-stack effect should show up in more players than just those that Doft is considering. As a result, even if he had looked at the probabilities underlying Jacobson, Cada and Lamb’s runs, he would have found it difficult to say whether the Day 1 chip lead was particularly significant or whether their results were a fluke. It’s a basic fact in stats that when you’re looking at low-probability occurrences within a small data set, the degree of variance involved is huge.

Broadening the search

So, I decided it was worth doing my own take on the question and being a little bit more scientific about it. Rather than looking only at chip leaders, I decided to look at everyone who has finished Day 1 with 150,000 chips or more in the WSOP Main Events from 2011 to 2014; the WSOP website doesn’t give official chip counts for Day 1 flights prior to 2011, so that was the furthest back I could go.

Note: Due to a glitch in the WSOP website, Day 1C chip counts for the 2013 Main Event are unavailable, so players from that flight are omitted from the data set.

This approach gives us 79 players to work with, rather than the 29 Doft looked at. Furthermore, I decided to look at final-27 appearances rather than just the final table. Broadening the target window like this further reduces the variance and therefore produces results that are a lot easier to interpret.


Direct chip odds vs. actual results

I combined the flights for each year and sorted the players by chip stack, then calculated the percentage of the chips in play held by each: the average is around 0.09%, both for the full list of players and for those who actually did make the final 27. Given the field sizes involved, ICM effects can be discounted, so on average, you would have predicted each of these players to be about 2.43% likely to make the final 27 based solely on their chip stacks.

Given that we’re looking at 79 players, then, you would expect to see about two of them making the final 27. Instead, we have seven: Martin Jacobson, Thomas Sarra Jr., Clement Tripodi, Sergio Castellucio, Daniel Strelitz, Ben Lamb and Andrew Hinrichsen.

We can also look at final tables, of course. There, the expected number of appearances is only 0.64, so it’s close to a coin flip whether any of them should have made it at all. Of course, what we actually got during this period was two: Jacobson and Lamb. (Cada won in 2009, which is outside the period I’m considering).

In both cases, the actual results are about triple the expectation based on simple chip counts, but the top-27 results are much more statistically meaningful. If poker were purely a game of chance, you would still see two of these players make the final table 16% of the time, but seven top-27 deep runs would only happen about one time in 300.

It therefore seems pretty likely that a player’s day one chip stack is a stronger predictor of a deep run than a naive probabilistic approach would indicate. That is to say that if poker were purely a game of chance, a player with five times the chips would be about five times as likely to make the final 27, but what we find is that the players with five times the starting stack at the end of Day One have historically been more like fifteen times as likely to make such a deep run. So, chipping up early may be about three times as big a deal as you might have thought.

Correlation is not causation

It’s important to take these results with a grain of salt, however, and remind ourselves that correlation doesn’t necessarily imply causation. The connection between end-of-Day-1 chip stacks and deep runs is probably twofold.

Firstly, I do believe that the chips themselves have an effect, especially in a tournament like the Main Event, which has a slow structure and a high percentage of players who are simply looking to cash. Getting an early chip lead therefore allows plenty of time and opportunity to put those chips to use bullying others and stealing pots by putting them on decisions for their tournament life and exploiting their ICM considerations prior to the money bubble bursting.

That said, it’s also obvious that the players who acquire lots of chips early on are both more likely to be good players, and more likely to have an aggressive go-big-or-go-home style. Both of these characteristics are sure to correlate with a higher frequency of deep runs, so we can be fairly sure this plays a part in the results too. Although leveraging a deep stack may help an aggressive player to run deep in the tournament, simply having that big stack is itself an indicator that the player is someone who may have been a favorite to go deep in the first place.

In summary, we can’t really be sure how much a deep stack helps any given player, although it’s probably at least a little bit more than straightforward chip odds would predict. We can, however, say that if you’re looking to guess who is going to be around on Day 7 and beyond, the chip counts at the end of Day 1 do seem quite significant.

Alex Weldon (@benefactumgames) is a freelance writer, game designer and semipro poker player from Montreal, Quebec, Canada.