ROI vs. Hourly Rate in Tournaments
Tournament poker players talk a lot about Return on Investment, or ROI, because it seems like a sensible measure of performance, similar to “Big Blinds per Hundred Hands” (BB/100) as used by cash game players. And there are several good arguments to be made for it.
It’s certainly more meaningful as a statistic than ITM (In the Money), since many losing players actually have a fairly high ITM – the best players are pursuing the win rather than a min-cash, so they tend to bust out before the money more often as they seek to accumulate chips.
It’s also more meaningful than raw cashes, or even net profits, since it eliminates bankroll and volume from the calculation – using ROI, you can compare players across stake levels and regardless of how often they play, and simply look at how well they tend to do in any given tournament.
The trouble with ROI
There’s one major problem with fixating on ROI, however, which is that it doesn’t take time into account at all, and time spent playing is important for players of all levels.
On the one hand, a recreational player, who is playing at negative ROI for the enjoyment of the game, would like to play as many hands as they can for their money. Conversely, for those of us who take the game seriously and are treating it as a source of revenue, the opposite is true: profits are only worth pursuing if they can be achieved within a reasonable timeframe. 100% ROI may sound good on paper, but if it’s achieved by single-tabling a $2 tournament which takes several hours to play, the player is not using her time efficiently.
To see just how misleading ROI can be, it suffices to compare professional players from different formats. At one extreme, a player who focuses on mid buy-in, huge field tournaments might manage close to 100% ROI, while at the other extreme, a rakeback grinder who mass-multitables hyper-turbo SNGs might actually operate at 0% or even -1% ROI before rakeback, but make more than the first guy in a year due to his enormous volume. Meanwhile, a high-stakes MTT shark might have 10% ROI but be making six figures because he plays for over $1 million in buy-ins in the course of a year.
Buy-ins per hour
Obviously, the real analog to BB/100 for tournaments is buy-ins per hundred hands, or buy-ins per hour. This can be hard to calculate, however, because most of us don’t keep detailed notes on how long we spent playing any given game. It’s easy to overestimate the average time spent if you’re only looking at how long a tournament runs – a naive approach would be to assume that the average playtime is half the tournament length, but this is very much incorrect, as the majority of players will have busted well before the halfway mark.
In general, tournament fields have an exponential falloff for most of their running time. The more players there are, the faster they bust out. There are other factors that shape the curve as well – large jumps in the blind structure can lead to a wave of bust-outs, while things are usually a bit slower both early on, when stacks are deep, and on the money and final table bubbles. But overall, you can expect that the majority of bust-outs happen early in a tournament, and that the mean playtime will be considerably less than half the tournament’s length.
Here is an example of a tournament bust-out curve, based several $2.50 Turbo 180-Man Sit-and-Gos on PokerStars, averaged together. Breaks have been disregarded.
The average run time for the tournament was almost exactly 100 minutes, but 50% of the field has busted by the 30-minute mark. The average playtime is also right around that, at just over 31 and a half minutes. Meanwhile, 25% of the total run time is the final table, reached by only 5% of the players. So even for a relatively small 180-man field, the average playtime is only 30% of the total. Adding more players to the tournament increases the total length without significantly impacting the time it takes the field to be cut in half (assuming similar stacks and blinds), so you would expect the average-to-maximum playtime ratio to decline slowly as you move to bigger fields.
Estimating your hourly rate
You can get a fairly good idea of a player’s average life expectancy based on their stack size and the blind structure; their mean expected bust-out time can be expected to be when the big blind reaches about 15% of their current stack (unless their stack is already quite small, in which case it’ll be a little longer). In other words, people tend to bust out once they’re forced into push-or-fold mode by the blinds, and you can expect on average that their stack will remain relatively constant between now and then – sometimes they chip up before going into push-or-fold, and sometimes they manage to double up as a short stack, but then there are times they will lose a big pot and bust out long before they were expected to. This estimate is born out by the statistics above – after 30 minutes in this tournament structure, the blinds are 125/250, with starting stacks of 1,500.
Thus, by inspecting a tournament’s structure, you can get an idea of what your average playtime is going to be like – if you know your ROI as well, then you can figure out a pretty good approximation of your hourly rate.
Can hourly rate be improved?
All of this leads one to wonder whether there are changes to one’s play that could improve hourly rate independently of ROI. Assuming equal ROIs, a more aggressive player is going to tend to bust early or run deep more often, while a more conservative one is going to have more small cashes, which tend to be time consuming – certainly bubble finishes are the worst thing for hourly rate, but for a good player in a huge field tournament with a trivial buy-in, it may actually hurt the hourly rate less to bust out on the first hand than to min-cash after many hours.
Just how much of an effect can play style have on average playtime? OfficialPokerRankings.com provides players’ finish position stats for multi-table tournaments, broken down as Bottom 10%, 10-30%, 30-70%, 70-90% and Top 10%. A typical tight, winning player might have numbers like 9/18/40/20/12 while a much more aggressive winning player might be more like 11/22/37/17/12. Both are running deep the same amount of the time, but the former busts early a little less often than the average, while the latter busts early a little more often, and in the middle stages considerably less.
Using the bust-out curve for the tournament structure above, the more aggressive player plays for 34.5 minutes on average, while the tighter one plays for 36.5, a difference of about 6%. Assuming good ROIs of around 50%, this means that the tighter player could make more per hour by polarizing his finish positions, even if it meant taking an ROI hit of 2% or so. That’s a fairly small amount, of course, so this isn’t to say that it’s a good idea to insist on doubling up or going bust within the first few levels. It is, however, on the same order as ICM considerations in the early stages of a multi-table tournament, with the bubble still a long way off.
Live tournament professionals are reluctant to bust out in freezeout events because the opportunities to play big tournaments are relatively rare, and travel is expensive. This has led to the wisdom that you always have to find an edge, and should avoid playing any break-even spots. Online, however, tournaments are starting up all the time, especially on the larger sites. If you’re already playing as many tables as you comfortably can, busting out of one tournament simply means being able to fire up a new one. In this context, thinking about things from an hourly rate perspective means those break-even spots may not be so bad after all.
Even more interesting is the question of late registration. Again, in a live tournament setting you’d rather play as many hands as you can, so it’s worth showing up on time. But online, let’s say you’ve just busted out of a tournament and are looking to fire up another one. Given two equally desirable tournaments, one of which is just about to start and the other of which is in Level 3 or 4, which is better?
Answering that question would require knowing how much of an ROI hit you’re going to take by jumping in at a later level, which in turn requires an estimate of how many chips you would have picked up on average playing those hands. That’s hard to calculate, but it would certainly depend on the field – in a loose, fishy tournament, it might be quite a lot of chips, and it would probably be worth playing from the beginning in the hopes of picking up a monster and getting paid off. On the other hand, in a tight tournament where there aren’t many chips getting traded around early, lopping 20 or 30 minutes off your playtime may be a very good idea.
Alex Weldon (@benefactumgames) is a freelance writer, game designer and semipro poker player from Montreal, Quebec, Canada.