Try to play against unskilled opponents rather than skilled opponents is pretty important if you can help it.
Other than that, generally the bigger contests are better if you're an above-average player. I'll quote myself from the Week 14 thread:
Other things equal, you want your teams to constitute the smallest percentage of the total action possible (above zero, of course). You can see this by considering a
reductio ad absurdum in which we enter ten entries into a ten-team 50/50, such that we constitute 100% of the action. In that case, all we're doing is paying the rake. We can't possibly make a profit.
It's a matter of semantics whether we call this an effect of the rake or something else -- but either way, if you're an above-average player, and if we hold the quality of your opponents constant, you're better off playing in a 100-team contest than in a 10-team contest, and your're better off playing in a 10-team contest than in a H2H contest. Jeff Pasquino shows you the math
here, but an easy way to think about it is that in a 100-team contest, a full 99% of the teams constitute "the field," which you're expected to have an advantage over. In a 10-team contest, only 90% of the teams constitute "the field." Playing in a 10-team contest is a bit like entering ten identical teams in a 100-team contest -- in which case each of your teams is facing itself nine times, which is a tough matchup and makes it harder to beat the rake.
The first statement is true, and honestly the single most important thing; if you want to win, play inferior opponents.
The second statement strikes me as intuitively true but I think the math you link is questionable. I'm too tired to prove it mathematically, but let me make a few points.
1) Jeff's math doesn't pass the smell test. If you have a 52% edge you will win a 10 person 50/50 56% of the time? Really? This sounds like the mathematical equivalent of alchemy. I think (again, too tired to debug fully) the problem is that Jeff is treating a 50/50 as a set of INDEPENDENT H2Hs, whereas of course they are not independent--your opponent's lineups are (somewhat) independent, but your line-up is the same throughout.
Put it this way, if I told you last week: "Take a random 100-man 50/50 I am in. Pull 5 random opponents in that 50/50. Suppose it turns out that i lost to all 5 of those opponents. Now pull a 6th random opponent. How likely do you think it is that I lost to that 6th opponent?" If you answered "way more likely than 50%" (and I hope you did!) you have just proven that they are not independent events.
2) There are actually two reasons that a large field is generally better from a pure winning percentage than a small field (not to say it's necessarily better from a long-term profitability standpoint, which is actually a more mathematically complex question due to issues related to kelly optimization and bankroll management).
a) The simplest and most important one: your opponents are worse. Look at a 10-man H2H roster sometime, particularly on the $25+ levels. It's all condia, makisupa etc. Those guys are not immortal but they are better than average.
b) The second reason is more subtle. Let's suppose that I am indeed better than average, i.e., in any given week, my expected score is 5 points better than the expected score of the FD population: E(me) = E(FD) + 5. And let's say that the expected average score of a given 50/50 is roughly equal to the expected score of FD as a whole, i.e., E(5050) = E(FD). That means that E(me) = E(5050) + 5.
If there were no variance, everything would be hunky dory and I would win every time. In fact, there are two types of variance that matter: variance in how much I beat the overall FD average, and variance in how the average in my 5050 differs from the overall FD average.
This framework lets us break down the disadvantages of a small 50/50 into a few different parts:
1) With a small 50/50, there is a lot of variance in how the 50/50 average differs from the global FD average. This variance hurts a good player (but helps a bad player...). For example, if the global FD average this week is 130, in a 100-man double up, you can be pretty sure that the cut-off will be ~128-132, but in a 10-man 50/50 it may be anywhere from 125-135. If my expected score is 135, I'd much rather have the 100-man double up.
2) With a small 50/50, my opponents are just better. This is hugely important. Look at who enters a 10-man $25 game on FD some time. It's all condia, makisupa etc.
ffmysoapbox:
