What Is the Most Underrated DotA 2 Team?

My previous posts about betting at the DotA 2 Lounge have been enormously popular.  There have been over 1000 games since my last post, and I decided to revisit the vastly expanded data set.  I have previously made the scripts available to anyone wishing to perform these analyses themselves.

First, a moment to talk about parimutuel betting.  The DotA 2 Lounge runs a parimutuel betting scheme.  Suppose that there are two teams playing and a better bets on the winning team.  That player's payout, assuming no house take, is simply given by the value of the total pool times the fraction of the pool in favor of the winning team that was bet by the player.

It's noteworthy that a successful gambler is not so much betting for the winning team as to bet for the team that maximizes their expected winnings.  Let's take a look at an example to demonstrate this.

Team	Team A	Team B
% of Bets	10%	90%
True Chance of Winning	25%	75%

In this example, I have two teams playing, Team A and Team B.  90% of the bets are in favor of Team B.  This means that if Team A wins, then the payout will be 9-to-1.  The important piece of information here is the true chance of winning.  In the real world, this is certainly not known exactly so I have made it up for this example.

The expected return on investment for a bet on Team A is then 0.25 / 0.1 = 2.5.  The expected payout for a bet on Team B per unit bet is  0.75 / 0.9 = 0.83.  Therefore, a smart better will bet on the underdog in this case.  A bet on Team B is actually more likely to lose money than to gain it.

The two important variables here are the proportion of bets on each team, which is given to you at the DotA 2 Lounge.  You should bet as late as possible so that you can get the best possible information on who the other gamblers are betting on.  Next, you should estimate the chances of each team winning.  Bet on the team that you believe has a higher chance of winning than the proportion of bets shown.  If you believe that the chances of each team winning are identical to the proportion of bets, then which team you bet on is irrelevant.

Parimutuel betting with no house take is a zero-sum game.  If the gamblers are good at appraising each team's chances of winning, then it is irrelevant which team you bet on.  This is the second figure I have shown in each of my previous studies.  Previously, I found that the crowd was very good at this: random betting neither had a significant profit or loss.  This still appears to be the case.

Figure 1:  Random betting strategy at the DotA 2 lounge in the first 1637 (1414 of them were bettable) games.  Average 48 rares lost.   Standard deviation 39.6.   Zero (the break even point) is within 2 standard deviations of the mean, so I conclude that the random betting strategy is neither a winning nor a losing one, and that the crowd is still rational.

Now I'd like to know what the most overrated and underrated teams are.  In order to determine this, I will use the following method:  For each team that played at least 10 games at the DotA 2 Lounge, I will propose that I bet one rare on them per game and record the payout.  Then, I will simulate 10,000 trials of random betting only on the set of games that this team played.  I will use these simulated random bets to determine the mean and standard deviation of the payouts in games played by each team.  The standard score of each team will be equal to:

Standard scores over 2 or below -2 will be considered significant enough to call a team "underrated" or "overrated", respectively.  All other standard scores will be considered statistically insignificant, and will not be reported.

Most Underrated Teams Team Score Alliance 15.0561 Na'Vi 8.79236 LGD.cn 8.74577 DK 8.02724 VG 5.32555 TongFu 5.19414 Kaipi 4.9593 Speed 4.7966 iG 4.08545 Fnatic.eu 3.77795 Liquid 3.57337 Orange 3.37028 Sigma.int 3.25397 Mski 3.15417 MiTH 2.91098 Empire 2.55101 mouz 2.24567 FD 2.20341 Most Overrated Teams Team Score WPCA -3.60975 RS -3.36541 aL -2.24014 MUFC -2.12442

Remarkably, many popular teams scored so well over time that I was actually unable to simulate a scenario where random betting did better than just betting in their favor every time in 10,000 trials.  Alliance, Na'Vi, LGD.cn, and DK in particular seem to be very underrated. The only significantly overrated teams at the DotA 2 Lounge were WPCA, RS, aL and MUFC.  Remarkably, WPCA never won a match, so random betting always did at least as well as betting on them!  These teams are all quite overrated, so next time you see them playing, you might consider betting for the opposition. Note that all of this is based on historical data and does not guarantee future results.  If based on this data everyone starts betting for Alliance then Alliance may soon be one of the most overrated teams!  Or, if aL picks up some awesome new players, it may not be at all fair or accurate to base their future performance on their past failure to deliver. Remember, like I said above: parimutuel betting is all about deciding whether the crowd has predicted the correct probabilities of winning, and betting against the crowd favorite is a good idea in any situation where you think that the crowd favorite's actual chance of winning is less than the proportion of bets in its favor. Good luck with your bets!