The group stage of the 2021 Mid-Season Invitational has wrapped up, and as promised it’s been quite the bumpy ride. This has been an incredibly favorite-dominated tournament, with very few upsets. However, because of payout compression due to how the vig works on heavy favorites, you would have lost money even if you had always bet on the favorite!
Our model’s view was that none of these matches were as lopsided as the market would imply - and generally, this is the case, as seen by our overall strategy performance, which almost always bets on the underdog if it bets at all. It’s possible that our model does not properly account for cross-regional differences. For now, let’s assume that the market-implied win probabilities were more correct than ours: even in this case, we’ll show that this was still a particularly lopsided tournament.
Let’s look at only the very lopsided games - games where the market believes the underdog to have under a 25% chance of winning. Of the 36 games in the group stage, 18 would have fit this bill - exactly half. So, right of the bat, half of the games are expected to be stomps. That doesn’t mean that there won’t be upsets, of course; market-implied win probabilities for these underdogs are low, but not zero:
| match_name | date | pct_win | win | |------------|------------|---------|-------| | C9 v DK | 2021-05-06 | 16.54% | FALSE | | PGG v RNG | 2021-05-06 | 10.99% | FALSE | | PGG v RNG | 2021-05-07 | 11.83% | FALSE | | UOL v RNG | 2021-05-07 | 16.54% | FALSE | | INF v DK | 2021-05-07 | 10.14% | FALSE | | UOL v RNG | 2021-05-08 | 15.05% | FALSE | | DFM v DK | 2021-05-08 | 10.99% | FALSE | | INF v C9 | 2021-05-08 | 22.1% | FALSE | | PNG v MAD | 2021-05-08 | 22.1% | FALSE | | UOL v RNG | 2021-05-09 | 15.05% | FALSE | | PGG v RNG | 2021-05-09 | 10.99% | FALSE | | UOL v RNG | 2021-05-09 | 12.66% | FALSE | | PGG v RNG | 2021-05-09 | 10.99% | FALSE | | PNG v MAD | 2021-05-10 | 23.42% | FALSE | | C9 v DK | 2021-05-11 | 18.01% | TRUE | | INF v DK | 2021-05-11 | 9.26% | FALSE | | DFM v DK | 2021-05-11 | 11.83% | FALSE | | INF v C9 | 2021-05-11 | 23.42% | FALSE |
Of these lopsided games, how many upsets would we expect to see? While our cutoff for these underdogs was 25%, each individual match had its own probability. Turns out, we’re just looking for the expected value of number of wins, which if you’ve read our EV article is just the sum of each individual match’s probability! Adding these up, we find that we would expect, on average, 2.72 upsets. How many were there? Just one, with Cloud9 squeezing out a win against DWG KIA yesterday.
Let’s repeat that: half of all matches in the group stage were considered fairly lopsided, and among those, there was only one upset.
If we had known things would be this one-sided, and had just bet on the favorite in every single match, we’d have made a killing, right?
As with all things in life, it’s not that simple:
First of all, so far we’ve covered only the very lopsided matches. Among the other half of the group stage, there were a fair number of minor upsets. Among teams with a 25-50% probability of winning, there were 7 upsets, which was fairly close to expectation.
Second, in heavily lopsided matches, the vig ends up affecting the payout of the favorite much more than the underdog (see our Vig article for more info). What this means, effectively, is that you’re getting paid out much less than you should be given the odds.
If we had bet $100 on every single match, always betting on either the favorite or on the underdog, we would have lost money either way:
Betting on the favorite would not have lost nearly as much, of course, but each win was worth so little due to the payout compression that it was still unprofitable.
Our own performance lagged behind these naive strategies. Our model generally believes matches to not be as lopsided as the market does, and thus is more likely to bet on underdogs. In addition, we scale our bets relative to our disagreement, which led to us putting more money on the more lopsided matches - which, as we’ve already shown, had disproportionately few payouts.
Here’s our overall performance:
And, if we compare it to the favorite/underdog-only betting, with those bets scaled up to match our average bet size:
(gaps in the model pnl are games that we did not place a bet on)
Even if we consider the market-implied probabilities to bet correct (or at the very least, more correct than our model), we still had significantly worse than expected performance.
If we run a Monte Carlo simulation of all of the matches, using market odds as the true probabilities, we would get this distribution of outcomes:
On average, we would expect to lose $457, due to just bleeding small amounts to the vig. In fact, this checks out pretty nicely: in total, we wagered ~$7000, and the market’s typical vig is around 6%, which would imply a $420 loss on average.
Our odds of being unprofitable were 59.56% (again, assuming the market probabilities to be correct), which again makes sense since the vig is a steady bleed, and this is a right-skewed distribution due to the payouts being high on underdog bets.
Our actual performance falls in the 13.53th percentile, which means that our odds of doing as poorly as we did, or worse, are only 13.53%. While this is hardly a statistically impossible result, it’s still painfully unlucky, and that’s assuming that the market is correct on these predictions. And after all, we’ve had quite strong performance by disagreeing with the market.
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