Jordan Lord

How often should a zombie team win?

22 Aug 2026

Motivation

I work on a football management game. One challenging problem has been the curse of "zombie" teams. A zombie team is a club that is unmanaged where the squad has deteriorated to only reserve players. It's basically the poorest quality team in the game.

The curse is that they still get results against strong teams. They score on average 0.4 goals per game and manage to get at least a draw in approximately 4% of matches. Before diving into changing the match engine, I needed a model that I could tune the match engine to, otherwise I'd just be moving multipliers until the results align. Changing modifiers based on feel has been our current approach so far.

One of the goals of this article is to provide a practical benchmark for further analysis and development of a football match simulation engine.

Why Elo?

Why Elo? Elo is able to calculate an expected result given the difference in team strengths. It gives a model that extrapolates intuitively from real teams that are equally matched to extreme mismatches that aren't usually seen in real world football. Those extreme mismatches are where real-world data is sparse. Also Elo has already been applied to football by Hvattum and Arntzen and also used by systems such as ClubElo.

The current zombie landscape

Production data showed that the favourite team, with a lineup-rating advantage of 20 or more, won 97.6%, drew 1.3% and lost 1.1% of the time. However, the controlled zombie test was worse at roughly a 4% result rate.

Looking at the tables later in this article, those result rates fit at around mismatches of +751 and +660 Elo respectively (using a 400-point benchmark). Intuitively this doesn't feel right. A real zombie would be equivalent to a non-professional team. As a comparison using data from ClubElo.com, we're actually seeing a result rate that would be closer to Arsenal or Manchester City being in League Two (as of August 2026), rather than in a non-professional league. That rate comes at +650 on average for an elite Premier League team vs a League Two team. Hence you could imagine the Premier League champions dropping a couple of points over the course of a 46 game League Two season. This would loosely align with the favourite's observed result rate of 97.6%. However, if we want the true zombie non-professional effect, then a zombie result should be extremely rare.

We can turn to chess to build an intuitive loose mental model for the zombie. A casual online chess player might have a rating of 1,000 while a grandmaster has a rating of 2,500. That's a +1,500 gap. Note this is only an initial observation based on intuition, not the actual method of calibration.

Adding draws with the Rao-Kupper model

Standard Elo formulas give an expected score given the rating difference between two competitors. In a binary game, the score can be treated as a win probability. However, that doesn't directly translate into football. Football is a ternary game, so we need to model draws if we want to build a model. To achieve this, I attempted both the Rao-Kupper and Davidson models. Although both fitted the data well, I found that the Rao-Kupper ordered-logistic model had a more intuitive extreme mismatch tail. So that's the one that's used moving forwards, as the extreme mismatch tail is where the zombies live.

For fitting, I took 46,652 matches for training and 10,916 as a chronological holdout from the public Club Football Match Data repository. The fitted model's chronological holdout log loss was 1.001, beating the frequency baseline on unseen matches at 1.075. The frequency baseline basically used the training set's overall home-win, draw, and away-win frequencies.

With the Elo scale fixed at 400, I used maximum likelihood to fit home advantage and the neutral draw margin. I found that the fitted equal-team draw probability was 30%.

In the dataset, there is a home advantage so we have to factor that in. Home advantage was fitted at approximately 59.8 Elo points. Although 430 was the Elo scale that fitted the given dataset, I chose to fix the Elo scale at 400 as that is more conventional, and refitted the other parameters. The neutralDrawMargin is the range around a neutral performance which becomes a draw at approximately 30%.

eloScale = 400
homeAdvantage = 59.8
neutralDrawMargin = 0.6195

P(draw | equal teams, neutral ground)
    = 1 - 2 * sigmoid(-neutralDrawMargin)
    = 30.0%

Using those formulas, we can calculate the probability of a home win, away win or a draw. d is the home team's Elo minus the away team's Elo.

effectiveDifference = d + homeAdvantage
z = ln(10) * effectiveDifference / eloScale

P(home win) = sigmoid(z - neutralDrawMargin)
P(away win) = sigmoid(-z - neutralDrawMargin)
P(draw)     = 1 - P(home win) - P(away win)

P(underdog result) = P(draw) + P(underdog win)

For a neutral match, we set homeAdvantage to zero. If the stronger team is away, we apply the home advantage to the opposition first.

P(home win) + P(draw) + P(away win) = 1

Result probabilities

Plugging all of our parameters together, and precalculating for a pre-set of Elo rating differences, we get the following table for a neutral venue match.

d P(favourite win) P(draw) P(underdog win) P(underdog result)
+0 34.990% 30.021% 34.990% 65.010%
+100 48.904% 27.862% 23.234% 51.096%
+200 62.990% 22.465% 14.544% 37.010%
+300 75.165% 16.100% 8.735% 24.835%
+400 84.331% 10.561% 5.107% 15.669%
+500 90.540% 6.522% 2.938% 9.460%
+600 94.451% 3.876% 1.673% 5.549%
+700 96.802% 2.250% 0.948% 3.198%
+800 98.176% 1.289% 0.535% 1.824%
+900 98.966% 0.732% 0.302% 1.034%
+1,000 99.416% 0.414% 0.170% 0.584%
+1,250 99.861% 0.099% 0.040% 0.139%
+1,500 99.967% 0.023% 0.010% 0.033%
+1,750 99.992% 0.006% 0.002% 0.008%
+2,000 99.998% 0.001% 0.001% 0.002%

Looking at 57,568 domestic league matches from July 2015 to June 2025 from the public Club Football Match Data repository, our calculations using the Rao-Kupper model approximately line up. At the extremes it's harder to align the dataset because outlier results have a bigger impact with less data available, e.g. the 500-600 row contains 18 matches which includes one underdog win. So we must use our intuition.

Elo difference Matches Favourite win Draw Underdog win Underdog result
0-25 10,153 36.4% 29.6% 34.0% 63.6%
25-50 9,184 39.6% 29.1% 31.3% 60.4%
50-100 14,841 43.8% 29.1% 27.1% 56.2%
100-150 9,514 50.4% 25.7% 24.0% 49.6%
150-200 5,377 58.3% 22.6% 19.1% 41.7%
200-250 3,381 64.8% 20.8% 14.5% 35.2%
250-300 2,116 70.6% 17.2% 12.1% 29.3%
300-400 2,406 77.5% 15.0% 7.5% 22.5%
400-500 578 84.3% 9.5% 6.2% 15.7%
500-600 18 94.4% 0.0% 5.6% 5.6%

For the fitted predictions below, we use each match's exact Elo gap after applying the fitted home advantage. This is a calibration check, although performance of the model remained similar on the chronological holdout.

Elo difference Fitted favourite win Fitted draw Fitted underdog win Fitted underdog result
0-25 36.82% 29.19% 33.99% 63.18%
25-50 40.38% 28.92% 30.70% 59.62%
50-100 45.23% 28.12% 26.66% 54.77%
100-150 52.04% 26.34% 21.62% 47.96%
150-200 59.08% 23.79% 17.13% 40.92%
200-250 65.48% 20.97% 13.55% 34.52%
250-300 71.86% 17.75% 10.39% 28.14%
300-400 78.78% 13.85% 7.37% 21.22%
400-500 85.89% 9.52% 4.60% 14.11%
500-600 91.45% 5.90% 2.65% 8.55%

Next steps

So how often should a zombie team win? The 1,500 rating gap gives a zombie a 0.010% chance of winning, which is roughly once in every 10,000 matches. That can act as a good stress-test target moving forward. However, it's not calibrated, for that we need more context from the game and its engine.

Although Elo gives us a mathematical bridge to real-world football, to really understand the zombie, we have to now bridge Elo to the game's engine. The next step is to map the 0-100 player ratings including tactics onto Elo, then test whether the engine follows the curve all the way to the extreme mismatches. Once the next bridge is built, there will be an intuitive statistical link between real-world football and the game's engine. Thus that will help build a better intuition to make solid decisions and evaluate the engine's output and finally kill zombies for good.

References