How does scoring rate change in a football match based on time elapsed and game state?

John Knight

22 July 2025

Creating a logistic regression model to predict the chance of scoring a goal in each minute of a football match based on the pre-match odds, current score, minutes elapsed, and any red cards.

When is a football team most likely to score? A simple hypothesis would be that the chance of scoring increases as the game goes on, and that teams who are ahead are less likely to score than teams who are behind as they defend their lead. But what do the data say?

I looked at goal times from the big 5 European leagues (England, Spain, Germany, Italy, France) since 2017. Now, a tricky part of goal times in football is injury time. Conventionally, these are often listed as 45’ for a goal in first half injury time and 90’ for second half injury time, so you naturally end up with larger goal totals in these minutes, which will skew the totals and trends.

Alternatively, you could try and look at injury time minutes individually; but then, how do you know which minutes were actually played, and played in full? I don’t currently have that level of detail, so I decided to ignore injury time goals for the purpose of this analysis, guaranteeing that the 90 minutes considered were all played in full.

So firstly, here is a summary of the goals in each of the 90 minutes:

It seems like we see the expected upward trend, with understandably low totals at the start of each half as it’s harder to score when each team’s entire XI start in their own half. But what’s that patch of high totals between 48 and 58 minutes? It doesn’t appear to be a data error, but why would there be a stretch of unusually high scoring just after half time like this?

Here is the same chart but with xG instead of goals. Compared to the previous chart, we can see that the trend is almost identical, but the variance is much lower. I will continue using goals for this particular analysis, but it’s a good demonstration of why xG is so useful in statistical analysis of football.

So why does scoring tend to increase as a game progresses? One obvious factor is that every game starts off at 0-0, so the scores are more likely to be level early in games than late in games. Here is a summary of the scoreline by minute:

As you can see, for almost the entire first half a level scoreline is most common, and thereafter it is more frequently a one-goal lead for either team. If level games generally play a bit tighter and more defensive than games where one team is leading, then that would explain the lower scoring early in games. When we look at a smoothed plot of scoring rate categorised by lead, we can see that teams with a two-goal lead score at the highest rate, followed by teams with a one-goal lead:

The problem here is we have an additional factor: the quality of the teams. If a team is leading by two goals, then it is more likely that they are simply much better than their opponent, and hence more likely to score next. So we need to also account for team strength. I divided all teams into quartiles, based on their pre-match bookmaker odds, with quartile 4 being the strongest teams and quartile 1 being the weakest:

So now it’s time to put it all together. The simplest way to estimate the effects of lots of variables when applied simultaneously is with a multiple regression. In this case we will use a logistic regression, since the outcome is binary (0 goals or 1 goal).

I categorized the current lead with a minimum of “-2 or less” and a maximum of “2 or more”. Additional features in the model were the minute, pre-match odds (converted to probability), and red cards for and against.

I decided to create separate models for the first and second halves, since the shape of some of the plots suggested it may not be a simple linear relationship for 90 minutes. Based on the low scoring in minutes 1, 2, 46 and 47, I also included flag variables for min1 and min2 of each half.

Finally, for each half I trained a second model including interactions between lead and minute, lead and pre-match odds, and between lead and red cards for and against. After inspecting the interaction terms’ p-values, plus a likelihood ratio test and Akaike Information Criterion (AIC), it seemed like the simpler model was about the same. If in doubt, always stick with the simpler model!

Logistic Regression: First Half

Coefficient Std. Error z-value p-value CI Lower CI Upper
Intercept -5.080 0.055 -92.566 0.000 -5.187 -4.972
Trailing (-1) -0.022 0.053 -0.417 0.677 -0.126 0.081
Level (0) -0.047 0.050 -0.929 0.353 -0.145 0.052
Leading (1) -0.132 0.053 -2.497 0.013 -0.236 -0.028
Leading (2 or more) -0.064 0.063 -1.022 0.307 -0.188 0.059
First Min of Half -0.620 0.075 -8.317 0.000 -0.767 -0.474
Second Min of Half -0.248 0.063 -3.968 0.000 -0.371 -0.126
Minute 0.004 0.001 5.421 0.000 0.002 0.005
Red Card -0.766 0.139 -5.507 0.000 -1.039 -0.493
Opponent Red Card 0.536 0.073 7.354 0.000 0.393 0.679
Pre-match Win Prob 1.752 0.038 45.761 0.000 1.677 1.827



If you aren’t familiar with logistic regression results, don’t worry too much about the columns other than Coefficient. Intercept is only used when making predictions, otherwise that isn’t too relevant.

Each coefficient represents the associated change in log odds of scoring a goal. Firstly, we can see that teams leading by 1 have a lower coefficient (-0.132) than other scorelines. The first two minutes of the half, as expected, have lower scoring, and then there is a small increase (0.004) for each minute as the half progresses. A red card (-0.766) reduces the chance of scoring more than an opposition red card (0.536) increases it. Predictably, pre-match win probability (1.752) has a strong positive correlation with scoring rate.

Logistic Regression: Second Half

Coefficient Std. Error z-value p-value CI Lower CI Upper
Intercept -4.758 0.029 -165.596 0.000 -4.814 -4.702
Trailing (-1) -0.036 0.027 -1.335 0.182 -0.088 0.017
Level (0) -0.143 0.026 -5.576 0.000 -0.193 -0.093
Leading (1) -0.228 0.028 -8.249 0.000 -0.282 -0.174
Leading (2 or more) -0.156 0.030 -5.243 0.000 -0.215 -0.098
First Min of Half -0.695 0.068 -10.218 0.000 -0.828 -0.561
Second Min of Half -0.170 0.053 -3.176 0.001 -0.274 -0.065
Minute -0.001 0.001 -1.866 0.062 -0.002 0.000
Red Card -0.643 0.058 -11.162 0.000 -0.756 -0.530
Opponent Red Card 0.475 0.034 14.071 0.000 0.409 0.542
Pre-match Win Prob 1.813 0.038 47.985 0.000 1.739 1.887



In the second half, the effects of the scorelines are a little more pronounced: a one goal lead has a coefficient of -0.228 compared to -0.132 in the first half. We can also see that the effect of each minute is actually slightly negative now (-0.001).

To demonstrate these results, I used the median of each quartile of pre-match odds and predicted each minute of the game with scorelines of -1, 0, and 1, with no red cards:

So to summarize our findings:

If we revisit the first plot in this article, the unusually high values between 48 and 58 minutes now make a little more sense. I have added a red line to the plot which now looks like a slight downward trend in the second half, rather than a series of observations above the overall trend:

There are, of course, some limitations to this analysis. Injury time in both halves has been ignored, as have factors like league- or game-specific goal totals. There is also the question of whether goals beget more goals: all other things being equal, does a scoreline of 1-1 tend to predict more goals than a scoreline of 0-0? I may visit these ideas in a future analysis.