Warning: what follows involves trying to generalise and abstract the season to date. If you think that’s impossible, skip this thread. Nothing below proves anything, but it suggests a lot.
For a few decades now, baseball has made use of the ‘Pythagorean expectation’, which estimates how many games a baseball team ‘should have’ won based on how many runs they scored and how many they allowed. Teams that win more games than they should have are considered ‘lucky’, and those that lost more are considered ‘unlucky’.
On the one hand, luck is probably best considered to be a random, uncontrollable fluctuation. It’s possible, for example, to roll a six with a single die four times in a row, but considering doing so has a probability of about .08%, successfully doing so can only be considered extremely lucky. On the other hand, it may be that teams are capable of ‘producing’ their own luck. More on that below.
Because of the presence of draws in football, matching the Pythagorean expectation to predict how many points a club ‘should’ score in a season based on how many goals they score and let in is a bit more complex, but, taking into account recent season performances, Martin Eastwood of Pena.lt/y has come up with an empirically deduced formula for an ‘MPE’ that calculates an expected point total for a club in the league based on goals scored and allowed. According to Eastwood, his formula has an MSE of 4.04, which means that, on average, the actual, real world number of points scored by a club tends to be about four points off (one way or the other) from what the predictor estimates. In terms of qualifying for fourth place, a difference of four points is a lot. But trying to rein in randomness in a sport like football is astonishingly tricky, and getting that error down to 4 is an impressive feat.
So how do Spurs fare with the MPE? Before showing the graph, there are a few considerations. First, many posters on the forum throughout the AVB reign complained about how ‘lucky’ we had been, winning 1–0 off lucky penalties (in contrast to last season’s dearth of penalties that I discussed). These lucky wins were the bare minimum route to three points. Our losses to West Ham, City, and Liverpool suggested what would happen once AVB’s luck ‘ran out’, so it was imperative to sack AVB to bring in a manager who would not be riding his luck off fluky 1–0 (Soldado, pen) matches.
Second, however, other posters have argued that Tim Sherwood has been the lucky one, getting a bunch of players back from injury just in time and reaping the benefits of a comparatively easier schedule. Facing City at home is a less terrifying proposition, for example, than going to the Etihad.
So, again, how do Spurs fare? Well, here’s the chart (calculations only done from the sixth match to reduce noise):
Most notable is the fact that we have scored far more points in the real world than we ‘should’ have. Currently, Spurs can attribute about 11.5 points strictly to luck, considering how little we have been scoring and how many goals we have been conceding. From the MPE, we should be expecting to to finish the season on about 54 points, yet we’re almost at that level now.
It’s clear, from looking at the expected season end (green), that both defeats to West Ham and City hurt our expected total badly. Since the 0–3 was early in the season, the subsequent two wins helped erase that fall, but the massacre in Manchester has taken the rest of the season to erase (not helped by a certain, job-costing 1–5 defeat). We haven’t lost a lot, but when we have, we’ve typically gotten absolutely pounded, which is, perversely, lucky. If City had beaten us 1–0 and those other five goals had been distributed across other matches, we’d probably have fewer points in real life. Better to lose 6–0 once than six times 1–0 and all that…
But what’s interesting is that we seem to have been getting luckier as the season has gone on. After City, we had seven more points than we should have. Now it’s almost 12 (though it has been falling since our win against Everton). Falling results are obvious: we lose/draw matches or tonk other sides (like Newcastle) to make our goal tallies more representative of the number of points we actually do have. But results that widen the gap are confusing: either we get tonked (so the predictor has pity on us) or we win ‘luckily’.
Under AVB, it looks like we ended up having ten extra ‘lucky’ points, while Sherwood has only brought in another point. That would suggest that, perhaps, Sherwood is getting results in line with Spurs’ skill, while AVB was riding Spurs’ luck. But the chart above is a bit unfair, since it adds the preëxisting goals for and against that we had under AVB to Sherwood’s account. It’s a kind of handicap. If we look only at the matches since Sherwood has been in charge, we see:
Once Sherwood has a blank slate in terms of MPE, then he’s now accumulated seven extra ‘lucky’ points in 11 matches. After 11 matches, AVB had only 2 ‘lucky’ points. So that suggests that Sherwood has been luckier than AVB so far this season. The ‘Soldado pen, lucky AVB’ crowd can’t have expected that, right?
But then there’s the question of ‘manufacturing’ luck alluded to above. On the one hand, luck should be random… It’s possible to have four instances of good luck in a row, but in the long run, it should even out. Maybe Sherwood has some kind of gift to grind out wins when matches are tight. Perhaps that’s the result of his man management alluded to by the article that suggested today that Sherwood could stick around even if we don’t get fourth. But when I consider our performance at Carrow Road and look at the table as a whole, sorted by MPE:
I think to myself, ‘Yeah, maybe eighth sounds about right.’
For a few decades now, baseball has made use of the ‘Pythagorean expectation’, which estimates how many games a baseball team ‘should have’ won based on how many runs they scored and how many they allowed. Teams that win more games than they should have are considered ‘lucky’, and those that lost more are considered ‘unlucky’.
On the one hand, luck is probably best considered to be a random, uncontrollable fluctuation. It’s possible, for example, to roll a six with a single die four times in a row, but considering doing so has a probability of about .08%, successfully doing so can only be considered extremely lucky. On the other hand, it may be that teams are capable of ‘producing’ their own luck. More on that below.
Because of the presence of draws in football, matching the Pythagorean expectation to predict how many points a club ‘should’ score in a season based on how many goals they score and let in is a bit more complex, but, taking into account recent season performances, Martin Eastwood of Pena.lt/y has come up with an empirically deduced formula for an ‘MPE’ that calculates an expected point total for a club in the league based on goals scored and allowed. According to Eastwood, his formula has an MSE of 4.04, which means that, on average, the actual, real world number of points scored by a club tends to be about four points off (one way or the other) from what the predictor estimates. In terms of qualifying for fourth place, a difference of four points is a lot. But trying to rein in randomness in a sport like football is astonishingly tricky, and getting that error down to 4 is an impressive feat.
So how do Spurs fare with the MPE? Before showing the graph, there are a few considerations. First, many posters on the forum throughout the AVB reign complained about how ‘lucky’ we had been, winning 1–0 off lucky penalties (in contrast to last season’s dearth of penalties that I discussed). These lucky wins were the bare minimum route to three points. Our losses to West Ham, City, and Liverpool suggested what would happen once AVB’s luck ‘ran out’, so it was imperative to sack AVB to bring in a manager who would not be riding his luck off fluky 1–0 (Soldado, pen) matches.
Second, however, other posters have argued that Tim Sherwood has been the lucky one, getting a bunch of players back from injury just in time and reaping the benefits of a comparatively easier schedule. Facing City at home is a less terrifying proposition, for example, than going to the Etihad.
So, again, how do Spurs fare? Well, here’s the chart (calculations only done from the sixth match to reduce noise):
Most notable is the fact that we have scored far more points in the real world than we ‘should’ have. Currently, Spurs can attribute about 11.5 points strictly to luck, considering how little we have been scoring and how many goals we have been conceding. From the MPE, we should be expecting to to finish the season on about 54 points, yet we’re almost at that level now.
It’s clear, from looking at the expected season end (green), that both defeats to West Ham and City hurt our expected total badly. Since the 0–3 was early in the season, the subsequent two wins helped erase that fall, but the massacre in Manchester has taken the rest of the season to erase (not helped by a certain, job-costing 1–5 defeat). We haven’t lost a lot, but when we have, we’ve typically gotten absolutely pounded, which is, perversely, lucky. If City had beaten us 1–0 and those other five goals had been distributed across other matches, we’d probably have fewer points in real life. Better to lose 6–0 once than six times 1–0 and all that…
But what’s interesting is that we seem to have been getting luckier as the season has gone on. After City, we had seven more points than we should have. Now it’s almost 12 (though it has been falling since our win against Everton). Falling results are obvious: we lose/draw matches or tonk other sides (like Newcastle) to make our goal tallies more representative of the number of points we actually do have. But results that widen the gap are confusing: either we get tonked (so the predictor has pity on us) or we win ‘luckily’.
Under AVB, it looks like we ended up having ten extra ‘lucky’ points, while Sherwood has only brought in another point. That would suggest that, perhaps, Sherwood is getting results in line with Spurs’ skill, while AVB was riding Spurs’ luck. But the chart above is a bit unfair, since it adds the preëxisting goals for and against that we had under AVB to Sherwood’s account. It’s a kind of handicap. If we look only at the matches since Sherwood has been in charge, we see:
Once Sherwood has a blank slate in terms of MPE, then he’s now accumulated seven extra ‘lucky’ points in 11 matches. After 11 matches, AVB had only 2 ‘lucky’ points. So that suggests that Sherwood has been luckier than AVB so far this season. The ‘Soldado pen, lucky AVB’ crowd can’t have expected that, right?
But then there’s the question of ‘manufacturing’ luck alluded to above. On the one hand, luck should be random… It’s possible to have four instances of good luck in a row, but in the long run, it should even out. Maybe Sherwood has some kind of gift to grind out wins when matches are tight. Perhaps that’s the result of his man management alluded to by the article that suggested today that Sherwood could stick around even if we don’t get fourth. But when I consider our performance at Carrow Road and look at the table as a whole, sorted by MPE:
I think to myself, ‘Yeah, maybe eighth sounds about right.’
