A Statistical Team of 2022, accounting for sample size
This post is largely building on the method used in my previous post, 'A Statistical Analysis to Determine and Improve upon the ICC's Team of the "Decade".
With the last of the Tests completed for the year, now seems a fitting time to put together a team by this method. Personally, I'd feel quite silly to write a team of the year post before the last test was even finished.
Broadly, the team will have the following structure:
2 × Openers
1 × Number 3
2 × Batters
1 × Allrounder
1 × Wicketkeeper
2 × Seamer
1 × Spinner
1 × Next Best Bowler
In order to select this though, we need to start with definitions for each position, and given we're dealing with a short time frame, we also need to take into account sample size. To pre-empt some hate mail, please note that some nations have only played 7 tests this year (3 have played exactly zero, but that's another point). To put that in context, if a player played 7 matches for England, but another played 4 for the West Indies, the West Indies player would have played a larger percentage of available tests. This means, to really do this justice, we have to take into account sample size, and do away with minimums for ranking players.
The method I'll use here involves a simplified type of Bayesian Analysis. In essence, any statistic in cricket has two features, a value and an uncertainty. Usually, only the value is given, for example, Adam Voges' batting average, which is usually reported as 61.87, but what is omitted is the uncertainty in this. Now, there are two ways of finding this, the proper way and the lazy way:
- Proper: Find the standard deviation of the population, and the uncertainty is that divided by the square root of times dismissed.
- Lazy: Use the fact that batting scores are roughly exponentially (well, geometrically really) distributed, so the standard deviation is generally about the batting average. This means that the uncertainty is just the average divided by the square root of number of number of times dismissed.
The first is really the one I should use, but the difference is generally within 10%, and scraping the data for the top one would take longer than it's really worth. The lazy one, for Voges, is 61.87 ± 12.62, ie his average is actually 61.87 ± 12.62. Compare this to Steve Smith, for example, which is 60.58 ± 5.10. It's worth noting, however, that Voges is a special edge case, the proper measure of his standard deviation is ridiculously high even for his average, but that's the subject of a different post. For those curious, his actual standard deviation is 124.29, so the actual uncertainty is ±25.37, but he is very much an anomaly. I can find no other examples of it getting this ridiculous.
To make use of this, we need two other pieces of information, these being the 'average' player and the 'standard deviation of the average player'. The reason for this is that what we're effectively going to do is look at how a player has performed, and the uncertainty, then compare this to the 'average player curve'. We'll then convert this to a new value, which is a kind of average. In essence, you can think of this as the balance between how certain we are in their performance, against how likely it is for someone to actually perform that well.
As a quick demonstration, let's say the average batsman has a batting average of 35, with a standard deviation of 10. Using this, we can convert Steven Smith and Voges' averages into this form:
| Player | Average | Uncertainty | Bayes |
|---|---|---|---|
| Steve Smith | 60.58 | 5.10 | 55.30 |
| Adam Voges | 61.87 | 25.37 | 38.61 |
Edit: Above is corrected. I buggered something in my code for the original values.
Basically, this resolves the issue of sample size without needing to resort to just completely culling the list. The only edge case here is where a player has not been dismissed yet, etc, so these players will be omitted. This means, technically, a player can be selected for a handful of ridiculously good performances, but they would have to be exactly that, ridiculously good.
Anyhow, with this method in mind, we need our definitions that we'll apply the above to. For the 2 specialist batters, this is very obvious. We'll rate them by batting average, using this method. The values for the 'average batter' will be found from the set of all batsmen batting 1-6 in the past 5 years, using a minimum of 40 innings. Why the last 5 years, not this year? Too little data, and too much noise, which will lead to wacky results for the standard deviation of the average batsman.
Using the same values, we'll also do a list for the specialist openers and number 3, as both are specialist positions.
Wicket keepers will be rated by batting average while keeping, against the same standards for batting. While there are some keeping statistics, and I've used them in the past, they're not well kept, and mostly a function of the team they play for anyhow. Without rate of catches versus drops, there's nothing really to use here, so I'll omit it this year. Basically, we're just picking the guy who batted best while keeping, in keeping with modern tradition.
For bowlers, I'll use both the bowling average and wickets per match. I come across people who occasionally get a bit grumpy with wickets per match being mentioned, ironically often on posts about how many wickets someone has taken. The pair of these together though work well, and I intend at some point to put together a longer stats post on the utility of this specific measure. As a side point, wickets per innings tends to not work as well, due to how some types of bowlers are used in some conditions. The final rating here will be the geometric mean of 1/bowling average and wickets per match (WPM). Seamers and spinners will be listed separately. For the comparison values, I'll be comparing to the first four bowlers used by teams for the last 5 years, with a minimum of 40 innings bowled, to match with the batters.
Finally, for all rounders, their ratings will be a geometric mean of batting average and the bowling rating noted above. The average allrounder has been found from the last 5 years as well, but requires that a player bat within the top 8, and bowl at least 1 innings per match on average.
Please note, in all of these, a column called 'Bayes' will be used to sort them. This will be these 'Bayesian' versions of the ratings as discussed above. I originally had this as 'Bayes-Bat', etc, but it just looked a bit messy.
In the final XI, players may be considered in all the categories, except the split between spin and seam bowling. A top 5 will be given to roles with 1 player selected, and top 10 for roles with 2 players selected. Players will be selected into each role in the following order:
- Wicket Keeper
- All Rounder
- Openers
- Number 3
- Other Batters
- Bowlers
ie, if a player is eligible as both a bowler and a batter, they'll be selected as a batter first, should they not already be picked as an allrounder.
Finally, the captain position will be given by going through the following:
- Find all players in the Final XI who Captained their side that year.
- Determine the Captain with the Best W/L Ratio
- If they are tied, the Captain with the most wins is selected.
- If they are stilled tied, the player who has had the most overall matches as captain is selected.
Please note, I wrote this part out a week or so back, before I dug into the data. Some of the above may become irrelevant with the real data.
In any case, below are the results:
#Wicket Keeper
| Player | Mat | Inns | Runs | Average | Bayes |
|---|---|---|---|---|---|
| RR Pant (IND) | 7 | 12 | 680 | 61.82 | 43.91 |
| TA Blundell (NZ) | 8 | 13 | 644 | 58.55 | 43.57 |
| Litton Das (BAN) | 5 | 8 | 448 | 56.00 | 42.29 |
| AT Carey (AUS) | 11 | 14 | 536 | 48.73 | 41.94 |
| OJ Pope (ENG) | 2 | 4 | 187 | 46.75 | 40.07 |
Pretty simple, Pant is in, and you can immediately see what this method is going on the right there. Note, this isn't 'their true average' or anything, just a value that derived from how much evidence this year has given us.
Let us all hope Pant has a speedy and comfortable recovery.
As a quick side note, all the keepers had about 2 dismissals per match, making any discussion of using this as part of the rating irrelevant anyhow in the end.
#All Rounder
| Player | Mat | Inns | R | Ave | W | WPM | Ave | Rating | AllRound | Bayes |
|---|---|---|---|---|---|---|---|---|---|---|
| KR Mayers (WI) | 4 | 5 | 192 | 38.40 | 14 | 3.500 | 11.86 | 0.5433 | 4.568 | 3.078 |
| RA Jadeja (IND) | 3 | 5 | 328 | 82.00 | 10 | 3.333 | 21.50 | 0.3937 | 5.682 | 3.046 |
| M Jansen (SA) | 8 | 13 | 234 | 21.27 | 36 | 4.500 | 19.03 | 0.4863 | 3.216 | 2.981 |
| R Ashwin (IND) | 6 | 10 | 270 | 30.00 | 20 | 3.333 | 27.70 | 0.3469 | 3.226 | 2.957 |
| SR Harmer (SA) | 3 | 5 | 96 | 24.00 | 14 | 4.667 | 19.29 | 0.4919 | 3.436 | 2.915 |
| Shakib Al Hasan (BAN) | 6 | 11 | 338 | 30.73 | 16 | 2.667 | 29.56 | 0.3003 | 3.038 | 2.893 |
| TM Head (AUS) | 10 | 15 | 655 | 50.38 | 6 | 0.600 | 19.00 | 0.1777 | 2.992 | 2.871 |
| BA Stokes (ENG) | 15 | 26 | 870 | 36.25 | 26 | 1.733 | 31.19 | 0.2357 | 2.923 | 2.871 |
| C Green (AUS) | 11 | 15 | 518 | 39.85 | 16 | 1.455 | 30.63 | 0.2179 | 2.947 | 2.861 |
| C de Grandhomme (NZ) | 3 | 5 | 225 | 75.00 | 2 | 0.667 | 30.00 | 0.1491 | 3.344 | 2.853 |
This table is a bit of a beast, and there's a lot going on. A few key things to note here, uncertainty in bowling drops way quicker than uncertainty in batting, as it both go with dismissals, but bowlers take more wickets per match than batters can be dismissed, usually. I figured giving the top 10 here would be worthwhile for some context. Travis Head has snuck into this top 10 on a mix of a weirdly low bowling average a strong batting average. Mayers is picked, largely on the back of that comically good bowling average, despite only playing 4 matches.
#Openers
| Player | Mat | Inns | Runs | Ave | 100s | 50s | Bayes |
|---|---|---|---|---|---|---|---|
| UT Khawaja (AUS) | 10 | 18 | 842 | 56.13 | 2 | 5 | 44.35 |
| Imam-ul-Haq (PAK) | 8 | 15 | 777 | 55.50 | 3 | 2 | 43.98 |
| KC Brathwaite (WI) | 7 | 14 | 687 | 62.45 | 2 | 5 | 43.96 |
| Abdullah Shafique (PAK) | 9 | 18 | 823 | 51.44 | 3 | 2 | 43.54 |
| BM Duckett (ENG) | 3 | 6 | 357 | 71.40 | 1 | 3 | 41.72 |
| Zakir Hasan (BAN) | 2 | 4 | 186 | 46.50 | 1 | 1 | 40.04 |
| BOP Fernando (SL) | 4 | 8 | 301 | 43.00 | 0 | 3 | 39.99 |
| DP Conway (NZ) | 1 | 2 | 110 | 110.00 | 0 | 1 | 39.45 |
| TWM Latham (NZ) | 8 | 13 | 517 | 39.77 | 2 | 1 | 39.27 |
| T Chanderpaul (WI) | 2 | 4 | 160 | 40.00 | 0 | 1 | 39.10 |
So, it's Khawaja and Imam-ul-Haq. Brathwaite could feel hard done by here, but this is kind of the point of how this works, accounting for the difference in sample sizes, which go in terms of number of dismissals. In essence, this is suggesting that if Brathwaite batted on long enough to reach 14 dismissals, he'd score slightly less than Imam-ul-Haq. Really, either could be picked quite happily.
If you're curious for what this explicitly means, by this method, this is saying that it's about 50/50 that Brathwaite scores 90 or more runs before being dismissed twice, so Imam-ul-Haq edges it. Just.
#Number 3
| Player | Match | Inns | Runs | Ave | 100s | 50s | Bayes |
|---|---|---|---|---|---|---|---|
| M Labuschagne (AUS) | 11 | 19 | 957 | 56.29 | 4 | 1 | 44.86 |
| DP Conway (NZ) | 5 | 8 | 486 | 60.75 | 2 | 2 | 42.70 |
| KS Williamson (NZ) | 3 | 5 | 296 | 74.00 | 1 | 0 | 41.21 |
| CA Pujara (IND) | 4 | 8 | 330 | 47.14 | 1 | 2 | 40.82 |
| OJ Pope (ENG) | 10 | 17 | 690 | 43.13 | 2 | 5 | 40.82 |
Arguably the most obvious one of the lot, Marnus is in. Really, you can pretty much immediately bin one of these team of the years if the guy dominating at 3 is left out.
#Batters
| Player | Mat | Inns | Runs | Average | 100s | 50s | Bayes |
|---|---|---|---|---|---|---|---|
| Babar Azam (PAK) | 9 | 17 | 1184 | 69.65 | 4 | 7 | 46.72 |
| UT Khawaja (AUS) | 11 | 20 | 1080 | 67.50 | 4 | 5 | 46.18 |
| JM Bairstow (ENG) | 10 | 19 | 1061 | 66.31 | 6 | 1 | 46.07 |
| M Labuschagne (AUS) | 11 | 19 | 957 | 56.29 | 4 | 1 | 44.86 |
| SPD Smith (AUS) | 11 | 18 | 876 | 58.40 | 2 | 5 | 44.74 |
| Imam-ul-Haq (PAK) | 8 | 16 | 837 | 55.80 | 3 | 3 | 44.29 |
| DJ Mitchell (NZ) | 7 | 11 | 683 | 68.30 | 3 | 3 | 43.97 |
| KC Brathwaite (WI) | 7 | 14 | 687 | 62.45 | 2 | 5 | 43.96 |
| RR Pant (IND) | 7 | 12 | 680 | 61.82 | 2 | 4 | 43.91 |
| TA Blundell (NZ) | 8 | 13 | 644 | 58.55 | 1 | 5 | 43.57 |
Babar and Bairstow are in, again, very obvious. It'd be pretty embarrassing to omit either on this list, so it's good that the method picked them with no concerns at all.
#Spin Bowler
| Player | Mat | W | WPM | Ave | Rating | Bayes |
|---|---|---|---|---|---|---|
| NGRP Jayasuriya (SL) | 3 | 29 | 9.667 | 20.38 | 0.6887 | 0.4203 |
| Abrar Ahmed (PAK) | 3 | 23 | 7.667 | 30.00 | 0.5055 | 0.4073 |
| SR Harmer (SA) | 3 | 14 | 4.667 | 19.29 | 0.4919 | 0.4034 |
| Kuldeep Yadav (IND) | 1 | 8 | 8.000 | 14.13 | 0.7526 | 0.3965 |
| IS Sodhi (NZ) | 1 | 8 | 8.000 | 21.63 | 0.6082 | 0.3953 |
This one took me by surprise a bit. I think this method, overall, works better for batters, though this is interesting in and of itself. As uncertainty tends with number of wickets taken, as well as matches, a player who has absolutely blown sides away for a few tests does rate highly. 29 wickets in 3 matches though, just damn! I'll back the method on this one, and Jayasuriya is the spinner.
Really though, this list comes across 'bugger the workhorse spinners, one test wonders are my new best friend'.
#Seam Bowlers
| Player | Mat | W | WPM | Ave | Rating | Bayes |
|---|---|---|---|---|---|---|
| K Rabada (SA) | 9 | 47 | 5.222 | 22.26 | 0.4844 | 0.4259 |
| M Jansen (SA) | 8 | 36 | 4.500 | 19.03 | 0.4863 | 0.4225 |
| SM Boland (AUS) | 5 | 21 | 4.200 | 13.67 | 0.5544 | 0.4217 |
| KR Mayers (WI) | 4 | 14 | 3.500 | 11.86 | 0.5433 | 0.4128 |
| JM Anderson (ENG) | 9 | 36 | 4.000 | 19.81 | 0.4494 | 0.4122 |
| OE Robinson (ENG) | 6 | 23 | 3.833 | 18.17 | 0.4593 | 0.4083 |
| JJ Bumrah (IND) | 5 | 22 | 4.400 | 20.32 | 0.4654 | 0.4074 |
| TA Boult (NZ) | 5 | 25 | 5.000 | 25.48 | 0.4430 | 0.4026 |
| SCJ Broad (ENG) | 9 | 40 | 4.444 | 25.75 | 0.4155 | 0.3989 |
| MJ Henry (NZ) | 3 | 16 | 5.333 | 26.31 | 0.4502 | 0.3980 |
The top two are obvious, Rabada and Jansen are in. I know I'll get asked, so I'll just put this here, Cummins is 13th on the list, with 0.3948. This is largely because he only took 3.600 wickets per match this year.
#Final Bowler
| Player | Mat | W | WPM | Ave | Rating | Bayes |
|---|---|---|---|---|---|---|
| K Rabada (SA) | 9 | 47 | 5.222 | 22.26 | 0.4844 | 0.4259 |
| M Jansen (SA) | 8 | 36 | 4.500 | 19.03 | 0.4863 | 0.4225 |
| SM Boland (AUS) | 5 | 21 | 4.200 | 13.67 | 0.5544 | 0.4217 |
| NGRP Jayasuriya (SL) | 3 | 29 | 9.667 | 20.38 | 0.6887 | 0.4203 |
| KR Mayers (WI) | 4 | 14 | 3.500 | 11.86 | 0.5433 | 0.4128 |
| JM Anderson (ENG) | 9 | 36 | 4.000 | 19.81 | 0.4494 | 0.4122 |
| OE Robinson (ENG) | 6 | 23 | 3.833 | 18.17 | 0.4593 | 0.4083 |
| JJ Bumrah (IND) | 5 | 22 | 4.400 | 20.32 | 0.4654 | 0.4074 |
| Abrar Ahmed (PAK) | 3 | 23 | 7.667 | 30.00 | 0.5055 | 0.4073 |
| SR Harmer (SA) | 3 | 14 | 4.667 | 19.29 | 0.4919 | 0.4034 |
Doesn't really need it's own section, but the final player is SCOTTY BOLAND! Not at the G though. The full list is below:
As an aside, the issue around the spinners becomes clearer now. The reason the one test wonders were making it so high is that the spinners performed comparatively worse than seamers this year, so the players putting in the overs weren't necessarily getting the rewards. All the one test wonders sunk out of the top 15 of the overall list here though.
Also, it's interesting that Jayasuriya is fourth, so really, all this business above was irrelevant, a method just picking the top four bowlers would have come to the same conclusion.
#Captain
The only captain who made it was Babar, so it's him by default.
#Final XI
So, the final team is:
| Position | Player | Mat | Runs | Bat Average | W | WPM | Bowl Average |
|---|---|---|---|---|---|---|---|
| 1 | UT Khawaja (AUS) | 10 | 842 | 56.13 | 0 | 0 | NA |
| 2 | Imam-ul-Haq (PAK) | 8 | 777 | 55.50 | 0 | 0 | NA |
| 3 | M Labuschagne (AUS) | 11 | 957 | 56.29 | 1 | 0.091 | 178.00 |
| 4 | Babar Azam* (PAK) | 9 | 1184 | 69.65 | 1 | 0.111 | 40.00 |
| 5 | JM Bairstow (ENG) | 10 | 1061 | 66.31 | 0 | 0 | NA |
| 6 | KR Mayers (WI) | 4 | 192 | 38.40 | 14 | 3.500 | 11.86 |
| 7 | RR Pant† (IND) | 7 | 680 | 61.82 | 0 | 0 | NA |
| 8 | M Jansen (SA) | 8 | 234 | 21.27 | 36 | 4.500 | 19.03 |
| 9 | K Rabada (SA) | 9 | 136 | 10.46 | 47 | 5.222 | 22.26 |
| 10 | SM Boland (AUS) | 5 | 19 | 9.50 | 21 | 4.200 | 13.67 |
| 11 | NGRP Jayasuriya (SL) | 3 | 15 | 3.75 | 29 | 9.667 | 20.38 |
So, apart from Mayers and Jayasuriya, not really all that surprising an XI. Brathwaite could feel hard done by, and would have given us something to talk about on captaincy. Boland might be controversial to some, but those people are wrong.
In terms of the method, it seems to work well for batters, but I'm less convinced by bowlers still, despite the discussion above. Again though, that'll be a topic for a different post.
All this in mind, the key point here is really around the batting. Labuschagne was a clear standout at 3 and had to be in, as did Babar and Bairstow in the middle order. Any side not picking those three is ridiculous. Some would try and argue 'context', but the only avenue I see to those arguments making sense is to simply ignore the context of what these players did themselves.
Posted Dec 30, 2022, 11:39 PM UTC · edited