# Adjusting averages (Lyon vs Ashwin)

Pick a big enough sample size and conditions should average out… At least that’s what I’d always assumed.

Let’s disprove that conceptually and then with numbers.

Is it fair to directly compare the averages of these two players? Bowler A plays his home Tests in Sri Lanka, ending his career with a bounty of Bangladesh wickets. Player B is part of a four man attack. Bowls a lot against the top order, and his home games are in Australia. He never gets a sniff of the tail – less than 10% of his wickets are batsmen averaging 10 or less.

No matter how big the sample size, A and B aren’t on a level playing field; there is a bias in favour of A.

How would we expect A or B to perform against a batsman that averaged 30, on an average pitch? Our best bet is to adjust their stats for:

1. Ground
2. Batsmen bowled to
3. Innings number
4. Specific pitch condition
5. Ball age (maybe)
6. Match situation (eg. Team playing for draw / declaration)

Here, I’ll do the first two, looking at the players with 50 wickets over the last four years. Will assume that factors 3-6 average out over a career.

For “Ground” take a weighted average of spinners’ averages at the stadia where each bowler has taken wickets (ie. Mehidy Hasan Miraz’s 29 wickets at 19 at Dhaka are still valuable, but worth more like 29 wickets at 21).

For “Batsman bowled to” each run conceded is worth one run – but the wickets are awarded a value based on who was dismissed – so getting Virat Kohli gives you more credit than Ishant Sharma.

The mean adjustment is really interesting: increasing spinners’ averages by 4%. This indicates that just looking at raw averages flatters spinners. Why is this? I think it’s a function of when spinners bowl. If they don’t get much action in the first 30 overs, three wickets will already be down. Thus they’ll disproportionately dismiss the (weaker) lower middle order.

### Lyon vs Ashwin

The similarity of their adjusted records looks striking when compared to raw averages. Let’s take a closer look and see if it stacks up.

Firstly, who they dismiss:

It’s not like Ashwin is getting an easy ride, but 30% of Lyon’s wickets come against batsmen who’ve averaged over 40, while for Ashwin that figure is 20%.

Again, Ashwin plays on a mix of pitches, while Lyon has taken over half his wickets at grounds where spinners traditionally struggle.

Overall, Lyon has done amazingly well to average under 30 over the last four years given where he has bowled and to whom.

### Other observations

While Ravi Jadeja’s raw average of 24.6 is flattering, he’s still right up there.

Moeen Ali can feel aggrieved not to be ahead of Dom Bess as England’s second spinner.

Roston Chase is better than his average would say – but with relatively little data the error bars get large (60 wickets means his rating is 37 +/- 5).

Nathan Lyon is the best current spinner – we adjust his average down by 11%, of which 8% comes from where he plays. He also gets a boost from who he bowls to: as part of a four man attack, Lyon does feature more against the top order.

Where do we go with this? Extending this to pace bowlers is harder, as strictly one should adjust for when in the innings they bowl (the new ball is helpful). This would need a model of wicket and run probability by ball bowled, and then to compare each player’s actual results to what the average player would achieve.

PS. This would be easy to check… if you had CricViz data. Expected averages would tell the story. Especially comparing head-to-head for the games in which both Lyon and Ashwin played. And splitting LHB and RHB so there was no bias driven by matchups.

## 2 thoughts on “Adjusting averages (Lyon vs Ashwin)”

1. Arjun says:

What about the peer support. Lyon has had the benefit of being part of almost always 3 good pacers. Thereby getting advantage of batsmen relaxing against him after they have faced likes of Ryan Haris, M Johnson, Starc, Hazelwood, Cummins, Pattinson etc.
Ashwin, unlike Lyon, has to share his wkts with 2nd spinner (Jadeja, P Ojha, Axar, etc)

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1. The rest of the attack does probably make a difference.
Lyon gets help because the strength of the other bowlers means he’ll rarely have to bowl to someone who’s 150*. On the other hand, as one of only four bowlers he can’t hide when the pitch isn’t spinning.

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