Definitive proof that not outs don't inflate batting averages

[ankitj]

Take any practical case and you will know. In case of Bevan you would have to assume 55 more runs every time he remained not out. Out of all the innings Bevan was dismissed he averaged 32. And out of all the innings he remained not out his runs/ innings is 42. So you are saying he would have averaged 95+ in those matches. Which is highly unlikely or I would say practically impossible.

That's precisely what will happen. Fact that Bevan averages higher in not out innings is completely in agreement with the predictions memorylessness property will make. I'm sure Bevan is not special case here. This will be true for almost all batsmen with reasonably large number of games.

So I went all geeky and performed simulation to prove this. Here's the spreadsheet: https://drive.google.com/file/d/1N8ZtJBijVofRhdX1JnqDiyfvpzy5Xy7z/view

I assumed a hypothetical batsman B who would average 53.6 if allowed to bat endless so that that is his true average. Simulated 1000 "untruncated scores" by B assuming geometric distribution. Then simulated random – and uncorrelated to score – truncation for each of the 1000 innings. This truncation is modeled as uniform distribution between 0 and 150 assuming that's max of what B (who is uncannily similar to Bevan) would get to score ever given his batting position. Anytime "truncation limit" is smaller than "untruncated score", the innings is assumed to be not out and the truncation limit becomes the "Actual score".

Here are the results for B that have an uncanny similarity to actual figures for Bevan:

Average untruncated scores	53.47
% of not outs	33.4%
Average of scores that are not truncated (Out)	31.02
Average of scores that are truncated (not out)	43.66
Average with Outs in denominator (conventional batting average)	52.92
Average additional runs that would have been scored if no truncation happened	54.57
Average score in not out innings if they were allowed to be continued	98.24
Average runs per innings	35.25

• Average of untruncated scores is unsurprisingly close to actual average -- 53.47 vs. 53.6
• % of not outs -- 33.4% vs. 34.2% [no reason for this to match but validates that selecting 150 as the upper limit of truncation is fair]
• Average of scores that are not truncated or equivalent of out -- 31.02 vs. 32
• Average of scores that are truncated or equivalent of not out -- 43.66 vs. 42
• Average additional runs would have been scored if no truncation happened -- 54.57 vs. 53.6
• Average score in not out innings if there was indefinite time -- 98.24 vs. 95+ you hypothesized
• Average runs per innings -- 35.25 vs. 35.27
• Average with only outs in denominator (conventional batting average) -- 52.92 vs. 53.6 [This is the one that shows not outs did not inflate average]

I hope no one ever again makes an argument that not outs inflate batting averages.

 

[ankitj]

Also posted here: http://www.cricketweb.net/forum/cricket-chat/80974-top-10-odi-batsmen-since-90s-3.html#post4277195

 

[Jack1]

I agree they don't inflate averages. Obviously there are other factors (but that wasn't your point, I agree with the not outs not inflating batting average for an individual it just doesn't make sense) like Batting lower in the order in limited overs can be bad for your average, unless you come in up top as a pinch hitter. Because you'll have to risk your wicket at the end scoring quickly and possibly risking run out. Interestingly in the men's game loads of players and teams seem to have a "protect your average" policy in which they don't run off the ball ball of the first innings which is super dumb. That's a thing the men's game can learn from the women's, the women literally don't give a damn about stats and averages I've seen more suicidal singles in the women's game in the past year (and I don't watch it much) than I've seen in the last 20 years in men's internationals and domestic cricket combined. Sometimes the risk brings an extra run or two at the end in women's cricket. This can be a factor in averages if you're a rare men's batter that always takes the risk at the end, but this sort of player is so rare I can't even think of one.

People like Kohli, Williamson, Root and players in this role..Smith.. in this era have the best chance to build a high average out of their team due to roles. Comparing average with role is important, but regardless not outs helping average for a specific role makes no sense especially when the hardest time to bat is before you're set. More not outs tends to mean you had less chance to cash in when set , so the way that averages work makes perfect sense runs divided by outs. Batting lower means you have to accelerate much sooner. The best place to bat in an ODI is probably 3 for the best chance of a high average, or a lower order batsman like Dhoni that scores overly slowly and cautiously for his individual role - i.e taking advantage of spread/defensive fields to boost his average and taking it so deep he ends up in the core of the earth if he's still there at the last over chasing. Dhoni is probably the only player I can think of that literally bats for his average. Not wanting to start a flame war here with that, we've done that before. It's just what I think - that Dhoni wants to win whilst claiming all the glory compared to a gun chaser like Bevan that didn't want to be flashy, just wanted to get the team the W. The painful thing being Dhoni can score faster (much faster and tee off sooner - more relevant to his prime), but won't/wouldn't take the risk due to fear of knocking his average. But apart from Dhoni it's incredibly rare a player has a stat pad mindset to his average. Tendulkar is arguably one, although Tendulkar mostly/predominately played to win.

 

[Red]

They don't inflate averages clearly because average is just run scored/dismissals.

They can clearly be misleading however.

 

[Starfighter]

Good to see Phil Tufnell's ODI average of 15 is actually reflective of his ability then.

 

[Jack1]

Good to see Phil Tufnell's ODI average of 15 is actually reflective of his ability then.

Phil Tufnell with aviators on, no helmet , opening the batting against prime Shoaib Akhtar would sure be one hell of a thing

 

[RossTaylorsBox]

I hope no one ever uses simulations to generate scores again.

 

[the big bambino]

Didn't Bill Johnston average 102 on the 53 tour with the assistance of not outs even though he couldn't bat?

 

[RossTaylorsBox]

Wait, are cricket innings actually a uniform distribution?

 

[mr_mister]

Didn't Bill Johnston average 102 on the 53 tour with the assistance of not outs even though he couldn't bat?

To score 100 runs and only get dismissed once tells me he could bat somewhat at least

 

[TheJediBrah]

good thread. Shouldn't need this much proof though, common sense should suffice.

Hypothetically, and simplifying this massively into just 1 innings to demonstrate the point, why would someone who makes 60 be better than someone who makes 30 and 30*?

If anything the latter is the more difficult achievement because you had to start your innings twice.

Didn't Bill Johnston average 102 on the 53 tour with the assistance of not outs even though he couldn't bat?

sample size m8

 

[Daemon]

good thread. Shouldn't need this much proof though, common sense should suffice.

Hypothetically, and simplifying this massively into just 1 innings to demonstrate the point, why would someone who makes 60 be better than someone who makes 30 and 30*?

If anything the latter is the more difficult achievement because you had to start your innings twice.



sample size m8

Tbf the guy who hit 60 gets to bat again and only maintains an average of 60 if he scores 60 again. In which case he’s clearly done better.

 

[TheJediBrah]

Tbf the guy who hit 60 gets to bat again and only maintains an average of 60 if he scores 60 again. In which case he’s clearly done better.

key words being "hypothetically" and "simplified massively", my intention was for the example to represent careers for 100+ innings

anyway why are 2 scores of 60 indicative of a "clearly better" batsman than 30 and 30*?

 

[ankitj]

Wait, are cricket innings actually a uniform distribution?

Nope. I think Geometric distribution captures cricket scores best.

 

[ankitj]

Shouldn't need this much proof though, common sense should suffice.

Agree. To imagine there can be a batsman who scores same number of runs but who gets out on the last ball of each not out innings is where the flaw lies. It's not possible for such a hypothetical batsman to exist because ability to stay not out is causally related to ability to score those runs.

 

[the big bambino]

To score 100 runs and only get dismissed once tells me he could bat somewhat at least

He couldn’t.

sample size m8

Smith averaged 100 plus in the Ashes but I don’t read anything into bcos hurr durr sample size m8

 

[GoodAreasShane]

Naveed Nawaz averaged 99 in Test cricket, and I had never even heard of the bloke until about 5 minutes ago.

All sorts of statistical anomalies in Test history when you look hard enough

 

[ankitj]

He couldn’t.



Smith averaged 100 plus in the Ashes but I don’t read anything into bcos hurr durr sample size m8

Johnston had a sample of 1, Smith 7. So no.

 

[Spark]

Nope. I think Geometric distribution captures cricket scores best.

it's poissonian, no? obviously not perfect as there's some correlation between one innings and the next, but i thought that was relatively well-established - at least amongst the people who care about these things.

 

[the big bambino]

Johnston had a sample of 1, Smith 7. So no.

The Johnston was over a season and many innings.