user4399: Question: On average, how many pawns are there at the start of the endgame?
To answer:

You can choose your definition of the endgame as long as you can show a credible reference that supports your choice of definition. What I have in mind is the same as lichess which I understand to be 6 or fewer non-pawn and non-king pieces.

You may answer for both sides total (e.g.,  10 pawns total on average) or for just 1 side (e.g., 5 pawns per side on average).

As to the sample...maybe the same/similar sample from which 38 moves average was obtained.



3.1. You can pick your own sample like, say, all standard world championships except 2021. Or 21st century standard world championships except 2021

What I tried:

Checking out some of my recent games on lichess (that reached the endgame), I see a lot of my games have at least 10 pawns. A few of my games have 6 or lower though. I estimate the average is at least 10 pawns.

Little context:

I think choker has too few pawns, relative to start of the endgame of regular chess/9LX. I want to verify/disprove this conjecture by seeing the average in actual games. In particular, choker seems to have, on average, 5 pawns total for both players. This is about half what I think the average for start of endgame in regular chess/9LX is.

Alternative question: Is the average number of pawns probably significantly greater than 5 (total, not per player)?



user4399: for all games in magnus carlsen world standard and world fischer random chess championship matches (basically all world championship matches except world rapid and world blitz)

Average throughout all championships:
for all: (13+10+11+12+10+12+8+14+11+14+14+13+12+12+14+10+12+12+9+9+10+14+12+12+14+11+12+13+12+11+6+16+15+14+12+14+8+10+9+12+11+10+10+10+14+7+5+12+14+14+14+12+9+6+12+5+11+10+8+6+11+9)/(4+2+4+11+11+12+10+8)=11.1129032258... ~ 11.11
for all classical (and thus excluding 9LX huhu): (13+10+11+12+10+12+8+14+11+14+14+13+12+12+14+10+12+12+9+9+10+14+12+12+14+11+12+13+12+11+6+16+15+14+12+14+8+10+9+12+11+10+10+10+14+7+5+12+14+14+14+12)/(11+11+12+10+8)=11.5769230769... ~ 11.58
for all rapid including 9LX: (9+6+12+5+11+10+8+6+11+9)/(4+2+4)=8.7
for all rapid excluding 9LX: (11+10+8+6+11+9)/6 = 9.1666666666... ~ 9.17

Average by championship, rounded to 2 decimal places:




Championship
Average




2021 vs nepo
11.73


2019 vs wesley (which was all rapid)
08.00


2018 vs fabi (classical only)
11.55


2018 vs fabi (classical and rapid)
11.38


2018 vs fabi (rapid only)
10.50


2016 vs sergey (classical only)
12.33


2016 vs sergey (classical and rapid)
11.38


2016 vs sergey (rapid only)
08.50


2014 vs vishy
10.60


2013 vs vishy
11.50




Remarks:

the lowest average in all these (8 pawns) is the 1 that magnus lost namely to wesley so in 2019 fischer random world championship. of course all those games were rapid.

Lowest in classical only is 10.60 in 2014 vs vishy. the 3 rapid only entries are all below 10.60: they are 08.00, 10.50 and 08.50. I guess pawns have a higher mortality rate in rapid compared to classical.



2021 vs nepo
https://lichess.org/study/1NIB7sSp
1 - 13
2 - 10
3 - 11
4 - 12
5 - 10
6 - 12
7 - 8
8 - 14
9 - 11
10 - 14
11 - 14
average: (13+10+11+12+10+12+8+14+11+14+14)/11=11.727272...

2019 vs wesley
https://lichess.org/broadcast/fischer-random-championship-finals-game-1/-/DM0hC3u1
1 - 9
2 - 6
3 - 12
4 - 5
5 - N/A
6 - N/A
average (all rapid): (9+6+12+5)/4=8

2018 vs fabi
https://lichess.org/study/fCum15PU
1 - 13
2 - 12
3 - 12
4 - 14
5 - 10
6 - 12
7 - 12
8 - 9
9 - 9
10 - 10
11 - 14
12 - N/A
T1 - 11
T2 - N/A
T3 - 10
average (classical only): (13+12+12+14+10+12+12+9+9+10+14)/11=11.545454...
average (classical and rapid): (13+12+12+14+10+12+12+9+9+10+14+11+10)/13=11.3846153846...
average (rapid only): (11+10)/2=10.5

2016 vs sergey
https://lichess.org/study/vENPCM25
1 - 12
2 - 12
3 - 14
4 - 11
5 - 12
6 - 13
7 - 12
8 - 11
9 - 6
10 - 16
11 - 15
12 - 14
T1 - 8
T2 - 6
T3 - 11
T4 - 9
average (classical only): (12+12+14+11+12+13+12+11+6+16+15+14)/12=12.3333333333
average (classical and rapid): (12+12+14+11+12+13+12+11+6+16+15+14+8+6+11+9)/16=11.375
average (rapid only): (8+6+11+9)/4=8.5

2014 vs vishy
https://lichess.org/study/nurfx2OL
1 - 12
2 - 14
3 - 8
4 - 10
5 - 9
6 - 12
7 - 11
8 - 10
9 - N/A
10 - 10
11 - 10
average: (12+14+8+10+9+12+11+10+10+10)/10=10.6

2013 vs vishy
https://lichess.org/study/9xUbdEqD
1 - N/A
2 - 14
3 - 7
4 - 5
5 - 12
6 - 14
7 - 14
8 - 14
9 - N/A
10 - 12
average: (14+7+5+12+14+14+14+12)/8=11.5

4399: <p><strong>Question</strong>: On average, how many pawns are there at the start of the endgame?</p>
<p>To answer:</p>
<ol>
<li><p>You can choose your definition of the <a href="https://chess.stackexchange.com/questions/19317/calculation-for-game-phase/19319#19319">endgame</a> as long as you can show a credible reference that supports your choice of definition. What I have in mind is the same as lichess which I understand to be 6 or fewer non-pawn and non-king pieces.</p>
</li>
<li><p>You may answer for both sides total (e.g.,  10 pawns total on average) or for just 1 side (e.g., 5 pawns per side on average).</p>
</li>
<li><p>As to the sample...maybe the same/similar sample from which <a href="https://chess.stackexchange.com/questions/2506/what-is-the-average-length-of-a-game-of-chess">38 moves average was obtained</a>.</p>
</li>
</ol>
<ul>
<li>3.1. <strong>You can pick your own sample</strong> like, say, all standard world championships except 2021. Or 21st century standard world championships except 2021</li>
</ul>
<p>What I tried:</p>
<ul>
<li>Checking out some of my recent games on lichess (that reached the endgame), I see a lot of my games have at least 10 pawns. A few of my games have 6 or lower though. I estimate the average is at least 10 pawns.</li>
</ul>
<p>Little context:</p>
<ul>
<li><p>I think <a href="https://chess.stackexchange.com/questions/27638/is-choker-balanced">choker</a> has too few pawns, relative to start of the endgame of regular chess/9LX. I want to verify/disprove this conjecture by seeing the average in actual games. In particular, choker seems to have, on average, 5 pawns total for both players. This is about half what I think the average for start of endgame in regular chess/9LX is.</p>
</li>
<li><p><strong>Alternative question</strong>: Is the average number of pawns probably significantly greater than 5 (total, not per player)?</p>
</li>
</ul>
 4399: <p>for all games in magnus carlsen world standard and world fischer random chess championship matches (basically <a href="https://chess.stackexchange.com/questions/33832/what-are-all-the-world-chess-championships-such-that">all world championship matches except world rapid and world blitz</a>)</p>
<hr />
<p><strong>Average throughout all championships</strong>:</p>
<p>for all: (13+10+11+12+10+12+8+14+11+14+14+13+12+12+14+10+12+12+9+9+10+14+12+12+14+11+12+13+12+11+6+16+15+14+12+14+8+10+9+12+11+10+10+10+14+7+5+12+14+14+14+12+9+6+12+5+11+10+8+6+11+9)/(4+2+4+11+11+12+10+8)=11.1129032258... ~ 11.11</p>
<p>for all classical (and thus excluding 9LX huhu): (13+10+11+12+10+12+8+14+11+14+14+13+12+12+14+10+12+12+9+9+10+14+12+12+14+11+12+13+12+11+6+16+15+14+12+14+8+10+9+12+11+10+10+10+14+7+5+12+14+14+14+12)/(11+11+12+10+8)=11.5769230769... ~ 11.58</p>
<p>for all rapid including 9LX: (9+6+12+5+11+10+8+6+11+9)/(4+2+4)=8.7</p>
<p>for all rapid excluding 9LX: (11+10+8+6+11+9)/6 = 9.1666666666... ~ 9.17</p>
<hr />
<p><strong>Average by championship</strong>, rounded to 2 decimal places:</p>
<div class="s-table-container">
<table class="s-table">
<thead>
<tr>
<th>Championship</th>
<th>Average</th>
</tr>
</thead>
<tbody>
<tr>
<td>2021 vs nepo</td>
<td>11.73</td>
</tr>
<tr>
<td>2019 vs wesley (which was all rapid)</td>
<td>08.00</td>
</tr>
<tr>
<td>2018 vs fabi (classical only)</td>
<td>11.55</td>
</tr>
<tr>
<td>2018 vs fabi (classical and rapid)</td>
<td>11.38</td>
</tr>
<tr>
<td>2018 vs fabi (rapid only)</td>
<td>10.50</td>
</tr>
<tr>
<td>2016 vs sergey (classical only)</td>
<td>12.33</td>
</tr>
<tr>
<td>2016 vs sergey (classical and rapid)</td>
<td>11.38</td>
</tr>
<tr>
<td>2016 vs sergey (rapid only)</td>
<td>08.50</td>
</tr>
<tr>
<td>2014 vs vishy</td>
<td>10.60</td>
</tr>
<tr>
<td>2013 vs vishy</td>
<td>11.50</td>
</tr>
</tbody>
</table>
</div>
<p><strong>Remarks</strong>:</p>
<ol>
<li><p>the lowest average in all these (8 pawns) is the 1 that magnus lost namely to wesley so in 2019 fischer random world championship. of course all those games were rapid.</p>
</li>
<li><p>Lowest in classical only is 10.60 in 2014 vs vishy. the 3 rapid only entries are all below 10.60: they are 08.00, 10.50 and 08.50. I guess pawns have a higher mortality rate in rapid compared to classical.</p>
</li>
</ol>
<hr />
<p>2021 vs nepo</p>
<p><a href="https://lichess.org/study/1NIB7sSp" rel="nofollow noreferrer">https://lichess.org/study/1NIB7sSp</a></p>
<p>1 - <a href="https://lichess.org/study/1NIB7sSp/nDuokoE5" rel="nofollow noreferrer">13</a></p>
<p>2 - <a href="https://lichess.org/study/1NIB7sSp/63R2CC8E" rel="nofollow noreferrer">10</a></p>
<p>3 - <a href="https://lichess.org/study/1NIB7sSp/FPoHYMUr" rel="nofollow noreferrer">11</a></p>
<p>4 - <a href="https://lichess.org/study/1NIB7sSp/dSf0d6LS" rel="nofollow noreferrer">12</a></p>
<p>5 - <a href="https://lichess.org/study/1NIB7sSp/ZviuiZ6f" rel="nofollow noreferrer">10</a></p>
<p>6 - <a href="https://lichess.org/study/1NIB7sSp/dffoJlfR" rel="nofollow noreferrer">12</a></p>
<p>7 - <a href="https://lichess.org/study/1NIB7sSp/r0VBjIUi" rel="nofollow noreferrer">8</a></p>
<p>8 - <a href="https://lichess.org/study/1NIB7sSp/RuvOfr3O" rel="nofollow noreferrer">14</a></p>
<p>9 - <a href="https://lichess.org/study/1NIB7sSp/j6ZeRee2" rel="nofollow noreferrer">11</a></p>
<p>10 - <a href="https://lichess.org/study/1NIB7sSp/hs17TtW4" rel="nofollow noreferrer">14</a></p>
<p>11 - <a href="https://lichess.org/study/1NIB7sSp/OH72jiGS" rel="nofollow noreferrer">14</a></p>
<p>average: (13+10+11+12+10+12+8+14+11+14+14)/11=11.727272...</p>
<hr />
<p>2019 vs wesley</p>
<p><a href="https://lichess.org/broadcast/fischer-random-championship-finals-game-1/-/DM0hC3u1" rel="nofollow noreferrer">https://lichess.org/broadcast/fischer-random-championship-finals-game-1/-/DM0hC3u1</a></p>
<p>1 - <a href="https://lichess.org/broadcast/fischer-random-championship-finals-game-1/-/DM0hC3u1" rel="nofollow noreferrer">9</a></p>
<p>2 - <a href="https://lichess.org/broadcast/fischer-random-championship-finals-game-2/-/QyqmRYgT" rel="nofollow noreferrer">6</a></p>
<p>3 - <a href="https://lichess.org/broadcast/fischer-random-championship-finals-game-3/-/SHljkTy4" rel="nofollow noreferrer">12</a></p>
<p>4 - <a href="https://lichess.org/broadcast/fischer-random-championship-finals-game-4/-/AS8MuiPN" rel="nofollow noreferrer">5</a></p>
<p>5 - <a href="https://lichess.org/broadcast/fischer-random-championship-finals-game-5/-/TYRLiqxv" rel="nofollow noreferrer">N/A</a></p>
<p>6 - <a href="https://lichess.org/broadcast/fischer-random-championship-finals-game-6/-/xhpI3MtT" rel="nofollow noreferrer">N/A</a></p>
<p>average (all rapid): (9+6+12+5)/4=8</p>
<hr />
<p>2018 vs fabi</p>
<p><a href="https://lichess.org/study/fCum15PU" rel="nofollow noreferrer">https://lichess.org/study/fCum15PU</a></p>
<p>1 - <a href="https://lichess.org/study/fCum15PU/MjZu9a7k" rel="nofollow noreferrer">13</a></p>
<p>2 - <a href="https://lichess.org/study/fCum15PU/x1qOQ1iK" rel="nofollow noreferrer">12</a></p>
<p>3 - <a href="https://lichess.org/study/fCum15PU/4kUWEemi" rel="nofollow noreferrer">12</a></p>
<p>4 - <a href="https://lichess.org/study/fCum15PU/nRRHALbA" rel="nofollow noreferrer">14</a></p>
<p>5 - <a href="https://lichess.org/study/fCum15PU/udy8ezNo" rel="nofollow noreferrer">10</a></p>
<p>6 - <a href="https://lichess.org/study/fCum15PU/xcabYHfK" rel="nofollow noreferrer">12</a></p>
<p>7 - <a href="https://lichess.org/study/fCum15PU/A7gYIcxG" rel="nofollow noreferrer">12</a></p>
<p>8 - <a href="https://lichess.org/study/fCum15PU/WVv47Mk2" rel="nofollow noreferrer">9</a></p>
<p>9 - <a href="https://lichess.org/study/fCum15PU/8LIj7sKb" rel="nofollow noreferrer">9</a></p>
<p>10 - <a href="https://lichess.org/study/fCum15PU/VpuF2yVQ" rel="nofollow noreferrer">10</a></p>
<p>11 - <a href="https://lichess.org/study/fCum15PU/sq97Zio8" rel="nofollow noreferrer">14</a></p>
<p>12 - <a href="https://lichess.org/study/fCum15PU/cdw4dqyu" rel="nofollow noreferrer">N/A</a></p>
<p>T1 - <a href="https://lichess.org/study/fCum15PU/5eYxFKB4" rel="nofollow noreferrer">11</a></p>
<p>T2 - <a href="https://lichess.org/study/fCum15PU/84jWPJte" rel="nofollow noreferrer">N/A</a></p>
<p>T3 - <a href="https://lichess.org/study/fCum15PU/WRuVkHBM" rel="nofollow noreferrer">10</a></p>
<p>average (classical only): (13+12+12+14+10+12+12+9+9+10+14)/11=11.545454...</p>
<p>average (classical and rapid): (13+12+12+14+10+12+12+9+9+10+14+11+10)/13=11.3846153846...</p>
<p>average (rapid only): (11+10)/2=10.5</p>
<hr />
<p>2016 vs sergey</p>
<p><a href="https://lichess.org/study/vENPCM25" rel="nofollow noreferrer">https://lichess.org/study/vENPCM25</a></p>
<p>1 - <a href="https://lichess.org/study/vENPCM25/IcO95dAl" rel="nofollow noreferrer">12</a></p>
<p>2 - <a href="https://lichess.org/study/vENPCM25/csQMrsvl" rel="nofollow noreferrer">12</a></p>
<p>3 - <a href="https://lichess.org/study/vENPCM25/x4jTEm1L" rel="nofollow noreferrer">14</a></p>
<p>4 - <a href="https://lichess.org/study/vENPCM25/7MNDhQJI" rel="nofollow noreferrer">11</a></p>
<p>5 - <a href="https://lichess.org/study/vENPCM25/pHVQYIVs" rel="nofollow noreferrer">12</a></p>
<p>6 - <a href="https://lichess.org/study/vENPCM25/ZmV7RuIm" rel="nofollow noreferrer">13</a></p>
<p>7 - <a href="https://lichess.org/study/vENPCM25/BOHrDIHi" rel="nofollow noreferrer">12</a></p>
<p>8 - <a href="https://lichess.org/study/vENPCM25/wkuvptDc" rel="nofollow noreferrer">11</a></p>
<p>9 - <a href="https://lichess.org/study/vENPCM25/E1ZujQDY" rel="nofollow noreferrer">6</a></p>
<p>10 - <a href="https://lichess.org/study/vENPCM25/CtnXiIkN" rel="nofollow noreferrer">16</a></p>
<p>11 - <a href="https://lichess.org/study/vENPCM25/Zos4PiR0" rel="nofollow noreferrer">15</a></p>
<p>12 - <a href="https://lichess.org/study/vENPCM25/1fgYVe4c" rel="nofollow noreferrer">14</a></p>
<p>T1 - <a href="https://lichess.org/study/vENPCM25/raM4vyAy" rel="nofollow noreferrer">8</a></p>
<p>T2 - <a href="https://lichess.org/study/vENPCM25/DZeN3Zpz" rel="nofollow noreferrer">6</a></p>
<p>T3 - <a href="https://lichess.org/study/vENPCM25/Yn4Aaulx" rel="nofollow noreferrer">11</a></p>
<p>T4 - <a href="https://lichess.org/study/vENPCM25/Q6rgMdfD" rel="nofollow noreferrer">9</a></p>
<p>average (classical only): (12+12+14+11+12+13+12+11+6+16+15+14)/12=12.3333333333</p>
<p>average (classical and rapid): (12+12+14+11+12+13+12+11+6+16+15+14+8+6+11+9)/16=11.375</p>
<p>average (rapid only): (8+6+11+9)/4=8.5</p>
<hr />
<p>2014 vs vishy</p>
<p><a href="https://lichess.org/study/nurfx2OL" rel="nofollow noreferrer">https://lichess.org/study/nurfx2OL</a></p>
<p>1 - <a href="https://lichess.org/study/nurfx2OL/Z42Dyl6S" rel="nofollow noreferrer">12</a></p>
<p>2 - <a href="https://lichess.org/study/nurfx2OL/pO3VsSUS" rel="nofollow noreferrer">14</a></p>
<p>3 - <a href="https://lichess.org/study/nurfx2OL/319OcmZy" rel="nofollow noreferrer">8</a></p>
<p>4 - <a href="https://lichess.org/study/nurfx2OL/tMsL34Tz" rel="nofollow noreferrer">10</a></p>
<p>5 - <a href="https://lichess.org/study/nurfx2OL/cIXcpYau" rel="nofollow noreferrer">9</a></p>
<p>6 - <a href="https://lichess.org/study/nurfx2OL/bMrqJA0Z" rel="nofollow noreferrer">12</a></p>
<p>7 - <a href="https://lichess.org/study/nurfx2OL/yYpH17Ot" rel="nofollow noreferrer">11</a></p>
<p>8 - <a href="https://lichess.org/study/nurfx2OL/fXdyHttM" rel="nofollow noreferrer">10</a></p>
<p>9 - <a href="https://lichess.org/study/nurfx2OL/FW2XY9vE" rel="nofollow noreferrer">N/A</a></p>
<p>10 - <a href="https://lichess.org/study/nurfx2OL/6BlHQKO2" rel="nofollow noreferrer">10</a></p>
<p>11 - <a href="https://lichess.org/study/nurfx2OL/XdwtzYNz" rel="nofollow noreferrer">10</a></p>
<p>average: (12+14+8+10+9+12+11+10+10+10)/10=10.6</p>
<hr />
<p>2013 vs vishy</p>
<p><a href="https://lichess.org/study/9xUbdEqD" rel="nofollow noreferrer">https://lichess.org/study/9xUbdEqD</a></p>
<p>1 - <a href="https://lichess.org/study/9xUbdEqD/vOPf0T1A" rel="nofollow noreferrer">N/A</a></p>
<p>2 - <a href="https://lichess.org/study/9xUbdEqD/hRCY0iaO" rel="nofollow noreferrer">14</a></p>
<p>3 - <a href="https://lichess.org/study/9xUbdEqD/PFv2RXJ4" rel="nofollow noreferrer">7</a></p>
<p>4 - <a href="https://lichess.org/study/9xUbdEqD/RD3Ujg9J" rel="nofollow noreferrer">5</a></p>
<p>5 - <a href="https://lichess.org/study/9xUbdEqD/k2XtWVnh" rel="nofollow noreferrer">12</a></p>
<p>6 - <a href="https://lichess.org/study/9xUbdEqD/zoyjSR2a" rel="nofollow noreferrer">14</a></p>
<p>7 - <a href="https://lichess.org/study/9xUbdEqD/xr8AeSDX" rel="nofollow noreferrer">14</a></p>
<p>8 - <a href="https://lichess.org/study/9xUbdEqD/alzje4Kw" rel="nofollow noreferrer">14</a></p>
<p>9 - <a href="https://lichess.org/study/9xUbdEqD/QVRyvXV3" rel="nofollow noreferrer">N/A</a></p>
<p>10 - <a href="https://lichess.org/study/9xUbdEqD/FPXvTybG" rel="nofollow noreferrer">12</a></p>
<p>average: (14+7+5+12+14+14+14+12)/8=11.5</p>
